implicit, torus: evaluates_as's bound derived term by term; the recognised torus's sweep frame from its form (#3185, #3199) (#13743)

Moved from tangency-labs/solidcore#3224.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

solidcore/.github/workflows/ci.yml

@@ -230,6 +230,20 @@ jobs:
       - run: rustup target add wasm32-unknown-unknown
       - run: cargo check -p solidcore --target wasm32-unknown-unknown
 
+  # Each package builds on the Rust release its `rust-version` declares (scripts/ci/
+  # check-rust-version.sh). Downstream users build on older pinned toolchains than
+  # rust-toolchain.toml's, and nothing else here runs one.
+  rust-version:
+    needs: changes
+    if: needs.changes.outputs.full == 'true'
+    runs-on: blacksmith-4vcpu-ubuntu-2404
+    steps:
+      - uses: actions/checkout@v4
+      - uses: Swatinem/rust-cache@v2
+        with:
+          workspaces: ". -> bin"
+      - run: scripts/ci/check-rust-version.sh
+
   # Same packaging check the release workflow runs before publishing (no secrets).
   publish-dry-run:
     needs: changes

solidcore/README.md

@@ -1,3 +1,5 @@
+> **solidcore is developed inside [SolidCraft](https://github.com/tangency-labs/solidcraft), at [`solidcore/`](https://github.com/tangency-labs/solidcraft/tree/main/solidcore).** The [tangency-labs/solidcore](https://github.com/tangency-labs/solidcore) repository is an automatic, read-only mirror of that folder. Open issues and pull requests in [tangency-labs/solidcraft](https://github.com/tangency-labs/solidcraft): kernel-only work against the `kernel` branch.
+
 <p align="center"><img src="assets/logo.svg" width="140" alt="solidcore logo: an isometric solid with one filleted edge and a NURBS curve on its top face"></p>
 
 # solidcore

solidcore/crates/goldens/expected/blend.feature_executive.jsonl

@@ -1,6 +1,8 @@
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solidcore/crates/goldens/expected/curve.ellipse_p2.jsonl

@@ -96,7 +96,7 @@
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@@ -909,7 +909,7 @@
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@@ -1655,7 +1655,7 @@
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solidcore/crates/goldens/expected/geom.extent1d.jsonl

@@ -26,7 +26,7 @@
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@@ -921,7 +921,7 @@
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@@ -1554,7 +1554,7 @@
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@@ -2114,7 +2114,7 @@
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@@ -2318,7 +2318,7 @@
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solidcore/crates/goldens/expected/geom.extent2d.jsonl

@@ -3029,7 +3029,7 @@
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 {"case":"my_test_extent2d_contains_periodic","deferred":null,"error":null,"ints":{"contained":[0],"contained_again":[0]},"topology":null,"values":{"periodic_point":[4.9,3.0]}}
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solidcore/crates/goldens/expected/known_failing.json

@@ -1,10 +1,5 @@
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-    "attributes_add_by_faces_extrusion": "tangency-labs/solidcore#3093: the base body is a closed solid or an open 9-face body depending on a few ulps of the extrusion surface's extended domain, with success either way",
-    "multi_feature_adv_extrusion": "tangency-labs/solidcore#3093: the base body is a closed solid or an open 9-face body depending on a few ulps of the extrusion surface's extended domain, with success either way",
-    "multi_feature_extrusion": "tangency-labs/solidcore#3093: the base body is a closed solid or an open 9-face body depending on a few ulps of the extrusion surface's extended domain, with success either way",
-    "multi_rebuild_0_extrusion": "tangency-labs/solidcore#3093: the base body is a closed solid or an open 9-face body depending on a few ulps of the extrusion surface's extended domain, with success either way",
     "single_face_fillet1019_6": "tangency-labs/solidcore#3093: success with a body that fails check_brep level 2 (11 lines, the first Bad Repeated CPts)"
   },
   "blend.fillet_executive_p3": {

solidcore/crates/goldens/expected/query.face_p3.jsonl

@@ -350,7 +350,7 @@
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solidcore/crates/goldens/expected/topology.brep_local_operation.jsonl

@@ -60,7 +60,7 @@
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@@ -81,7 +81,7 @@
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-{"case":"gen0059","deferred":null,"error":null,"ints":{"graph":{"blocks":[[2508,322157],[2737,381059],[5730,644350],[3544,630392],[6005,593789],[9923,1440534],[12774,1466844]],"n":1777}},"topology":null,"values":{"edge_curve_owners":{"blocks":[[351.0,351.0,6552.0]],"n":27},"geometry":{"blocks":[[2.1599999999999874e+22,2.1599999999999874e+22,2.3436e+24],[576.479912043791,9877403.191385778,9922263.828823194]],"n":424},"record":{"blocks":[[140960.93079587494,141032.93079587494,18166850.62474821],[127255.44270984929,127414.00046731443,17659903.3699522],[127999.14773026791,128178.73507590464,17389989.730407752],[91113.69032347939,43510619.86313032,96805260.33414717],[60762.71681469282,60811.28318530718,5140971.371759845]],"n":1210},"surface_owners":[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],"uv_curve_owners":{"blocks":[[-108.0,108.0,-5886.0]],"n":108}}}
+{"case":"gen0059","deferred":null,"error":null,"ints":{"graph":{"blocks":[[2468,318735],[2755,382199],[5710,650567],[3534,632497],[6013,592519],[9779,1412900],[12928,1499698]],"n":1777}},"topology":null,"values":{"edge_curve_owners":{"blocks":[[351.0,351.0,6552.0]],"n":27},"geometry":{"blocks":[[2.1599999999999874e+22,2.1599999999999874e+22,2.3436e+24],[431.5198428883937,624.652584117112,27447.906125791415]],"n":424},"record":{"blocks":[[156224.41673182778,156297.18329645565,19149526.127055034],[154598.40251211118,154985.87177838173,20301423.514221795],[140664.7203279845,140836.2024273099,17905887.2094762],[154920.03783534584,154938.03783534584,19116535.34318591],[154743.16176198598,154820.03053193798,20312026.989448104],[140446.0,140764.0,17885794.0],[154426.5,154613.5,19052446.0],[129684.24687969516,129844.4946593029,14955378.32523922],[91187.66304535375,91247.66304535375,11441009.498965224],[30370.71681469282,30387.28318530718,1022758.4248081051]],"n":2398},"surface_owners":[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],"uv_curve_owners":{"blocks":[[1377.0,1485.0,48069.0]],"n":108}}}
 {"case":"gen0060","deferred":null,"error":null,"ints":{"graph":{"blocks":[[50,1663]],"n":71}},"topology":null,"values":{"edge_curve_owners":[0.0],"geometry":[1e+20,1e+20,1e+20,1e+20,0.0,0.0,0.7261627726849257,0.00001,-1234567.0,-1234567.0,1234567.0,1234567.0,0.00001,-30.61467458920718,0.0,0.00001],"record":{"blocks":[[29005.551604228152,19782192.780953407,123949089.18024483]],"n":70},"surface_owners":[1.0],"uv_curve_owners":[-1.0,-1.0]}}
 {"case":"gen0061","deferred":null,"error":null,"ints":{"graph":{"blocks":[[50,1663]],"n":71}},"topology":null,"values":{"edge_curve_owners":[0.0],"geometry":[1e+20,1e+20,1e+20,1e+20,0.0,5.0,0.0,0.00001,-10.0,-5.0,0.0,4.999999999999999,0.00001,-30.61467458920718,0.0,0.00001],"record":{"blocks":[[29010.385325410793,29185.614674589207,492554.5413016432]],"n":70},"surface_owners":[1.0],"uv_curve_owners":[-1.0,-1.0]}}
 {"case":"gen0062","deferred":null,"error":null,"ints":{"graph":{"blocks":[[682,105286],[29,96]],"n":261}},"topology":null,"values":{"edge_curve_owners":[0.0,1.0,2.0],"geometry":{"blocks":[[2.4e+21,2.4e+21,2.9999999999999996e+22]],"n":56},"record":{"blocks":[[142982.44946801648,143164.44946801648,15937837.083377652],[30107.0,30287.0,771201.0]],"n":342},"surface_owners":[1.0,1.0,1.0],"uv_curve_owners":[0.0,1.0,2.0,3.0,4.0,5.0,-1.0,-1.0,-1.0,-1.0,-1.0,-1.0]}}
@@ -136,7 +136,7 @@
 {"case":"gen0073","deferred":null,"error":null,"ints":{"graph":{"blocks":[[101,5336]],"n":97}},"topology":null,"values":{"edge_curve_owners":[0.0,1.0],"geometry":{"blocks":[[8e+20,8e+20,3.6e+21]],"n":27},"record":{"blocks":[[72141.8827762868,72278.09763810274,3691636.3260077816]],"n":140},"surface_owners":[1.0],"uv_curve_owners":[0.0,1.0,-1.0,-1.0]}}
 {"case":"gen0074","deferred":null,"error":null,"ints":{"graph":{"blocks":[[1277,174490],[2444,346534],[4114,669278],[778,14800]],"n":804}},"topology":null,"values":{"edge_curve_owners":[0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0,11.0],"geometry":{"blocks":[[9.6e+21,9.600000000000025e+21,4.6559999999999995e+23]],"n":194},"record":{"blocks":[[141078.67945932975,141262.36447332427,18213079.47648731],[-2365134.5339968833,49170000.150317684,-534069203.35257745],[2484425.6882363446,12360978.591230411,116552981.21678422]],"n":585},"surface_owners":[1.0,1.0,1.0,1.0,1.0,1.0],"uv_curve_owners":{"blocks":[[-48.0,48.0,-1176.0]],"n":48}}}
 {"case":"gen0075","deferred":null,"error":null,"ints":{"graph":{"blocks":[[1172,159991],[1948,311927],[978,28202]],"n":573}},"topology":null,"values":{"edge_curve_owners":[0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0],"geometry":{"blocks":[[6.4e+21,6.4e+21,2.0799999999999997e+23]],"n":133},"record":{"blocks":[[156360.52780532837,158006.30563557148,19068776.25026989],[153903.1388885975,156472.02783429623,20181493.582973957],[104892.00006401539,108480.00015670061,12407745.286694974],[258.6666741371155,509.33334589004517,2804.4445185661316]],"n":784},"surface_owners":[1.0,1.0,1.0,1.0,1.0],"uv_curve_owners":{"blocks":[[360.0,392.0,9416.0]],"n":32}}}
-{"case":"gen0076","deferred":null,"error":null,"ints":{"graph":{"blocks":[[1191,161874],[1949,313933],[974,28428]],"n":573}},"topology":null,"values":{"edge_curve_owners":[0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0],"geometry":{"blocks":[[6.4e+21,6.400000000000004e+21,2.0799999999999997e+23]],"n":133},"record":{"blocks":[[-3573955.801055106,13714426.230891941,-884935273.6169126],[3765521.6562693026,6237320.46813458,20670087.030879214]],"n":432},"surface_owners":[1.0,1.0,1.0,1.0,1.0],"uv_curve_owners":{"blocks":[[-32.0,32.0,-528.0]],"n":32}}}
+{"case":"gen0076","deferred":null,"error":null,"ints":{"graph":{"blocks":[[1172,159991],[1948,311927],[978,28202]],"n":573}},"topology":null,"values":{"edge_curve_owners":[0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0],"geometry":{"blocks":[[6.4e+21,6.4e+21,2.0799999999999997e+23]],"n":133},"record":{"blocks":[[156360.52780532837,158006.30563557148,19068776.25026989],[153903.1388885975,156472.02783429623,20181493.582973957],[104892.00006401539,108480.00015670061,12407745.286694974],[258.6666741371155,509.33334589004517,2804.4445185661316]],"n":784},"surface_owners":[1.0,1.0,1.0,1.0,1.0],"uv_curve_owners":{"blocks":[[360.0,392.0,9416.0]],"n":32}}}
 {"case":"gen0077","deferred":null,"error":null,"ints":{"graph":{"blocks":[[50,1663]],"n":71}},"topology":null,"values":{"edge_curve_owners":[0.0],"geometry":[1e+20,1e+20,1e+20,1e+20,0.0,5.0,0.0,0.00001,-10.0,-5.0,0.0,4.999999999999999,0.00001,-30.61467458920718,0.0,0.00001],"record":{"blocks":[[29010.385325410793,29185.614674589207,492554.5413016432]],"n":70},"surface_owners":[1.0],"uv_curve_owners":[-1.0,-1.0]}}
 {"case":"gen0078","deferred":null,"error":null,"ints":{"graph":{"blocks":[[101,5336]],"n":97}},"topology":null,"values":{"edge_curve_owners":[0.0,1.0],"geometry":{"blocks":[[8e+20,8e+20,3.6e+21]],"n":27},"record":{"blocks":[[72141.8827762868,72278.09763810274,3691636.3260077816]],"n":140},"surface_owners":[1.0],"uv_curve_owners":[0.0,1.0,-1.0,-1.0]}}
 {"case":"gen0079","deferred":null,"error":null,"ints":{"graph":{"blocks":[[1881,231784],[3468,553413],[2259,207996],[5091,517645],[9023,1312991],[4471,251788]],"n":1396}},"topology":null,"values":{"edge_curve_owners":{"blocks":[[210.0,210.0,3080.0]],"n":21},"geometry":{"blocks":[[1.6799999999999925e+22,1.679999999999995e+22,1.4196e+24],[247.87446819416934,292.6310905949567,11255.605714095394]],"n":337},"record":{"blocks":[[140956.03803434453,141040.53803434453,18185296.49393398],[127239.77528722705,127311.77528722705,17668690.287975267],[-3599843.39161713,48252017.31114167,-789183361.4693285],[3779671.2271521315,11187235.78436824,114616369.86204277]],"n":1001},"surface_owners":[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],"uv_curve_owners":{"blocks":[[-84.0,84.0,-3570.0]],"n":84}}}

solidcore/crates/goldens/src/soundness.rs

@@ -11,6 +11,7 @@
 use std::cell::RefCell;
 
 use solidcore::kernel::Kernel;
+use solidcore::mass::enclosure::VolumeSign;
 use solidcore::topology::brep::validation;
 use solidcore::topology::Brep;
 
@@ -25,8 +26,8 @@ pub struct Soundness {
     pub check: Result<Vec<String>, String>,
     /// Whether the body is a manifold solid.
     pub manifold: Option<bool>,
-    /// Its volume, when it is a manifold solid.
-    pub volume: Option<f64>,
+    /// Its volume's sign, when it is a manifold solid.
+    pub volume: Option<VolumeSign>,
     /// Its face, edge and vertex counts.
     pub counts: [usize; 3],
 }
@@ -35,7 +36,7 @@ impl Soundness {
     /// Whether the check is clean and a manifold body has a positive volume.
     pub fn sound(&self) -> bool {
         self.check.as_ref().is_ok_and(Vec::is_empty)
-            && (self.manifold != Some(true) || self.volume.is_some_and(|v| v > 0.0))
+            && (self.manifold != Some(true) || matches!(self.volume, Some(VolumeSign::Positive(_))))
     }
 
     /// One line: `sound`, the check's line count, manifold, volume and counts.
@@ -164,7 +165,7 @@ pub fn probe(runner: &dyn crate::UnitDiff) {
 
 #[cfg(test)]
 mod tests {
-    use super::{measure, start, take};
+    use super::{measure, start, take, VolumeSign};
     use solidcore::kernel::Kernel;
 
     fn cube() -> solidcore::topology::Brep {
@@ -198,8 +199,7 @@ mod tests {
         assert!(s.sound(), "{}", s.line());
         assert_eq!(s.manifold, Some(true));
         assert!(
-            s.volume
-                .is_some_and(|v| (v - 1000.0).abs() <= 1e-6 * 1000.0),
+            matches!(s.volume, Some(VolumeSign::Positive(e)) if e.lo <= 1000.0 && 1000.0 <= e.hi),
             "{}",
             s.line()
         );

solidcore/crates/solidcore-convert/Cargo.toml

@@ -5,7 +5,8 @@ edition.workspace = true
 license.workspace = true
 version.workspace = true
 publish = false
-rust-version.workspace = true
+# solidcore-record needs Rust 1.88 (edition 2024 let chains).
+rust-version = "1.88"
 repository = "https://github.com/tangency-labs/solidcore"
 keywords = ["cad", "brep", "nurbs", "geometry"]
 categories = ["data-structures", "science"]

solidcore/crates/solidcore-convert/src/brep.rs

@@ -21,6 +21,8 @@
 #![allow(clippy::field_reassign_with_default)]
 #![allow(clippy::neg_cmp_op_on_partial_ord)] // NaN-refusing tests
 
+use std::collections::BTreeMap;
+
 use solidcore::curve::curve::Curve as KernelCurve;
 use solidcore::curve::from_parameters::{
     self as curves, approx_tolerance, zone_tolerance, MAX_TOLERANCE,
@@ -93,6 +95,86 @@ pub struct Order {
     pub vertices: Vec<VertexId>,
 }
 
+/// A kernel edge solids touch along, as [`to_record`] writes it: one record edge per pair of
+/// faces it separates (SolidCraft's `history::Piece`). An edge with uses on three or more faces
+/// has one [`Piece`] per record edge [`to_record`] copied it into, each with the faces of that
+/// copy's own uses (two, for the sector pairs the radial order gives); none is merged or split
+/// here.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct Piece {
+    /// The kernel edge.
+    pub kernel: EdgeId,
+    /// One of its record edges.
+    pub edge: u32,
+    /// The record faces that record edge bounds, ascending.
+    pub faces: Vec<u32>,
+}
+
+impl Order {
+    /// Each kernel face's record face (the inverse of [`Order::faces`]).
+    #[must_use]
+    pub fn record_faces(&self) -> BTreeMap<FaceId, u32> {
+        inverse(&self.faces)
+    }
+
+    /// Each kernel edge's first record edge (the inverse of [`Order::edges`]; a kernel edge
+    /// solids touch along has more, its [`Order::pieces`]).
+    #[must_use]
+    pub fn record_edges(&self) -> BTreeMap<EdgeId, u32> {
+        inverse(&self.edges)
+    }
+
+    /// Each kernel vertex's first record vertex (the inverse of [`Order::vertices`]).
+    #[must_use]
+    pub fn record_vertices(&self) -> BTreeMap<VertexId, u32> {
+        inverse(&self.vertices)
+    }
+
+    /// Every record edge of each kernel edge that has more than one, in record order, with the
+    /// record faces it bounds (`record` is the record this order came with): the faces of that
+    /// record edge's uses, sorted and without repeats.
+    ///
+    /// # Errors
+    ///
+    /// [`Unsupported::Invalid`] for a record whose edges are not this order's.
+    pub fn pieces(&self, record: &r::Brep) -> R<Vec<Piece>> {
+        if record.edges.len() != self.edges.len() {
+            return Err(Unsupported::Invalid("a record not of this order"));
+        }
+        let mut count: BTreeMap<EdgeId, usize> = BTreeMap::new();
+        for &e in &self.edges {
+            *count.entry(e).or_default() += 1;
+        }
+        let mut out = Vec::new();
+        for (i, (&kernel, e)) in self.edges.iter().zip(&record.edges).enumerate() {
+            if count.get(&kernel).copied().unwrap_or(0) < 2 {
+                continue;
+            }
+            let mut faces: Vec<u32> = e.uses.iter().map(|u| u.face).collect();
+            faces.sort_unstable();
+            faces.dedup();
+            out.push(Piece {
+                kernel,
+                edge: u32::try_from(i).map_err(|_| Unsupported::Invalid("index"))?,
+                faces,
+            });
+        }
+        Ok(out)
+    }
+}
+
+/// Each entity's first index in `list`. An index past `u32` is left out: unreachable, since
+/// every list is an [`Order`]'s, indexed by a record's `u32` indices.
+fn inverse<T: Copy + Ord>(list: &[T]) -> BTreeMap<T, u32> {
+    let mut out = BTreeMap::new();
+    for (i, &x) in list.iter().enumerate() {
+        if let Ok(i) = u32::try_from(i) {
+            out.entry(x).or_insert(i);
+        }
+    }
+    out
+}
+
 fn int(n: usize) -> R<u64> {
     u64::try_from(n).map_err(|_| Unsupported::Invalid("count"))
 }
@@ -231,8 +313,8 @@ fn build(
 }
 
 /// The record as the kernel's B-rep data: edgeuses face by face, loop by loop, in loop order;
-/// edges and vertices in the record's order. Each edge and vertex keeps its own tolerance (at
-/// least the body's); the body and every face take the body's. The record has no face
+/// edges and vertices in the record's order. Each edge and vertex keeps its own tolerance; the
+/// body's and each face's are the least of theirs ([`own_tolerances`]). The record has no face
 /// tolerance: a face's own crosses as its edges' (`to_record` puts it into them).
 fn data(k: &Kernel, rec: &r::Brep, bare: &[(u32, u32, u32)]) -> R<BrepData> {
     let zone = zone_tolerance(rec.tolerance);
@@ -318,7 +400,7 @@ fn data(k: &Kernel, rec: &r::Brep, bare: &[(u32, u32, u32)]) -> R<BrepData> {
     // Edges first (their kernel intervals are the trims' parameter), in the record's order.
     let mut intervals = Vec::new();
     for e in &rec.edges {
-        let tolerance = e.tolerance.max(rec.tolerance);
+        let tolerance = e.tolerance;
         if !(tolerance <= MAX_TOLERANCE) {
             return Err(Unsupported::NotYet(
                 "an edge tolerance over the kernel's limit",
@@ -475,9 +557,18 @@ fn data(k: &Kernel, rec: &r::Brep, bare: &[(u32, u32, u32)]) -> R<BrepData> {
                             let interval = intervals
                                 .get(u.edge as usize)
                                 .ok_or(Unsupported::Invalid("edge"))?;
+                            let source_interval = rec
+                                .edges
+                                .get(u.edge as usize)
+                                .ok_or(Unsupported::Invalid("edge"))?
+                                .interval;
                             ud.uv_curve = int(d.uv_curves.len())?;
-                            let trim =
-                                curves::uv_trim(&crate::curve2(&u.pcurve), interval, made.scale)?;
+                            let trim = curves::uv_trim_on_edge(
+                                &crate::curve2(&u.pcurve),
+                                source_interval,
+                                interval,
+                                made.scale,
+                            )?;
                             d.uv_curves.push(Keyed {
                                 key: key(),
                                 object: trim,
@@ -500,9 +591,9 @@ fn data(k: &Kernel, rec: &r::Brep, bare: &[(u32, u32, u32)]) -> R<BrepData> {
         }
     }
 
-    // Vertices, each with its own tolerance, never below the body's.
+    // Vertices, each with its own tolerance.
     for v in &rec.vertices {
-        let tolerance = v.tolerance.max(rec.tolerance);
+        let tolerance = v.tolerance;
         if !(tolerance <= MAX_TOLERANCE) {
             return Err(Unsupported::NotYet(
                 "a vertex tolerance over the kernel's limit",
@@ -514,9 +605,62 @@ fn data(k: &Kernel, rec: &r::Brep, bare: &[(u32, u32, u32)]) -> R<BrepData> {
         vd.point = Vec3::new(v.point[0], v.point[1], v.point[2]);
         d.vertices.push(vd);
     }
+    own_tolerances(&mut d, rec, zone)?;
     Ok(d)
 }
 
+/// The body's and each face's tolerance from the edges' and vertices' own, as SolidCraft's
+/// flat import took them (`own_tolerances`, after the capi's): the kernel's build raises every
+/// entity to the body's, so the body's is the least of the record's and its edges' and
+/// vertices', and a face's the least of its loops' edges' and vertices', at most the record's.
+/// Each entity keeps its own across the crossing, none raised to the body's.
+///
+/// This keeps invariant 5 of `docs/validity-and-tolerances.md` §10 (every local tolerance at
+/// least the body's) by the other route from raising each entity to the body's (8252ae3e93,
+/// "never below the body's"): the body comes down to the least of them instead, so no entity
+/// is below it and none is changed. A face's is at least the body's (both are minima, the
+/// body's over more) and at most its loops' edges' and vertices'.
+///
+/// # Errors
+///
+/// [`Unsupported::Invalid`] when the least zone is not positive and finite: a tolerance so
+/// small that its zone (half of it) underflows to zero passes the record's validation.
+fn own_tolerances(d: &mut BrepData, rec: &r::Brep, zone: f64) -> R<()> {
+    let edge_zone = |e: u32| -> R<f64> { Ok(at(&d.edges, e)?.zone_tol_3d) };
+    let vertex_zone = |v: u32| -> R<f64> { Ok(at(&d.vertices, v)?.zone_tol_3d) };
+    let mut faces = Vec::with_capacity(rec.faces.len());
+    for f in &rec.faces {
+        let mut t = f64::INFINITY;
+        for l in &f.loops {
+            match l {
+                r::Loop::Edges { edges } => {
+                    for oe in edges {
+                        t = t.min(edge_zone(oe.edge)?);
+                    }
+                }
+                r::Loop::Vertex { vertex } => t = t.min(vertex_zone(*vertex)?),
+            }
+        }
+        faces.push(if t.is_finite() { t.min(zone) } else { zone });
+    }
+    let least = d
+        .edges
+        .iter()
+        .map(|e| e.zone_tol_3d)
+        .chain(d.vertices.iter().map(|v| v.zone_tol_3d))
+        .fold(zone, f64::min);
+    if !(least.is_finite() && least > 0.0) {
+        return Err(Unsupported::Invalid(
+            "a tolerance whose zone (half of it) is zero or not finite",
+        ));
+    }
+    d.zone_tol_3d = least;
+    for (fd, t) in d.faces.iter_mut().zip(faces) {
+        fd.zone_tol_3d = t;
+    }
+    Ok(())
+}
+
 /// The curves of a ball patch face's loops, for [`face_surface`] to certify on its sphere:
 /// each edge's NURBS form, or its curve; empty for any other face, whose label is not
 /// checked against its loops.

solidcore/crates/solidcore-convert/src/brep/record.rs

@@ -3,7 +3,7 @@
 //! B-rep data, with no arrays between. What is done here is index mapping and field copies:
 //!
 //! - **Geometry:** each edge's curve and each face's surface as the kernel writes its record
-//!   ([`record_of`], [`record_face`]): a line by its two end points, a conic by its own frame and
+//!   ([`record_of`], [`record_face`]): a line as the kernel holds it, a conic by its own frame and
 //!   its NURBS form, proved on each other; an analytic face by its label and its NURBS form,
 //!   proved (`lies_on`); a plane by its placement, its parameters its kernel ones times its
 //!   scales. Nothing is sampled. A curve or surface with no NURBS form (an offset) is refused.

solidcore/crates/solidcore-convert/tests/brep.rs

@@ -226,6 +226,29 @@ fn a_cube_record_builds_the_kernels_cube() {
     }
 }
 
+#[test]
+fn a_pcurve_support_may_extend_past_its_edge_interval() {
+    let mut record = cube(1.0);
+    let Curve::Line { start, end } = &record.edges[0].curve else {
+        panic!("cube line")
+    };
+    let (start, end) = (*start, *end);
+    record.edges[0].curve = Curve::Spline {
+        knots: vec![0.0, 0.0, 1.0, 1.0],
+        points: vec![start, end],
+    };
+    record.edges[0].interval = [0.0, f64::from_bits(1.0_f64.to_bits() - 2)];
+    record.validate().unwrap();
+    let original = record.faces.clone();
+    let mut k = kernel();
+    let (mut body, _) = to_kernel(&mut k, &record, true).unwrap();
+    let (saved, _) = to_record(&mut k, &mut body).unwrap();
+    assert_eq!(
+        saved.faces.iter().map(|f| &f.loops).collect::<Vec<_>>(),
+        original.iter().map(|f| &f.loops).collect::<Vec<_>>()
+    );
+}
+
 #[test]
 fn records_the_conversion_cannot_carry_are_refused() {
     let mut k = kernel();
@@ -556,8 +579,8 @@ fn lumps_and_solids_touching_along_an_edge_go_round() {
 }
 
 /// An analytic body's record: its curved faces are labels on their NURBS forms, its circles
-/// labels on theirs, its lines their two end points over [0, 1]; each pcurve on its edge's
-/// interval.
+/// labels on theirs, its lines as the kernel holds them (its point and unit vector, over the
+/// height); each pcurve on its edge's interval.
 #[test]
 fn analytic_records_carry_labels_on_their_forms() {
     let mut k = kernel();
@@ -576,8 +599,9 @@ fn analytic_records_carry_labels_on_their_forms() {
     for e in &r.edges {
         match &e.curve {
             Curve::Line { start, end } => {
-                assert_eq!(e.interval, [0.0, 1.0]);
-                assert_eq!((start[2], end[2]), (0.0, 5.0));
+                // as the kernel holds the seam: its point and unit vector, over its height
+                assert_eq!(e.interval, [0.0, 5.0]);
+                assert_eq!((start[2], end[2]), (0.0, 1.0));
                 assert!(e.nurbs.is_none());
             }
             Curve::Circle { radius, .. } => {
@@ -1146,3 +1170,51 @@ fn a_ball_patch_far_from_the_origin_reads_as_one() {
         assert!(read_ball(&mut k, &off, i).is_none(), "face {i}");
     }
 }
+
+/// A record whose body tolerance is above its edges' and vertices' builds with the body's
+/// lowered to the least of them (the flat import's `own_tolerances`): valid at Level 2, and
+/// every edge and vertex at least the body's (invariant 5 of `docs/validity-and-tolerances.md`
+/// §10), each at its own (the zone, half the record's), none raised.
+#[test]
+fn a_body_tolerance_above_its_entities_comes_down_to_theirs() {
+    let mut k = kernel();
+    let mut r = cube(10.0);
+    r.tolerance = 1e-4;
+    r.edges[3].tolerance = 4e-6;
+    r.vertices[5].tolerance = 2e-6;
+    r.validate().unwrap();
+    let (mut b, _) = to_kernel(&mut k, &r, true).unwrap();
+    valid(&mut k, &mut b);
+    // the least is the other edges' 1e-6, as a zone: half of it
+    assert_eq!(b.tolerance(), 5e-7);
+    for &e in b.edge_list() {
+        assert!(b.edge(e).unwrap().tolerance >= b.tolerance(), "edge {e:?}");
+    }
+    for &v in b.vertex_list() {
+        assert!(
+            b.vertex(v).unwrap().tolerance >= b.tolerance(),
+            "vertex {v:?}"
+        );
+    }
+    let mut own: Vec<f64> = b
+        .edge_list()
+        .iter()
+        .map(|&e| b.edge(e).unwrap().tolerance)
+        .collect();
+    own.sort_by(f64::total_cmp);
+    own.dedup();
+    assert_eq!(own, vec![5e-7, 2e-6], "edges keep their own zones");
+}
+
+/// A tolerance so small that its zone (half of it) underflows to zero passes the record's
+/// validation and is refused by the conversion, not dropped to the body's.
+#[test]
+fn a_tolerance_whose_zone_underflows_is_refused() {
+    let mut k = kernel();
+    let mut r = cube(1.0);
+    r.vertices[0].tolerance = f64::from_bits(1);
+    assert!(matches!(
+        to_kernel(&mut k, &r, true),
+        Err(Unsupported::Invalid(_))
+    ));
+}

solidcore/crates/solidcore-convert/tests/flat_parity.rs

@@ -0,0 +1,602 @@
+//! Parity with SolidCraft's flat-array hop (#3137): every operand record of the rig corpus
+//! (`crates/solidcore/tests/kernel_cases/`) is what SolidCraft's flat export wrote (record →
+//! arrays → kernel → arrays → record), or, for a body SolidCraft made or read itself (not
+//! `trusted`), what it handed the kernel. Each goes to the kernel ([`to_kernel`]) and back
+//! ([`to_record`]); the record that comes back is compared with the one that went in, field by
+//! field, bit for bit. A difference is classed by where it is (indices dropped) and, for a
+//! kind, by what it became; a number within [`ROUNDING`] of its size (relative, no floor) is
+//! counted as rounding, with its count and the largest.
+//!
+//! On the whole corpus (1,333 bodies, at #3199 with kernel case 11991 (#3231) in): 1,259 come
+//! back bit for bit, 36 within rounding (the largest 4.9e-16 relative), and 38 differ, each in exactly the classes
+//! [`pinned`] lists for it.
+#![allow(
+    clippy::unwrap_used,
+    clippy::expect_used,
+    clippy::panic,
+    clippy::indexing_slicing,
+    clippy::print_stderr
+)] // test
+
+use std::collections::{BTreeMap, BTreeSet};
+use std::fmt::Write as _;
+use std::io::Read as _;
+use std::path::{Path, PathBuf};
+
+use serde_json::Value;
+use solidcore::kernel::{Kernel, KernelOptions, UpstreamFixes};
+use solidcore_convert::brep::{to_kernel, to_kernel_body, to_record, Unsupported};
+use solidcore_record::brep::Brep as Record;
+
+fn corpus() -> PathBuf {
+    Path::new(env!("CARGO_MANIFEST_DIR")).join("../solidcore/tests/kernel_cases")
+}
+
+fn entries(dir: &Path, out: &mut Vec<PathBuf>) {
+    let mut paths: Vec<PathBuf> = std::fs::read_dir(dir)
+        .unwrap()
+        .map(|e| e.unwrap().path())
+        .collect();
+    paths.sort();
+    for p in paths {
+        if p.is_dir() {
+            entries(&p, out);
+        } else if p.extension().is_some_and(|x| x == "json")
+            && !p.to_string_lossy().ends_with(".bodies.json")
+            && p.parent() != Some(corpus().as_path())
+        {
+            out.push(p);
+        }
+    }
+}
+
+#[derive(Default)]
+struct Class {
+    bodies: usize,
+    places: usize,
+    examples: Vec<String>,
+}
+
+#[derive(Default)]
+struct Tally {
+    bodies: usize,
+    identical: usize,
+    rounding_only: usize,
+    rounding_places: usize,
+    rounding_largest: f64,
+    refused_in: Vec<String>,
+    /// Sheets with a face used on its reverse side (every difference follows from that).
+    sheet_side: Vec<String>,
+    refused_out: Vec<String>,
+    classes: BTreeMap<String, Class>,
+    /// Each differing body's classes (sheet-side bodies' too).
+    per_body: BTreeMap<String, BTreeSet<String>>,
+    /// Bodies whose `.tolerance` moved other than down to the least of the record's.
+    tolerance_wrong: Vec<String>,
+    /// Sheet-side bodies whose geometry differs as multisets (not only renumbered).
+    sheet_geometry: Vec<String>,
+    /// (body, face, the record's kind, the kind that came back, trusted)
+    relabelled: Vec<(String, usize, String, String, bool)>,
+}
+
+/// The relative size of a difference counted as rounding, not a class: a few ulps.
+const ROUNDING: f64 = 1e-15;
+
+fn normal(path: &str) -> String {
+    let mut out = String::new();
+    let mut in_index = false;
+    for c in path.chars() {
+        match c {
+            '[' => {
+                in_index = true;
+                out.push_str("[*]");
+            }
+            ']' => in_index = false,
+            _ if in_index => {}
+            _ => out.push(c),
+        }
+    }
+    out
+}
+
+/// Every place `a` and `b` differ: (class, place); numbers within [`ROUNDING`] of their size
+/// (relative, no floor) counted apart, with the largest relative difference.
+fn walk(
+    at: &str,
+    a: &Value,
+    b: &Value,
+    diffs: &mut Vec<(String, String)>,
+    rounding: &mut (usize, f64),
+) {
+    if a == b {
+        return;
+    }
+    if let (Some(x), Some(y)) = (a.as_f64(), b.as_f64()) {
+        let rel = (x - y).abs() / x.abs().max(y.abs());
+        if rel <= ROUNDING {
+            rounding.0 += 1;
+            rounding.1 = rounding.1.max(rel);
+            return;
+        }
+        diffs.push((normal(at), format!("{at}: {x} -> {y}")));
+        return;
+    }
+    match (a, b) {
+        (Value::Object(x), Value::Object(y)) => {
+            for (k, v) in x {
+                walk(
+                    &format!("{at}.{k}"),
+                    v,
+                    y.get(k).unwrap_or(&Value::Null),
+                    diffs,
+                    rounding,
+                );
+            }
+            for (k, w) in y {
+                if !x.contains_key(k) {
+                    walk(&format!("{at}.{k}"), &Value::Null, w, diffs, rounding);
+                }
+            }
+        }
+        (Value::Array(x), Value::Array(y)) if x.len() == y.len() => {
+            for (i, (v, w)) in x.iter().zip(y).enumerate() {
+                walk(&format!("{at}[{i}]"), v, w, diffs, rounding);
+            }
+        }
+        (Value::Array(x), Value::Array(y)) => diffs.push((
+            format!("{}: length", normal(at)),
+            format!("{at}: {} -> {}", x.len(), y.len()),
+        )),
+        (Value::String(x), Value::String(y)) => {
+            diffs.push((format!("{}: {x} -> {y}", normal(at)), at.to_owned()));
+        }
+        _ => {
+            let short = |v: &Value| {
+                let s = v.to_string();
+                s.chars().take(60).collect::<String>()
+            };
+            diffs.push((normal(at), format!("{at}: {} -> {}", short(a), short(b))));
+        }
+    }
+}
+
+/// A record's geometry as multisets, its numbering dropped: the vertex points, each edge's
+/// curve (a line's two ends unordered), each face's surface and NURBS form.
+fn geometry(r: &Value) -> [Vec<String>; 3] {
+    let list = |key: &str, f: &dyn Fn(&Value) -> String| -> Vec<String> {
+        let mut v: Vec<String> = r[key]
+            .as_array()
+            .map(|a| a.iter().map(f).collect())
+            .unwrap_or_default();
+        v.sort();
+        v
+    };
+    let curve = |e: &Value| {
+        let c = &e["curve"];
+        if c["kind"] == "line" {
+            let mut ends = [c["start"].to_string(), c["end"].to_string()];
+            ends.sort();
+            format!("line {ends:?}")
+        } else {
+            c.to_string()
+        }
+    };
+    [
+        list("vertices", &|v| v["point"].to_string()),
+        list("edges", &curve),
+        list("faces", &|f| format!("{} {}", f["surface"], f["nurbs"])),
+    ]
+}
+
+fn kind(face: &Value) -> String {
+    face["surface"]["kind"].as_str().unwrap_or("?").to_owned()
+}
+
+fn one(name: &str, record: &Record, trusted: bool, fixes: &UpstreamFixes, t: &mut Tally) {
+    t.bodies += 1;
+    // a sheet face used on its reverse side: the kernel keeps both uses of a sheet's face and
+    // the record comes back with the `same` one, as SolidCraft's flat export wrote it
+    // (a sheet's shell is listed by one region; a closed shell by the two it separates)
+    let listed = |i: usize| {
+        record
+            .regions
+            .iter()
+            .filter(|r| r.shells.iter().any(|&s| s as usize == i))
+            .count()
+    };
+    let sheet_side = record.shells.iter().enumerate().any(|(i, s)| match s {
+        solidcore_record::brep::Shell::Faces { faces, .. } => {
+            listed(i) == 1 && faces.iter().any(|f| !f.forward)
+        }
+        _ => false,
+    });
+    let mut k = Kernel::new(&KernelOptions::default());
+    k.fixes = *fixes;
+    let built = match to_kernel(&mut k, record, trusted) {
+        Ok((b, _)) => Ok(b),
+        Err(Unsupported::NotYet(w)) if w.contains("healer") => {
+            to_kernel_body(&mut k, record, trusted)
+        }
+        Err(e) => Err(e),
+    };
+    let mut b = match built {
+        Ok(b) => b,
+        Err(e) => {
+            t.refused_in.push(format!("{name}: {e}"));
+            return;
+        }
+    };
+    let back = match to_record(&mut k, &mut b) {
+        Ok((r, _)) => r,
+        Err(e) => {
+            t.refused_out.push(format!("{name}: {e}"));
+            return;
+        }
+    };
+    let (a, z) = (
+        serde_json::to_value(record).unwrap(),
+        serde_json::to_value(&back).unwrap(),
+    );
+    // `PARITY_DUMP=<dir>` and `PARITY_ONLY=<part of a name>`: both records written there
+    if let (Ok(dir), Ok(only)) = (std::env::var("PARITY_DUMP"), std::env::var("PARITY_ONLY")) {
+        if name.contains(&only) {
+            let stem = name.replace(['/', ':'], "_");
+            std::fs::write(format!("{dir}/{stem}.in.json"), a.to_string()).unwrap();
+            std::fs::write(format!("{dir}/{stem}.out.json"), z.to_string()).unwrap();
+        }
+    }
+    let mut diffs = Vec::new();
+    let mut rounding = (0, 0.0_f64);
+    walk("", &a, &z, &mut diffs, &mut rounding);
+    t.rounding_places += rounding.0;
+    t.rounding_largest = t.rounding_largest.max(rounding.1);
+    if let (Some(fa), Some(fz)) = (a["faces"].as_array(), z["faces"].as_array()) {
+        for (i, (x, y)) in fa.iter().zip(fz).enumerate() {
+            if kind(x) != kind(y) {
+                t.relabelled
+                    .push((name.to_owned(), i, kind(x), kind(y), trusted));
+            }
+        }
+    }
+    if diffs.is_empty() {
+        if rounding.0 == 0 {
+            t.identical += 1;
+        } else {
+            t.rounding_only += 1;
+        }
+        return;
+    }
+    let classes: BTreeSet<String> = diffs.iter().map(|(c, _)| c.clone()).collect();
+    if classes.contains(".tolerance") {
+        // lowered, to the least of the record's own (the flat import's `own_tolerances`)
+        let least = record
+            .edges
+            .iter()
+            .map(|e| e.tolerance)
+            .chain(record.vertices.iter().map(|v| v.tolerance))
+            .fold(record.tolerance, f64::min);
+        if !(back.tolerance < record.tolerance && back.tolerance == least) {
+            t.tolerance_wrong.push(format!(
+                "{name}: {} -> {} (least {least})",
+                record.tolerance, back.tolerance
+            ));
+        }
+    }
+    t.per_body.insert(name.to_owned(), classes);
+    if sheet_side && geometry(&a) != geometry(&z) {
+        t.sheet_geometry.push(name.to_owned());
+    }
+    if sheet_side {
+        t.sheet_side.push(name.to_owned());
+        return;
+    }
+    let mut seen = BTreeMap::new();
+    for (class, place) in diffs {
+        seen.entry(class).or_insert((0, place)).0 += 1;
+    }
+    for (class, (n, place)) in seen {
+        let tag = if trusted { "" } else { "(untrusted) " };
+        let c = t.classes.entry(format!("{tag}{class}")).or_default();
+        c.bodies += 1;
+        c.places += n;
+        if c.examples.len() < 3 {
+            c.examples.push(format!("{name} {place}"));
+        }
+    }
+}
+
+fn fixes() -> UpstreamFixes {
+    let fixes_json: Value =
+        serde_json::from_str(&std::fs::read_to_string(corpus().join("fixes.json")).unwrap())
+            .unwrap();
+    let mut fixes = UpstreamFixes::default();
+    for flag in fixes_json.as_array().unwrap() {
+        *fixes.flag_mut(flag.as_str().unwrap()).unwrap() = true;
+    }
+    fixes
+}
+
+const LABEL: [&str; 6] = [
+    ".faces[*].nurbs",
+    ".faces[*].surface.frame",
+    ".faces[*].surface.homogeneous",
+    ".faces[*].surface.u_knots",
+    ".faces[*].surface.v_knots",
+    "",
+];
+
+/// Every body that does not come back bit for bit (or within [`ROUNDING`]), with exactly the
+/// classes it differs in: a body that newly differs, one that no longer does, and one whose
+/// classes change all fail (#3187 review). Each group says why its difference is intended.
+fn pinned() -> BTreeMap<String, BTreeSet<String>> {
+    let set = |classes: &[&str]| -> BTreeSet<String> {
+        classes
+            .iter()
+            .filter(|c| !c.is_empty())
+            .map(|c| (*c).to_owned())
+            .collect()
+    };
+    let label = |kind: &str, radii: &[&str]| {
+        let mut c = set(&LABEL);
+        c.insert(format!(".faces[*].surface.kind: {kind}"));
+        c.extend(radii.iter().map(|r| format!(".faces[*].surface.{r}")));
+        c
+    };
+    let groups: Vec<(BTreeSet<String>, &[&str])> = vec![
+        // a record whose body tolerance is above its least entity's: the import lowers it to
+        // that least, as the flat import's `own_tolerances` does (checked: only lowered, and
+        // only to the least of the record's own)
+        (
+            set(&[".tolerance"]),
+            &[
+                "continuity/cov-patch-g1-caps-an-opened-tube-end.json:b3",
+                "continuity/cov-patch-g2-caps-an-opened-tube-end.json:b3",
+                "continuity/g1-patch-g2-at-a-corner-whose-rounds-clash.json:b13",
+                "continuity/g1-patch-g3-at-a-corner-whose-rounds-clash.json:b13",
+                "continuity/g2-patch-g2-on-a-hole-in-one-sheet.json:b11",
+                "continuity/g3-patch-g3-on-a-hole-in-one-sheet.json:b11",
+                "fillets/9-fillet-corner-r5-curvature-default-setback.json:b8",
+                "fillets/cov-fillet-g2-pocket-corner.json:b18",
+                "fillets/every-box-corner-three-edges-r3-curvature-setback-3-5.json:b8",
+                "fillets/report-fillet-curvature-three-edges-at-bar-corner-solver-residues.json:b18",
+                "fillets/report-fillet-curvature-three-edges-at-bar-corner.json:b18",
+                "fillets/report-fillet-g2-corner-of-bar-running-into-cylinder.json:b18",
+                "ladder/07-fillets/015-corner-g2-patch.json:b8",
+                "ladder/07-fillets/019-concave-corner-g2-patch.json:b18",
+                "surfaces/cov-blend-step-between-offset-sheets-g1.json:b1",
+                "surfaces/cov-blend-step-between-offset-sheets-g2.json:b1",
+                "surfaces/cov-blend-step-between-offset-sheets-g3.json:b1",
+                "surfaces/cov-patch-g0-fills-a-240-deg-window-in-a-cylinder.json:b13",
+                "surfaces/cov-patch-g0-fills-a-saddle-window-in-a-torus.json:b13",
+                "surfaces/cov-patch-g1-fills-a-240-deg-window-in-a-cylinder.json:b13",
+                "surfaces/cov-patch-g1-fills-a-saddle-window-in-a-torus.json:b13",
+                "surfaces/cov-patch-open-box-rim-and-stitch-closes-it.json:b3",
+            ],
+        ),
+        // a plane through three points: the kernel's plane holds no record of which kind it
+        // came from, and the flat export never writes this kind
+        (
+            set(&[
+                ".faces[*].surface.kind: plane_through -> plane",
+                ".faces[*].surface.u_axis",
+                ".faces[*].surface.u_point",
+                ".faces[*].surface.v_axis",
+                ".faces[*].surface.v_point",
+            ]),
+            &[
+                "surfaces/cov-ruled-box-edge-along-the-top-normal.json:b2",
+                "surfaces/cov-ruled-closed-top-chain-tangent-mitred-frame.json:b2",
+                "surfaces/cov-ruled-cylinder-rim-tangent-to-the-top-is-a-flat-ring.json:b2",
+            ],
+        ),
+        // a label its form is not proved on goes as the form alone (#2540): cylinders whose
+        // frames are off their forms past the rounding `evaluates_as` derives (margins 1.23 to
+        // 2.03, tests/issue_3185_label_margins.rs)
+        (
+            label("cylinder -> rational_spline", &["radius"]),
+            &[
+                "booleans/3456-deep-cut-through-drilled-taper-leaves-base.json:b94",
+                "crashes/2243-step-export-flanged-enclosure.json:b43",
+                "fillets/2903-original-rim-chamfer.json:b0",
+                "fillets/2903-original-rim-round.json:b0",
+            ],
+        ),
+        // a torus label whose frame is off its form's own first sweep row past the rounding
+        // `evaluates_as` derives (margin 1.69, tests/issue_3185_label_margins.rs)
+        (
+            label(
+                "torus -> rational_spline",
+                &["major_radius", "minor_radius"],
+            ),
+            &["sweeps/4280-circular-pattern-of-sweep-cut-groove-on-hub.json:b46"],
+        ),
+        // an extruded circle the flat hop left a spline, proved a cylinder
+        (
+            label("rational_spline -> cylinder", &["radius"]),
+            &[
+                "tessellation/1615-crossed-lofted-tubes.json:b3",
+                "tessellation/1615-crossed-lofted-tubes.json:b6",
+            ],
+        ),
+        // a line end the export wrote as 3.1e-16 (a cos 90 deg residue) where the kernel's
+        // line, point plus its vector, holds 0: an absolute 3e-16 on a coordinate of size 0
+        (
+            set(&[".edges[*].curve.end[*]"]),
+            &["assemblies/cov-contact-check-touching-faces-do-not-overlap.json:b725"],
+        ),
+    ];
+    let mut out = BTreeMap::new();
+    for (classes, bodies) in groups {
+        for b in bodies {
+            out.insert((*b).to_owned(), classes.clone());
+        }
+    }
+    // a sheet face used on its reverse side: the kernel keeps both uses of a sheet's face and
+    // the record comes back with the `same` one, as the flat export's rule says; every
+    // difference is the renumbering that follows (checked: the same vertex points, edge curves
+    // and face surfaces, as multisets), and two of them also lower `.tolerance`
+    let renumbered = [
+        ".edges[*].uses[*].position",
+        ".faces[*].loops[*].edges[*].edge",
+        ".shells[*].faces[*].forward",
+        ".vertices[*].point[*]",
+    ];
+    let match_sheet = [
+        ".edges[*].curve.knots: length",
+        ".edges[*].curve.points: length",
+        ".edges[*].uses[*].upper",
+    ];
+    let reverse = [
+        ".edges[*].curve.end[*]",
+        ".edges[*].curve.start[*]",
+        ".edges[*].vertices[*]",
+    ];
+    let with = |extra: &[&[&str]]| {
+        let mut c = set(&renumbered);
+        for e in extra {
+            c.extend(set(e));
+        }
+        c
+    };
+    for (b, classes) in [
+        (
+            "surfaces/cov-match-coplanar-sheet-onto-the-near-edge.json:b1",
+            with(&[&match_sheet]),
+        ),
+        (
+            "surfaces/cov-match-raised-sheet-down-onto-the-edge-g1.json:b1",
+            with(&[&match_sheet, &[".tolerance"]]),
+        ),
+        (
+            "surfaces/cov-match-raised-sheet-down-onto-the-edge-g3.json:b1",
+            with(&[&match_sheet, &[".tolerance"]]),
+        ),
+        (
+            "surfaces/cov-reverse-normal-l-sheet-swaps-the-thicken-side.json:b2",
+            with(&[&reverse, &[".edges[*].uses: length"]]),
+        ),
+        (
+            "surfaces/cov-reverse-normal-then-thicken-goes-down.json:b1",
+            with(&[&reverse]),
+        ),
+    ] {
+        out.insert(b.to_owned(), classes);
+    }
+    out
+}
+
+/// Every `stride`th entry; the report is written to `$PARITY_OUT` when set. No body is refused
+/// either way, and every difference is a named one.
+fn parity(stride: usize) {
+    let mut files = Vec::new();
+    entries(&corpus(), &mut files);
+    let fixes = fixes();
+    let mut t = Tally::default();
+    let with_bodies = files.iter().filter_map(|f| {
+        let e: Value = serde_json::from_str(&std::fs::read_to_string(f).unwrap()).unwrap();
+        let bodies = e["bodies"].as_object()?.clone();
+        (!bodies.is_empty()).then_some((f.clone(), bodies))
+    });
+    for (f, bodies) in with_bodies.step_by(stride) {
+        let gz = f.with_extension("bodies.json.gz");
+        let mut text = String::new();
+        flate2::read::GzDecoder::new(std::fs::File::open(&gz).unwrap())
+            .read_to_string(&mut text)
+            .unwrap();
+        let records: Value = serde_json::from_str(&text).unwrap();
+        let short = f.strip_prefix(corpus()).unwrap_or(&f).display().to_string();
+        for (id, how) in bodies {
+            let record: Record = serde_json::from_value(records[&id].clone()).unwrap();
+            one(
+                &format!("{short}:{id}"),
+                &record,
+                how["trusted"].as_bool().unwrap_or(true),
+                &fixes,
+                &mut t,
+            );
+        }
+    }
+    let mut report = String::new();
+    let _ = writeln!(
+        report,
+        "bodies {} identical {} rounding-only {} (places {}, largest {:e}) differing {} refused in {} refused out {}",
+        t.bodies,
+        t.identical,
+        t.rounding_only,
+        t.rounding_places,
+        t.rounding_largest,
+        t.bodies - t.identical - t.rounding_only - t.refused_in.len() - t.refused_out.len(),
+        t.refused_in.len(),
+        t.refused_out.len()
+    );
+    for (class, c) in &t.classes {
+        let _ = writeln!(
+            report,
+            "CLASS {class} | bodies {} places {}",
+            c.bodies, c.places
+        );
+        for e in &c.examples {
+            let _ = writeln!(report, "    {e}");
+        }
+    }
+    for n in &t.sheet_side {
+        let _ = writeln!(report, "SHEET-SIDE {n}");
+    }
+    for (n, classes) in &t.per_body {
+        let list: Vec<&str> = classes.iter().map(String::as_str).collect();
+        let _ = writeln!(report, "BODY {n} | {}", list.join(" ; "));
+    }
+    for w in &t.tolerance_wrong {
+        let _ = writeln!(report, "TOLERANCE-WRONG {w}");
+    }
+    for (n, f, a, b, trusted) in &t.relabelled {
+        let _ = writeln!(report, "RELABEL {n} face {f}: {a} -> {b} trusted {trusted}");
+    }
+    for r in &t.refused_in {
+        let _ = writeln!(report, "REFUSED-IN {r}");
+    }
+    for r in &t.refused_out {
+        let _ = writeln!(report, "REFUSED-OUT {r}");
+    }
+    if let Ok(p) = std::env::var("PARITY_OUT") {
+        std::fs::write(p, &report).unwrap();
+    }
+    eprintln!("{}", report.lines().next().unwrap_or(""));
+    assert!(t.bodies > 0);
+    assert!(t.refused_in.is_empty(), "{:#?}", t.refused_in);
+    assert!(t.refused_out.is_empty(), "{:#?}", t.refused_out);
+    assert!(t.tolerance_wrong.is_empty(), "{:#?}", t.tolerance_wrong);
+    assert!(t.sheet_geometry.is_empty(), "{:#?}", t.sheet_geometry);
+    let pinned = pinned();
+    let seen: BTreeMap<&String, &BTreeSet<String>> = t.per_body.iter().collect();
+    for (b, classes) in &seen {
+        assert_eq!(pinned.get(*b), Some(*classes), "{b}: classes not as pinned");
+    }
+    if stride == 1 {
+        let missing: Vec<&String> = pinned.keys().filter(|b| !seen.contains_key(b)).collect();
+        assert!(
+            missing.is_empty(),
+            "pinned bodies that no longer differ: {missing:#?}"
+        );
+        // The corpus grows as cases are added, so the totals aren't pinned: every body that
+        // differs is pinned above, and the rest must be identical or within rounding.
+        assert_eq!(
+            (t.bodies - t.identical - t.rounding_only, t.rounding_only),
+            (pinned.len(), 36),
+            "bodies that differ, bodies within rounding"
+        );
+        // the largest rounding difference, relative (#3137: 4.885e-16)
+        assert!(t.rounding_largest <= 4.9e-16, "{:e}", t.rounding_largest);
+    }
+}
+
+/// The whole corpus (`PARITY_STRIDE` takes every nth entry; the run takes seconds in release).
+#[test]
+fn every_corpus_body_comes_back_as_the_flat_export_wrote_it() {
+    parity(
+        std::env::var("PARITY_STRIDE")
+            .ok()
+            .and_then(|s| s.parse().ok())
+            .unwrap_or(1),
+    );
+}

solidcore/crates/solidcore-convert/tests/issue_3185_label_margins.rs

@@ -0,0 +1,258 @@
+//! (#3185) An analytic label is kept on its NURBS form when the kernel's analytic surface,
+//! carrying the label's numbers, evaluates as the form within the rounding
+//! `AnalyticSupport::build` derives term by term (`surface::implicit`'s `evaluates_as`):
+//! [`AnalyticSupport::parametrisation_margin`] is the largest ratio of distance to bound over
+//! the form's Greville points, at most 1 where the label stands.
+//!
+//! - The corpus labels #3137's parity run refused under the old constant `gamma(16 (p + q +
+//!   2)) size`, each pinned to its margin as measured under the derived bound: the three tori
+//!   of b6 and b85 (0.02 to 0.50) stand; b46's torus (1.69) and the four cylinders (b94 1.23,
+//!   b43 1.40, the 2903 rims 1.52 and 2.03) do not: their frames are off their forms past
+//!   the rounding at their size. Since #3199 the kernel's recognised sweep frame is the form's
+//!   own (its end meridians), so a label is measured against the form, not against a fit
+//!   that shared the label's error.
+//! - A torus the kernel makes at the groove's sizes stands on its own form, and the same label
+//!   turned about its axis by four times what the bound allows is refused.
+#![allow(
+    clippy::unwrap_used,
+    clippy::expect_used,
+    clippy::panic,
+    clippy::indexing_slicing,
+    clippy::print_stderr,
+    clippy::disallowed_methods
+)] // test (the turn's cos and sin)
+
+use std::fmt::Write as _;
+use std::io::Read as _;
+use std::path::{Path, PathBuf};
+
+use serde_json::Value;
+use solidcore::blend::fillet_section::station::as_b_spline;
+use solidcore::geom::axis2_placement::Axis2Placement;
+use solidcore::geom::extent2d::Extent2d;
+use solidcore::geom::vector3d::{Point3, Vec3};
+use solidcore::kernel::{Kernel, KernelOptions, UpstreamFixes};
+use solidcore::surface::from_parameters::from_parameters;
+use solidcore::surface::implicit::AnalyticSupport;
+use solidcore::surface::surface::{Surface, SurfaceKind};
+use solidcore::surface::torus::{Torus, TorusOptions};
+use solidcore_record::brep::Brep as Record;
+
+fn corpus() -> PathBuf {
+    Path::new(env!("CARGO_MANIFEST_DIR")).join("../solidcore/tests/kernel_cases")
+}
+
+/// The corpus's kernel, its fixes on (as the parity run and SolidCraft run it).
+fn kernel() -> Kernel {
+    let v: Value =
+        serde_json::from_str(&std::fs::read_to_string(corpus().join("fixes.json")).unwrap())
+            .unwrap();
+    let mut fixes = UpstreamFixes::default();
+    for flag in v.as_array().unwrap() {
+        *fixes.flag_mut(flag.as_str().unwrap()).unwrap() = true;
+    }
+    let mut k = Kernel::new(&KernelOptions::default());
+    k.fixes = fixes;
+    k
+}
+
+fn body(case: &str, id: &str) -> Record {
+    let gz = corpus().join(format!("{case}.bodies.json.gz"));
+    let mut text = String::new();
+    flate2::read::GzDecoder::new(std::fs::File::open(&gz).unwrap())
+        .read_to_string(&mut text)
+        .unwrap();
+    let records: Value = serde_json::from_str(&text).unwrap();
+    serde_json::from_value(records[id].clone()).unwrap()
+}
+
+fn placement(f: &solidcore::eval::Frame) -> Axis2Placement {
+    let v = |a: [f64; 3]| Vec3::new(a[0], a[1], a[2]);
+    Axis2Placement::from_stored(
+        Point3::new(f.origin[0], f.origin[1], f.origin[2]),
+        v(f.x_axis),
+        v(f.y_axis),
+    )
+}
+
+/// A corpus face's label as the kernel's support, and its NURBS form.
+fn label_and_form(
+    k: &Kernel,
+    case: &str,
+    id: &str,
+    face: usize,
+) -> (
+    AnalyticSupport,
+    solidcore::nurbs::b_spline_surface::BSplineSurface,
+) {
+    let r = body(case, id);
+    let f = &r.faces[face];
+    let nurbs = solidcore_convert::surface(f.nurbs.as_ref().unwrap()).unwrap();
+    let (s, _) = from_parameters(k, &nurbs, f.domain).unwrap();
+    let SurfaceKind::BSpline(form) = s.kind() else {
+        panic!("{case} {id} {face}: the form is not a B-spline")
+    };
+    let support = match solidcore_convert::surface(&f.surface).unwrap() {
+        solidcore::eval::Surface::Torus {
+            frame,
+            major_radius,
+            minor_radius,
+            ..
+        } => AnalyticSupport::Torus {
+            placement: placement(&frame),
+            major_radius,
+            minor_radius,
+        },
+        solidcore::eval::Surface::Cylinder { frame, radius } => AnalyticSupport::Cylinder {
+            placement: placement(&frame),
+            radius,
+        },
+        other => panic!("{case} {id} {face}: {other:?}"),
+    };
+    (support, form.copy())
+}
+
+/// (case, body, face, the margin measured at #3185, whether the label stands)
+const CASES: &[(&str, &str, usize, f64, bool)] = &[
+    (
+        "sweeps/3897-sweep-ring-along-a-short-arc-joined-to-a-collar",
+        "b6",
+        1,
+        0.0201,
+        true,
+    ),
+    (
+        "sweeps/4280-circular-pattern-of-sweep-cut-groove-on-hub",
+        "b46",
+        1,
+        1.6943,
+        false,
+    ),
+    (
+        "sweeps/4280-circular-pattern-of-sweep-cut-groove-on-hub",
+        "b85",
+        15,
+        0.4995,
+        true,
+    ),
+    (
+        "sweeps/4280-circular-pattern-of-sweep-cut-groove-on-hub",
+        "b85",
+        21,
+        0.4245,
+        true,
+    ),
+    (
+        "booleans/3456-deep-cut-through-drilled-taper-leaves-base",
+        "b94",
+        3,
+        1.2339,
+        false,
+    ),
+    (
+        "crashes/2243-step-export-flanged-enclosure",
+        "b43",
+        1,
+        1.4008,
+        false,
+    ),
+    ("fillets/2903-original-rim-chamfer", "b0", 1, 1.5243, false),
+    ("fillets/2903-original-rim-chamfer", "b0", 3, 2.0275, false),
+    ("fillets/2903-original-rim-round", "b0", 1, 1.5243, false),
+    ("fillets/2903-original-rim-round", "b0", 3, 2.0275, false),
+];
+
+/// Each corpus label's margin, pinned to 1 % of what #3185 measured, on its side of 1, and
+/// `build` agreeing with it.
+#[test]
+fn the_corpus_labels_stand_or_fall_by_the_derived_bound() {
+    let k = kernel();
+    let mut report = String::new();
+    let mut wrong = Vec::new();
+    for &(case, id, face, pinned, stands) in CASES {
+        let (support, form) = label_and_form(&k, case, id, face);
+        let m = support.parametrisation_margin(&k, &form).unwrap().unwrap();
+        let _ = writeln!(report, "{case} {id} face {face}: margin {m:.4}");
+        let built = support.build(&k, form).is_ok();
+        if (m <= 1.0) != stands || built != stands || (m - pinned).abs() > 0.01 * pinned {
+            wrong.push(format!(
+                "{case} {id} face {face}: margin {m} (pinned {pinned}, stands {stands}), build {built}"
+            ));
+        }
+    }
+    eprintln!("{report}");
+    assert!(wrong.is_empty(), "{wrong:#?}");
+}
+
+/// A torus at the groove's sizes (#3185's b46: centre (19.375, -33.558, 37.5), R 33.657, r 2,
+/// a 43.6 degree sweep of the whole tube), made by the kernel: its own label stands on its
+/// form; turned about its axis by four times the turn the bound allows (the margin is linear
+/// in a small turn: a turn of `t` reads `m(t)`, so `4 t / m(t)` reads 4), it is refused.
+#[test]
+fn a_torus_label_turned_past_its_bound_is_refused() {
+    let k = kernel();
+    let o = Point3::new(19.374_999_999_999_975, -33.558_484_396_647_01, 37.5);
+    let x = Vec3::new(
+        -0.427_099_277_807_218_7,
+        0.739_757_649_038_078_7,
+        -0.519_946_946_895_745_4,
+    );
+    let y = Vec3::new(
+        0.259_973_473_447_872_36,
+        -0.450_287_264_631_874_2,
+        -0.854_198_555_614_438_5,
+    );
+    let domain = Extent2d::from_bounds(0.0, -180.0, 43.602_818_972_703_645, 180.0);
+    let made = Torus::new(
+        &k,
+        o,
+        x,
+        y,
+        domain,
+        33.657_280_044_590_65,
+        2.0,
+        TorusOptions::default(),
+    )
+    .unwrap();
+    let s = Surface::from(made);
+    let form = as_b_spline(&k, &s).unwrap().unwrap().into_owned();
+    let own = AnalyticSupport::of(&s).unwrap();
+    let m0 = own.parametrisation_margin(&k, &form).unwrap().unwrap();
+    assert!(m0 <= 1.0, "own label: {m0}");
+    assert!(own.build(&k, form.copy()).is_ok());
+    let turned = |t: f64| {
+        let AnalyticSupport::Torus {
+            placement,
+            major_radius,
+            minor_radius,
+        } = own
+        else {
+            panic!()
+        };
+        let (c, sn) = (t.cos(), t.sin());
+        let (px, py) = (placement.x_axis(), placement.y_axis());
+        AnalyticSupport::Torus {
+            placement: Axis2Placement::from_stored(
+                placement.origin(),
+                px * c + py * sn,
+                py * c - px * sn,
+            ),
+            major_radius,
+            minor_radius,
+        }
+    };
+    let probe = 1e-11;
+    let m1 = turned(probe)
+        .parametrisation_margin(&k, &form)
+        .unwrap()
+        .unwrap();
+    assert!(m1 > 1.0, "a turn of {probe} rad reads {m1}");
+    let four = 4.0 * probe / m1;
+    let m4 = turned(four)
+        .parametrisation_margin(&k, &form)
+        .unwrap()
+        .unwrap();
+    eprintln!("own {m0:.4}; turn {probe:e}: {m1:.3}; turn {four:e}: {m4:.3}");
+    assert!(m4 > 1.0, "a turn of {four:e} rad reads {m4}");
+    assert!(turned(four).build(&k, form).is_err());
+}

solidcore/crates/solidcore-convert/tests/order_pieces.rs

@@ -0,0 +1,70 @@
+//! [`Order`]'s inverse and its pieces (#3137): what SolidCraft's `history::Order` gave, read off
+//! the conversion's order. A body whose solids touch along an edge comes back with one record
+//! edge per pair of faces that edge separates: each is a piece of that kernel edge.
+#![allow(
+    clippy::unwrap_used,
+    clippy::expect_used,
+    clippy::panic,
+    clippy::indexing_slicing
+)] // test
+
+use solidcore::boolean::api_brep::boolean_union;
+use solidcore::kernel::Kernel;
+use solidcore::math::Point3;
+use solidcore::primitive::api_primitives::create_box;
+use solidcore_convert::brep::to_record;
+
+/// Two unit boxes touching along one edge (the line x = y = 1): one body, its shared edge one
+/// kernel edge with four uses, two record edges.
+#[test]
+fn an_edge_solids_touch_along_is_two_pieces() {
+    let mut k = Kernel::default();
+    let a = create_box(&mut k, Point3::ZERO, 1.0, 1.0, 1.0).unwrap();
+    let c = create_box(&mut k, Point3::new(1.0, 1.0, 0.0), 1.0, 1.0, 1.0).unwrap();
+    let mut b = boolean_union(&mut k, a, c).unwrap();
+    let (record, order) = to_record(&mut k, &mut b).unwrap();
+    let pieces = order.pieces(&record).unwrap();
+    assert_eq!(pieces.len(), 2, "{pieces:?}");
+    assert_eq!(pieces[0].kernel, pieces[1].kernel);
+    assert_ne!(pieces[0].edge, pieces[1].edge);
+    for p in &pieces {
+        assert_eq!(p.faces.len(), 2, "{p:?}");
+        assert_eq!(order.edges[p.edge as usize], p.kernel);
+        // the faces are those of that record edge's own uses
+        let mut uses: Vec<u32> = record.edges[p.edge as usize]
+            .uses
+            .iter()
+            .map(|u| u.face)
+            .collect();
+        uses.sort_unstable();
+        uses.dedup();
+        assert_eq!(p.faces, uses, "{p:?}");
+    }
+    // the two pieces bound four different faces, two of each box
+    let mut all: Vec<u32> = pieces.iter().flat_map(|p| p.faces.clone()).collect();
+    all.sort_unstable();
+    all.dedup();
+    assert_eq!(all.len(), 4);
+    // the inverses name each entity's first record index
+    for (i, f) in order.faces.iter().enumerate() {
+        assert_eq!(order.record_faces()[f] as usize, i);
+    }
+    let first = order.record_edges()[&pieces[0].kernel];
+    assert_eq!(first, pieces[0].edge.min(pieces[1].edge));
+    for (i, v) in order.vertices.iter().enumerate() {
+        assert!(order.record_vertices()[v] as usize <= i);
+    }
+}
+
+/// A body with no touching edge has no pieces.
+#[test]
+fn a_box_has_no_pieces() {
+    let mut k = Kernel::default();
+    let mut b = create_box(&mut k, Point3::ZERO, 1.0, 1.0, 1.0).unwrap();
+    let (record, order) = to_record(&mut k, &mut b).unwrap();
+    assert!(order.pieces(&record).unwrap().is_empty());
+    // one record edge per kernel edge here; in general there are at most as many kernel edges
+    // as record edges (a touching edge is copied)
+    assert!(order.record_edges().len() <= record.edges.len());
+    assert_eq!(order.record_edges().len(), record.edges.len());
+}

solidcore/crates/solidcore-ops/Cargo.toml

@@ -5,7 +5,8 @@ edition.workspace = true
 license.workspace = true
 version.workspace = true
 publish = false
-rust-version.workspace = true
+# solidcore-record needs Rust 1.88 (edition 2024 let chains).
+rust-version = "1.88"
 repository = "https://github.com/tangency-labs/solidcore"
 keywords = ["cad", "brep", "nurbs", "modelling"]
 categories = ["science"]

solidcore/crates/solidcore-ops/src/blend.rs

@@ -824,13 +824,11 @@ fn overflow_first(
     }
     // a round mitred to one that goes first goes with it, through every mitre
     let place = |e: &EdgeId| edges.iter().position(|p| p == e);
-    let pairs: Vec<(usize, usize)> = mitred
-        // two by two (an odd last one is no pair); the chunk size 2 is not 0: cannot panic
-        .chunks_exact(2)
-        .filter_map(|pair| match pair {
-            [a, b] => Some((place(a)?, place(b)?)),
-            _ => None,
-        })
+    // two by two (an odd last one is no pair)
+    let (mitred_pairs, _) = mitred.as_chunks::<2>();
+    let pairs: Vec<(usize, usize)> = mitred_pairs
+        .iter()
+        .filter_map(|[a, b]| Some((place(a)?, place(b)?)))
         .collect();
     let mut grew = true;
     while grew {

solidcore/crates/solidcore-ops/src/contact.rs

@@ -0,0 +1,140 @@
+//! Contact between bodies: whether two bodies meet (share material or touch within a
+//! tolerance) and the distance between their boundaries, each decided by the kernel's
+//! certified bracket ([`solidcore::query::contact`]). Ops passes the tolerance on as the
+//! caller gives it and reads the kernel's verdict; it computes no distance of its own.
+
+use solidcore::geom::certified::Verdict;
+use solidcore::kernel::Kernel;
+use solidcore::query::contact::{self as c, Contact, Prepared};
+use solidcore::topology::brep::p3::brep_copy;
+use solidcore::topology::Brep;
+use solidcore::Point3;
+
+use crate::body::Body;
+use crate::session::{run_on, Answer};
+use crate::{Error, Result};
+
+impl Answer for Contact {}
+impl Answer for Vec<Contact> {}
+
+/// The bracket of the distance between two bodies' boundaries, at most the width asked.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct Gap {
+    /// No point of either boundary is nearer the other than this.
+    pub lower: f64,
+    /// The distance of the witness points, rounded up.
+    pub upper: f64,
+    /// A point on each body `upper` apart, when one is known (the first on this body).
+    pub witness: Option<[[f64; 3]; 2]>,
+}
+
+fn array(p: Point3) -> [f64; 3] {
+    [p.x, p.y, p.z]
+}
+
+/// A copy of `body`'s kernel body, the body released at once: the contact test takes its
+/// operands mutably (for its classifications' caches) and never edits the caller's, and a
+/// body tested against itself is locked only once at a time.
+fn copy_of(k: &mut Kernel, body: &Body) -> solidcore::Result<Brep> {
+    let b = body.lock();
+    brep_copy(k, &b)
+}
+
+/// The verdict as an answer: `Yes` meets, `No` does not, `Undecided` refused with the
+/// bracket, which names the tolerance that would decide.
+fn decided(contact: &Contact, other: usize) -> Result<bool> {
+    match contact.verdict {
+        Verdict::Yes => Ok(true),
+        Verdict::No => Ok(false),
+        Verdict::Undecided => Err(Error::ContactUndecided {
+            other,
+            lower: contact.lower,
+            upper: contact.upper,
+        }),
+    }
+}
+
+fn poisoned(bodies: &[&Body]) -> Result<()> {
+    if bodies.iter().any(|b| b.is_poisoned()) {
+        return Err(Error::Internal(
+            "contact: a body was left unfinished by an earlier panic".to_owned(),
+        ));
+    }
+    Ok(())
+}
+
+impl Body {
+    /// Whether this body and `other` meet at `tol` (the caller's: ops invents none): share
+    /// material, or have boundaries within `tol` of each other
+    /// ([`solidcore::query::contact::meets`]). Neither body changes; `other` may be this body.
+    ///
+    /// # Errors
+    /// [`Error::ContactUndecided`] when the kernel's bracket does not decide it (`other` 0):
+    /// the bracket, never read as either answer; [`Error::Status`] `SM_ERR_INVALID_INPUT` for a
+    /// tolerance not finite and positive or a body without faces; those of the session.
+    pub fn meets(&self, other: &Body, tol: f64) -> Result<bool> {
+        poisoned(&[self, other])?;
+        let contact = run_on("contact::meets", &[("a", self), ("b", other)], |k| {
+            let mut a = copy_of(k, self)?;
+            let mut b = copy_of(k, other)?;
+            c::meets(k, &mut a, &mut b, tol)
+        })?;
+        decided(&contact, 0)
+    }
+
+    /// [`Body::meets`] against each of `others`, each with its own tolerance, this body
+    /// prepared once (its faces' pieces about the centre of its box,
+    /// [`Prepared::about`]).
+    ///
+    /// # Errors
+    /// [`Error::ContactUndecided`] for the first of `others` the kernel's bracket does not
+    /// decide, by its index; those of [`Body::meets`].
+    pub fn meets_each(&self, others: &[(&Body, f64)]) -> Result<Vec<bool>> {
+        let mut bodies: Vec<&Body> = vec![self];
+        bodies.extend(others.iter().map(|(b, _)| *b));
+        poisoned(&bodies)?;
+        let inputs: Vec<(&'static str, &Body)> = bodies.iter().map(|b| ("brep", *b)).collect();
+        let contacts = run_on("contact::meets_each", &inputs, |k| {
+            let mut a = copy_of(k, self)?;
+            let prepared = Prepared::about(k, &a)?;
+            let mut contacts = Vec::new();
+            for (other, tol) in others {
+                let mut b = copy_of(k, other)?;
+                contacts.push(c::meets_prepared(k, &mut a, &prepared, &mut b, *tol)?);
+            }
+            Ok(contacts)
+        })?;
+        contacts
+            .iter()
+            .enumerate()
+            .map(|(i, contact)| decided(contact, i))
+            .collect()
+    }
+
+    /// The distance between this body's boundary and `other`'s, bracketed to at most `width`
+    /// (relative to its upper end, absolute below 1;
+    /// [`solidcore::query::contact::boundary_distance`]).
+    ///
+    /// # Errors
+    /// [`Error::ContactUndecided`] (`other` 0) with the narrowest bracket reached, when the
+    /// kernel's work runs out before `width`; [`Error::Status`] `SM_ERR_INVALID_INPUT` for a
+    /// width not finite and positive or a body without faces; those of the session.
+    pub fn boundary_distance(&self, other: &Body, width: f64) -> Result<Gap> {
+        poisoned(&[self, other])?;
+        let contact = run_on(
+            "contact::boundary_distance",
+            &[("a", self), ("b", other)],
+            |k| {
+                let mut a = copy_of(k, self)?;
+                let mut b = copy_of(k, other)?;
+                c::boundary_distance(k, &mut a, &mut b, width)
+            },
+        )?;
+        decided(&contact, 0)?;
+        Ok(Gap {
+            lower: contact.lower,
+            upper: contact.upper,
+            witness: contact.witness.map(|[p, q]| [array(p), array(q)]),
+        })
+    }
+}

solidcore/crates/solidcore-ops/src/error.rs

@@ -134,6 +134,19 @@ pub enum Error {
     /// The kernel found its own state inconsistent part way through a call, or was called
     /// before the preparation it needs.
     Exception,
+    /// A contact test the kernel's certified bracket of the boundary distance does not decide
+    /// (`solidcore::query::contact`): the tolerance lies inside `[lower, upper]` (or the
+    /// boundaries are apart but one body's enclosure of the other is not decided), or a
+    /// distance's bracket is still wider than asked. Never read as either answer. `other` is
+    /// the index of the body tested among the call's others.
+    ContactUndecided {
+        /// The other body's index among the call's (0 for one).
+        other: usize,
+        /// No point of either boundary is nearer the other than this.
+        lower: f64,
+        /// A pair of points, one on each boundary, is this far apart.
+        upper: f64,
+    },
     /// The application cancelled the call.
     Cancelled,
     /// Ops was called from inside a kernel call or from the failure callback.
@@ -325,6 +338,14 @@ impl std::fmt::Display for Error {
             ),
             Error::TooFar { largest } => write!(f, "too far to extend (largest {largest:?})"),
             Error::Exception => write!(f, "solidcore raised an internal exception"),
+            Error::ContactUndecided {
+                other,
+                lower,
+                upper,
+            } => write!(
+                f,
+                "contact with body {other} is undecided: the boundary distance is in [{lower}, {upper}]"
+            ),
             Error::Cancelled => write!(f, "cancelled"),
             Error::Reentered => write!(
                 f,

solidcore/crates/solidcore-ops/src/lib.rs

@@ -19,8 +19,8 @@
 //! - [`provenance`]: the hook an application's construction history rides on.
 //!
 //! The families: [`measure`] (mass properties, area, box, point class, gap samples, the picks'
-//! distances and normals), [`boolean`], [`stitch`], [`prism`] (planar region booleans and
-//! extrusion, prism sections).
+//! distances and normals), [`contact`] (whether bodies meet, their boundary distance),
+//! [`boolean`], [`stitch`], [`prism`] (planar region booleans and extrusion, prism sections).
 //!
 //! Operations change the body they are given, as the kernel does. An application that keeps
 //! its input copies it first ([`Body::copy`]).
@@ -32,6 +32,7 @@ pub mod blend;
 pub mod body;
 pub mod boolean;
 pub mod check;
+pub mod contact;
 pub mod error;
 pub mod extend;
 pub mod file;
@@ -42,8 +43,10 @@ pub mod prism;
 pub mod provenance;
 pub mod session;
 pub mod split;
+pub mod step_assembly;
 pub mod stitch;
 pub mod sweep;
+pub mod tangent;
 pub mod untrim;
 
 pub use blend::{
@@ -54,6 +57,7 @@ pub use blend::{
 pub use body::{make_box, make_cone, make_cylinder, make_sphere, make_torus, Body};
 pub use boolean::BooleanOp;
 pub use check::{CheckLevel, CheckReport};
+pub use contact::Gap;
 pub use error::{Error, FitKind, Result, RoomReason, Unblendable};
 pub use measure::{
     point_distance, Distance, EdgePoint, FaceCentroid, GapSample, MassPropertiesEstimate, Normal,
@@ -61,7 +65,10 @@ pub use measure::{
 };
 pub use offset::{draft, offset_faces, offset_sheet, shell, thicken};
 pub use order::Order;
+pub use step_assembly::{placed_bodies, PlacedBody};
 
+#[cfg(test)]
+mod noisy_round_tests;
 #[cfg(test)]
 mod test_corpus;
 #[cfg(test)]

solidcore/crates/solidcore-ops/src/noisy_round_tests.rs

@@ -0,0 +1,199 @@
+//! #3066: a round on supports read from a record with rounding in their frames keeps its exact
+//! definition. The class is decided within the body's tolerance; the round lies on a torus of
+//! its own, its net certified there at bound 0, and that torus's distance from the class's
+//! torus from the supports is held to the body's tolerance, so the round answers
+//! `procedural_blend()`.
+#![allow(
+    clippy::unwrap_used,
+    clippy::expect_used,
+    clippy::panic,
+    clippy::indexing_slicing,
+    clippy::disallowed_methods
+)] // test
+
+use std::f64::consts::PI;
+
+use solidcore::surface::surface::SurfaceKind;
+use solidcore::topology::face::p2 as face;
+use solidcore_record::brep::Brep as Record;
+
+use crate::blend::{blend, Blend, Corners};
+use crate::boolean::boolean;
+use crate::{make_box, make_cylinder, session, Body, BooleanOp, CheckLevel};
+
+fn fixes() {
+    let fixes: Vec<String> = serde_json::from_str(include_str!(
+        "../../solidcore/tests/kernel_cases/fixes.json"
+    ))
+    .unwrap();
+    session::set_fixes(fixes.iter().map(String::as_str)).unwrap();
+}
+
+/// The faces of `b` that are no plane, as (with a definition, without one).
+fn definitions(b: &Body) -> (usize, usize) {
+    let brep = b.lock();
+    let (mut with, mut without) = (0, 0);
+    for &f in brep.face_list() {
+        let s = face::surface(&brep, f).unwrap().unwrap();
+        if matches!(s.kind(), SurfaceKind::Plane(_)) {
+            continue;
+        }
+        if s.procedural_blend().is_some() {
+            with += 1;
+        } else {
+            without += 1;
+        }
+    }
+    (with, without)
+}
+
+/// The edge of `b` through `p`.
+fn edge_through(b: &Body, p: [f64; 3]) -> usize {
+    let k = solidcore::Kernel::default();
+    let brep = b.lock();
+    let q = solidcore::Vec3::new(p[0], p[1], p[2]);
+    brep.edge_list()
+        .iter()
+        .position(|&e| {
+            solidcore::query::api_queries::edge_closest_point(&k, &brep, e, q)
+                .unwrap()
+                .closest
+                .distance
+                < 1e-6
+        })
+        .unwrap()
+}
+
+/// A boss R 8 standing 10 out of a 40 x 40 x 10 block, its axis turned 1e-10 off square to the
+/// block's top, its root rounded 2: a circle-class round on supports only that close to the
+/// class (the error the 1e-10 turn makes over the part is far inside the body's tolerance, and
+/// far outside the rounding the net is certified to). The round is concave: the corner between
+/// the wall and the top, less the quarter disc, turned about the axis. By Pappus, it adds
+/// 2 pi (R + x) r^2 (1 - pi / 4), x = r (10 - 3 pi) / (12 - 3 pi) the corner's centroid from the
+/// wall.
+#[test]
+fn a_round_on_a_boss_tilted_off_the_class_keeps_its_definition() {
+    fixes();
+    let block = make_box([0.0; 3], [40.0, 40.0, 10.0]).unwrap();
+    // the boss from z = 5 to 20, its axis turned 1e-10 about x off square to the block's top
+    let boss = make_cylinder([0.0; 3], 8.0, 15.0).unwrap();
+    let (c, s) = (1e-10_f64.cos(), 1e-10_f64.sin());
+    boss.transform(&[
+        [1.0, 0.0, 0.0, 0.0],
+        [0.0, c, s, 0.0],
+        [0.0, -s, c, 0.0],
+        [20.0, 20.0, 5.0, 1.0],
+    ])
+    .unwrap();
+    let b = boolean(block, boss, BooleanOp::Union).unwrap().unwrap();
+    let e = edge_through(&b, [28.0, 20.0, 10.0]);
+    let (r, big_r) = (2.0, 8.0);
+    blend(&b, Blend::Round, &[e], &[r], &[], Corners::Filled).unwrap();
+    let report = b.check(CheckLevel::All).unwrap();
+    assert!(report.is_valid(), "{}", report.text);
+    // the boss's wall and the round: the round keeps its definition
+    assert_eq!(definitions(&b), (1, 1));
+    let x = r * (10.0 - 3.0 * PI) / (12.0 - 3.0 * PI);
+    let want =
+        16000.0 + PI * big_r * big_r * 10.0 + 2.0 * PI * (big_r + x) * r * r * (1.0 - PI / 4.0);
+    let got = b.volume(1e-10).unwrap();
+    assert!((got - want).abs() <= 1e-9 * want, "{got} {want}");
+}
+
+/// SolidCraft's raked wedge (`tests/data/raked_wedge_noisy_cylinders.json`): its end outline's
+/// rounds keep their definitions, the two circle-class rounds on the read-back cylinders among
+/// them; the operand's own faces, read from the record, have none.
+#[test]
+fn the_raked_wedges_rounds_keep_their_definitions() {
+    fixes();
+    let record: Record = serde_json::from_str(include_str!(
+        "../tests/data/raked_wedge_noisy_cylinders.json"
+    ))
+    .unwrap();
+    let (b, _) = Body::from_record(&record, true).unwrap();
+    let (_, before) = definitions(&b);
+    let top = 60.0 - 60.0 * 10f64.to_radians().tan();
+    let mut seeds = Vec::new();
+    for x in [-69.0, 69.0] {
+        for p in [
+            [x, -41.0, 22.0],
+            [x, 8.0, 41.0],
+            [x, (38.0 + top) / 2.0, 60.0],
+        ] {
+            seeds.push(edge_through(&b, p));
+        }
+    }
+    let chain = crate::blend::tangent_chain(&b, &seeds, 0.5_f64.to_radians()).unwrap();
+    blend(&b, Blend::Round, &chain, &[0.854], &[], Corners::Filled).unwrap();
+    let report = b.check(CheckLevel::All).unwrap();
+    assert!(report.is_valid(), "{}", report.text);
+    let (with, without) = definitions(&b);
+    // as many of the new rounds keep their definitions as on the same wedge with exact
+    // cylinders, and the rest are as bare there
+    let (exact_with, exact_bare) = exact_wedge_rounds();
+    assert_eq!((with, without - before), (exact_with, exact_bare));
+    assert_eq!(with + without - before, chain.len());
+}
+
+/// The same wedge built here, its cylinders exact, its end outline rounded as SolidCraft's: of the
+/// rounds that last call makes, how many keep a definition and how many don't.
+fn exact_wedge_rounds() -> (usize, usize) {
+    use crate::sweep::{extrude, Curve, DraftCorner};
+    let top = 60.0 - 60.0 * 10f64.to_radians().tan();
+    let profile = [
+        [-60.0, 0.0],
+        [60.0, 0.0],
+        [top, 60.0],
+        [38.0, 60.0],
+        [-22.0, 22.0],
+        [-60.0, 22.0],
+    ];
+    let at = |p: [f64; 2]| [-69.0, p[0], p[1]];
+    let curves: Vec<Curve> = (0..6)
+        .map(|i| Curve::Line {
+            start: at(profile[i]),
+            end: at(profile[(i + 1) % 6]),
+        })
+        .collect();
+    let b = extrude(
+        &curves,
+        [1.0, 0.0, 0.0],
+        138.0,
+        0.0,
+        DraftCorner::Curvature,
+        true,
+    )
+    .unwrap();
+    let round = |pts: &[[f64; 3]], r: f64, chain: bool| {
+        let seeds: Vec<usize> = pts.iter().map(|&p| edge_through(&b, p)).collect();
+        let edges = if chain {
+            crate::blend::tangent_chain(&b, &seeds, 0.5_f64.to_radians()).unwrap()
+        } else {
+            seeds
+        };
+        blend(&b, Blend::Round, &edges, &[r], &[], Corners::Filled).unwrap();
+    };
+    round(&[[0.0, -60.0, 22.0]], 1.2, true);
+    round(&[[0.0, -22.0, 22.0]], 1.5, true);
+    round(&[[0.0, 38.0, 60.0]], 1.5, true);
+    let back = (60.0 + top) / 2.0;
+    let four = [
+        [-69.0, -60.0, 12.0],
+        [69.0, -60.0, 12.0],
+        [-69.0, back, 30.0],
+        [69.0, back, 30.0],
+    ];
+    round(&four, 4.0, false);
+    let (with_before, bare_before) = definitions(&b);
+    let mut ends = Vec::new();
+    for x in [-69.0, 69.0] {
+        ends.extend([
+            [x, -41.0, 22.0],
+            [x, 8.0, 41.0],
+            [x, (38.0 + top) / 2.0, 60.0],
+        ]);
+    }
+    round(&ends, 0.854, true);
+    let (with, bare) = definitions(&b);
+    (with - with_before, bare - bare_before)
+}

solidcore/crates/solidcore-ops/src/step_assembly.rs

@@ -0,0 +1,467 @@
+//! Compose a STEP product structure into placed body instances.
+//!
+//! The record reader keeps the placements exactly as the file writes them: assembly
+//! occurrences, `MAPPED_ITEM` targets, representation maps and transformation operators.
+//! This module turns those raw placements into kernel matrices, walks the product tree and
+//! returns every body with the transform that places it in the file's world frame.
+//!
+//! It computes no geometry of its own: frame and operator matrices, their products and
+//! inverses come from `solidcore::geom::step_matrix`. Body construction is the caller's:
+//! each returned [`PlacedBody::entity`] is a STEP entity id and every occurrence of a shared
+//! body is emitted separately with its own transform.
+
+use std::collections::BTreeSet;
+
+use solidcore::geom::step_matrix::{
+    concat, frame_matrix, inverse, operator_matrix, Matrix4, IDENTITY,
+};
+use solidcore_record::step::geom::Placement;
+use solidcore_record::step::product::{
+    Frame, ItemKind, Link, Occurrence, ProductStructure, Transformation, MAX_ASSEMBLY_DEPTH,
+    MAX_VISITS,
+};
+
+/// One body as it appears in the expanded product structure.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct PlacedBody {
+    /// The STEP entity id of the body (`MANIFOLD_SOLID_BREP`, …).
+    pub entity: u64,
+    /// The body's placement in the file's world frame, in millimetres.
+    pub transform: Matrix4,
+}
+
+struct Walk<'a> {
+    structure: &'a ProductStructure,
+    /// Representations reachable from each definition's own shapes through plain
+    /// representation relationships.
+    closure: Vec<Vec<usize>>,
+    /// Child occurrences of each definition, in file order.
+    children: Vec<Vec<usize>>,
+    /// The definitions on the current path, to refuse a cycle.
+    path: Vec<usize>,
+    visits: usize,
+    out: Vec<PlacedBody>,
+}
+
+/// Expand the product structure and return every body with its world placement.
+///
+/// A root definition is placed by the identity. Each occurrence multiplies the child's
+/// placement by the occurrence transformation, and each mapped item places the mapped
+/// representation by `target · origin⁻¹`. Refuses cycles and past the record's depth or
+/// instance bounds.
+pub fn placed_bodies(structure: &ProductStructure) -> Result<Vec<PlacedBody>, String> {
+    let mut children = vec![Vec::new(); structure.definitions.len()];
+    for (index, occurrence) in structure.occurrences.iter().enumerate() {
+        if let Some(list) = children.get_mut(occurrence.parent) {
+            list.push(index);
+        }
+    }
+    let closure = (0..structure.definitions.len())
+        .map(|definition| representation_closure(structure, definition))
+        .collect();
+    let mut walk = Walk {
+        structure,
+        closure,
+        children,
+        path: Vec::new(),
+        visits: 0,
+        out: Vec::new(),
+    };
+    for &root in &structure.roots {
+        walk.definition(root, IDENTITY, 0)?;
+    }
+    Ok(walk.out)
+}
+
+fn representation_closure(structure: &ProductStructure, definition: usize) -> Vec<usize> {
+    let Some(definition) = structure.definitions.get(definition) else {
+        return Vec::new();
+    };
+    let mut seen = BTreeSet::new();
+    let mut out = Vec::new();
+    let mut stack = definition.shapes.clone();
+    while let Some(representation) = stack.pop() {
+        if !seen.insert(representation) {
+            continue;
+        }
+        out.push(representation);
+        for link in &structure.links {
+            if link.transformation.is_some() {
+                continue;
+            }
+            if link.rep_1 == representation {
+                stack.push(link.rep_2);
+            } else if link.rep_2 == representation {
+                stack.push(link.rep_1);
+            }
+        }
+    }
+    out
+}
+
+impl Walk<'_> {
+    fn definition(
+        &mut self,
+        definition: usize,
+        world: Matrix4,
+        depth: usize,
+    ) -> Result<(), String> {
+        if depth > MAX_ASSEMBLY_DEPTH {
+            return Err("assembly nested too deeply".into());
+        }
+        if self.path.contains(&definition) {
+            return Err("assembly cycle".into());
+        }
+        self.visits += 1;
+        if self.visits > MAX_VISITS {
+            return Err(format!("more than {MAX_VISITS} assembly instances"));
+        }
+        self.path.push(definition);
+        let reps = self.closure.get(definition).cloned().unwrap_or_default();
+        let mut walked = BTreeSet::new();
+        for representation in reps {
+            self.representation(representation, world, &mut walked, depth)?;
+        }
+        let child_definitions: Vec<usize> =
+            self.children.get(definition).cloned().unwrap_or_default();
+        for occurrence_index in child_definitions {
+            let Some(occurrence) = self.structure.occurrences.get(occurrence_index) else {
+                continue;
+            };
+            let child_reps = self
+                .closure
+                .get(occurrence.child)
+                .cloned()
+                .unwrap_or_default();
+            let local = occurrence_matrix(self.structure, occurrence, &child_reps)?;
+            self.definition(occurrence.child, concat(&world, &local), depth + 1)?;
+        }
+        self.path.pop();
+        Ok(())
+    }
+
+    fn representation(
+        &mut self,
+        representation: usize,
+        world: Matrix4,
+        walked: &mut BTreeSet<usize>,
+        depth: usize,
+    ) -> Result<(), String> {
+        if depth > MAX_ASSEMBLY_DEPTH {
+            return Err("mapped items nested too deeply".into());
+        }
+        if !walked.insert(representation) {
+            return Ok(());
+        }
+        let Some(rep) = self.structure.representations.get(representation) else {
+            return Err(format!("missing representation #{representation}"));
+        };
+        for item in &rep.items {
+            match &item.kind {
+                ItemKind::Body(_) => self.out.push(PlacedBody {
+                    entity: item.entity,
+                    transform: world,
+                }),
+                ItemKind::Mapped { map, target } => {
+                    let Some(map) = self.structure.maps.get(*map) else {
+                        return Err(format!("missing representation map #{}", item.entity));
+                    };
+                    let target = frame(target)?;
+                    let origin = frame(&map.origin)?;
+                    let origin_inverse = inverse(&origin)
+                        .ok_or_else(|| format!("singular map origin #{}", map.entity))?;
+                    let local = concat(&target, &origin_inverse);
+                    let placed = concat(&world, &local);
+                    let mapped = map.representation;
+                    let mut mapped_walked = BTreeSet::new();
+                    self.representation(mapped, placed, &mut mapped_walked, depth + 1)?;
+                    for link in &self.structure.links {
+                        if link.transformation.is_some() {
+                            continue;
+                        }
+                        let other = if link.rep_1 == mapped {
+                            Some(link.rep_2)
+                        } else if link.rep_2 == mapped {
+                            Some(link.rep_1)
+                        } else {
+                            None
+                        };
+                        if let Some(other) = other {
+                            self.representation(other, placed, &mut mapped_walked, depth + 1)?;
+                        }
+                    }
+                }
+                ItemKind::Other(_) => {}
+            }
+        }
+        Ok(())
+    }
+}
+
+fn occurrence_matrix(
+    structure: &ProductStructure,
+    occurrence: &Occurrence,
+    child_reps: &[usize],
+) -> Result<Matrix4, String> {
+    let Some(&link_index) = occurrence.placements.first() else {
+        return Ok(IDENTITY);
+    };
+    let Some(link) = structure.links.get(link_index) else {
+        return Err(format!("missing placement link #{link_index}"));
+    };
+    link_matrix(link, child_reps)
+}
+
+fn link_matrix(link: &Link, child_reps: &[usize]) -> Result<Matrix4, String> {
+    let Some(transformation) = &link.transformation else {
+        return Ok(IDENTITY);
+    };
+    match transformation {
+        Transformation::Frame(frame_value) => frame(frame_value),
+        Transformation::Items { item_1, item_2, .. } => {
+            let first = frame(item_1)?;
+            let second = frame(item_2)?;
+            let child_is_first =
+                child_reps.contains(&link.rep_1) || !child_reps.contains(&link.rep_2);
+            // Row-vector convention: a child in rep_1 is placed by
+            // `item_1⁻¹ · item_2`; a child in rep_2 by `item_2⁻¹ · item_1`.
+            let (from, to) = if child_is_first {
+                (&first, &second)
+            } else {
+                (&second, &first)
+            };
+            let inverse_from = inverse(from)
+                .ok_or_else(|| format!("singular occurrence placement #{}", link.entity))?;
+            Ok(concat(&inverse_from, to))
+        }
+    }
+}
+
+fn frame(value: &Frame) -> Result<Matrix4, String> {
+    match value {
+        Frame::Placement(Placement {
+            origin,
+            axis,
+            ref_direction,
+        }) => frame_matrix(*origin, *axis, *ref_direction)
+            .ok_or_else(|| "degenerate placement".to_string()),
+        Frame::Operator(operator) => operator_matrix(
+            operator.axis1,
+            operator.axis2,
+            operator.axis3,
+            operator.origin,
+            operator.scale,
+            operator.scale2,
+            operator.scale3,
+        )
+        .ok_or_else(|| "degenerate transformation operator".to_string()),
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use solidcore_record::step::geom::Placement;
+    use solidcore_record::step::product::{
+        BodyKind, Definition, Item, OccurrenceKind, Representation,
+    };
+    use solidcore_record::step::units::{Context, Units};
+
+    fn translation(x: f64, y: f64, z: f64) -> Frame {
+        Frame::Placement(Placement {
+            origin: [x, y, z],
+            axis: None,
+            ref_direction: None,
+        })
+    }
+
+    fn body(entity: u64) -> Item {
+        Item {
+            entity,
+            name: String::new(),
+            kind: ItemKind::Body(BodyKind::ManifoldSolidBrep),
+        }
+    }
+
+    fn representation(entity: u64, items: Vec<Item>) -> Representation {
+        Representation {
+            entity,
+            kind: "SHAPE_REPRESENTATION".into(),
+            name: String::new(),
+            items,
+            context: None,
+            units: Context {
+                units: Units { len: 1.0, ang: 1.0 },
+                uncertainty: None,
+            },
+        }
+    }
+
+    fn definition(entity: u64, shape: usize) -> Definition {
+        Definition {
+            entity,
+            id: format!("def{entity}"),
+            description: String::new(),
+            formation: 0,
+            product: 0,
+            shapes: vec![shape],
+        }
+    }
+
+    fn structure() -> ProductStructure {
+        ProductStructure {
+            products: Vec::new(),
+            definitions: vec![definition(1, 0), definition(2, 1)],
+            representations: vec![
+                representation(10, Vec::new()),
+                representation(20, vec![body(200)]),
+            ],
+            maps: Vec::new(),
+            links: Vec::new(),
+            occurrences: Vec::new(),
+            roots: vec![0],
+            styles: Vec::new(),
+        }
+    }
+
+    #[test]
+    fn a_placed_child_body_is_transformed_by_its_occurrence() {
+        let mut structure = structure();
+        structure.representations[0] = representation(10, Vec::new());
+        structure.occurrences.push(Occurrence {
+            entity: 30,
+            kind: OccurrenceKind::NextAssemblyUsage,
+            id: "occ".into(),
+            name: String::new(),
+            description: String::new(),
+            parent: 0,
+            child: 1,
+            reference_designator: None,
+            placements: vec![0],
+        });
+        structure.links.push(Link {
+            entity: 40,
+            rep_1: 1,
+            rep_2: 0,
+            transformation: Some(Transformation::Items {
+                entity: 41,
+                item_1: translation(0.0, 0.0, 0.0),
+                item_2: translation(2.0, 3.0, 0.0),
+            }),
+        });
+        let placed = placed_bodies(&structure).unwrap();
+        assert_eq!(placed.len(), 1);
+        assert_eq!(placed[0].entity, 200);
+        assert_eq!(
+            placed[0].transform,
+            [
+                [1.0, 0.0, 0.0, 0.0],
+                [0.0, 1.0, 0.0, 0.0],
+                [0.0, 0.0, 1.0, 0.0],
+                [2.0, 3.0, 0.0, 1.0],
+            ]
+        );
+    }
+
+    #[test]
+    fn mapped_items_place_the_map_origin_onto_their_target() {
+        let mut structure = structure();
+        structure.representations[0] = representation(10, Vec::new());
+        structure.representations[0].items.push(Item {
+            entity: 100,
+            name: String::new(),
+            kind: ItemKind::Mapped {
+                map: 0,
+                target: translation(5.0, 0.0, 0.0),
+            },
+        });
+        structure
+            .maps
+            .push(solidcore_record::step::product::RepresentationMap {
+                entity: 50,
+                origin: translation(1.0, 0.0, 0.0),
+                representation: 1,
+            });
+        let placed = placed_bodies(&structure).unwrap();
+        assert_eq!(placed.len(), 1);
+        assert_eq!(placed[0].transform[3], [4.0, 0.0, 0.0, 1.0]);
+    }
+
+    #[test]
+    fn nested_occurrence_placements_compose() {
+        let mut structure = structure();
+        structure.definitions.push(definition(3, 2));
+        structure
+            .representations
+            .push(representation(30, vec![body(300)]));
+        structure.occurrences.extend([
+            Occurrence {
+                entity: 31,
+                kind: OccurrenceKind::NextAssemblyUsage,
+                id: "a".into(),
+                name: String::new(),
+                description: String::new(),
+                parent: 0,
+                child: 1,
+                reference_designator: None,
+                placements: vec![0],
+            },
+            Occurrence {
+                entity: 32,
+                kind: OccurrenceKind::NextAssemblyUsage,
+                id: "b".into(),
+                name: String::new(),
+                description: String::new(),
+                parent: 1,
+                child: 2,
+                reference_designator: None,
+                placements: vec![1],
+            },
+        ]);
+        structure.links.extend([
+            Link {
+                entity: 40,
+                rep_1: 1,
+                rep_2: 0,
+                transformation: Some(Transformation::Items {
+                    entity: 41,
+                    item_1: translation(0.0, 0.0, 0.0),
+                    item_2: translation(1.0, 0.0, 0.0),
+                }),
+            },
+            Link {
+                entity: 42,
+                rep_1: 2,
+                rep_2: 1,
+                transformation: Some(Transformation::Items {
+                    entity: 43,
+                    item_1: translation(0.0, 0.0, 0.0),
+                    item_2: translation(0.0, 2.0, 0.0),
+                }),
+            },
+        ]);
+        let placed = placed_bodies(&structure).unwrap();
+        let grandchild = placed
+            .iter()
+            .find(|body| body.entity == 300)
+            .expect("grandchild body");
+        assert_eq!(grandchild.transform[3], [1.0, 2.0, 0.0, 1.0]);
+    }
+
+    #[test]
+    fn a_cycle_is_refused() {
+        let mut structure = structure();
+        structure.occurrences.push(Occurrence {
+            entity: 30,
+            kind: OccurrenceKind::NextAssemblyUsage,
+            id: "occ".into(),
+            name: String::new(),
+            description: String::new(),
+            parent: 0,
+            child: 0,
+            reference_designator: None,
+            placements: Vec::new(),
+        });
+        assert!(placed_bodies(&structure).is_err());
+    }
+}

solidcore/crates/solidcore-ops/src/tangent.rs

@@ -0,0 +1,223 @@
+//! Tangent chains on record order: the edges a pick runs on into tangentially, and the faces
+//! joined to picked faces across smooth edges. The walks are here; every measure they stop
+//! on is the kernel's: whether an edge's faces meet tangentially all along it
+//! ([`solidcore::query::tangent_edge`]), how far one edge turns from running straight on into
+//! another at a vertex and whether an edge is convex there ([`solidcore::query::edge_turn`]).
+//!
+//! The caller's `angle` (radians) is the one tolerance: edges meeting at less than it continue
+//! one another, and faces meeting at less than it all along an edge make it smooth. Nothing
+//! here picks one (SolidCraft passes its shaded view's half a degree).
+//!
+//! - [`tangent_chain_ordered`]: the picked edges, then every edge that continues one of them
+//!   within `angle` at a shared vertex, and so on. An edge does not join when it is not
+//!   between two faces (a one-face edge), when it is smooth (its faces meet tangentially all
+//!   along it, a seam among them), or when it turns over (convex where the edge it continues
+//!   is concave, or the reverse).
+//! - [`tangent_face_chain_ordered`]: the picked faces, then every face across a smooth edge
+//!   from one of them, and so on.
+//!
+//! An edge whose smoothness the kernel leaves undecided (a blend's net within its margin of
+//! the angle, [`solidcore::query::tangent_edge::Tangency::Undecided`]) joins nothing and is
+//! named in the answer.
+
+use solidcore::query::edge_turn::{convex_at, turn_at};
+use solidcore::query::tangent_edge::{tangent_all_along, Tangency};
+use solidcore::topology::edge;
+use solidcore::{Brep, EdgeId, FaceId, Kernel};
+
+use crate::session::with_body;
+use crate::{Body, Error, Order, Result};
+
+/// What [`tangent_chain_ordered`] and [`tangent_face_chain_ordered`] answer, in record
+/// indices.
+#[derive(Clone, Debug, Default, PartialEq, Eq)]
+pub struct Chain {
+    /// The picks (each once, in order), then what joined them, in the order it joined.
+    pub members: Vec<usize>,
+    /// Edges the walk met whose smoothness the kernel left undecided: they joined nothing.
+    pub undecided: Vec<usize>,
+}
+
+/// A kernel edge's smoothness, decided once.
+struct Smooth {
+    known: Vec<(EdgeId, Option<Tangency>)>,
+}
+
+impl Smooth {
+    fn of(
+        &mut self,
+        k: &Kernel,
+        b: &mut Brep,
+        e: EdgeId,
+        angle: f64,
+    ) -> solidcore::Result<Option<Tangency>> {
+        if let Some((_, t)) = self.known.iter().find(|(f, _)| *f == e) {
+            return Ok(*t);
+        }
+        let t = tangent_all_along(k, b, e, angle)?;
+        self.known.push((e, t));
+        Ok(t)
+    }
+}
+
+/// An angle a chain takes: finite, strictly between 0 and a right angle.
+fn angle_ok(angle: f64) -> bool {
+    angle > 0.0 && angle < std::f64::consts::FRAC_PI_2
+}
+
+fn index_of<T: PartialEq + Copy>(list: &[T], x: T) -> Option<usize> {
+    list.iter().position(|&y| y == x)
+}
+
+/// The tangent chain of `body`'s edges at record indices `edges` (through `order`, its
+/// record's [`Order`]), as the module documentation describes, at the caller's `angle`;
+/// `passed_over` names edges a pick passes over, which never join.
+///
+/// # Errors
+/// [`Error::Argument`] for no edges, an angle not finite and strictly between 0 and a right
+/// angle, or an index past the order or naming an edge the body does not have; the kernel's
+/// refusals (a face with no NURBS form, an edge use with no pcurve, an edge too costly to
+/// decide).
+pub fn tangent_chain_ordered(
+    body: &Body,
+    order: &Order,
+    edges: &[usize],
+    passed_over: &[usize],
+    angle: f64,
+) -> Result<Chain> {
+    if edges.is_empty() || !angle_ok(angle) {
+        return Err(Error::Argument);
+    }
+    let (copy, mapped) = body.copy_with_order(order)?;
+    with_body("tangent_chain_ordered", &copy, |k, b| {
+        let list = mapped.edges.clone();
+        let mut chain: Vec<EdgeId> = Vec::new();
+        for &i in edges {
+            match list.get(i) {
+                Some(&e) if b.edge_list().contains(&e) => {
+                    if !chain.contains(&e) {
+                        chain.push(e);
+                    }
+                }
+                _ => return Ok(Err(Error::Argument)),
+            }
+        }
+        let skip: Vec<EdgeId> = passed_over
+            .iter()
+            .filter_map(|&i| list.get(i).copied())
+            .collect();
+        let mut smooth = Smooth { known: Vec::new() };
+        let mut undecided: Vec<EdgeId> = Vec::new();
+        let mut next = 0;
+        while let Some(&e) = chain.get(next) {
+            next += 1;
+            let ends = [edge::start_vertex(b, e)?, edge::end_vertex(b, e)?];
+            for v in ends.into_iter().flatten() {
+                for &f in &list {
+                    if chain.contains(&f) || skip.contains(&f) {
+                        continue;
+                    }
+                    let meets = [edge::start_vertex(b, f)?, edge::end_vertex(b, f)?];
+                    if !meets.contains(&Some(v)) {
+                        continue;
+                    }
+                    match smooth.of(k, b, f, angle)? {
+                        None | Some(Tangency::Tangent) => continue,
+                        Some(Tangency::Undecided { .. }) => {
+                            if !undecided.contains(&f) {
+                                undecided.push(f);
+                            }
+                            continue;
+                        }
+                        Some(Tangency::NotTangent) => {}
+                    }
+                    let turns_over = matches!(
+                        (convex_at(k, b, e, v)?, convex_at(k, b, f, v)?),
+                        (Some(a), Some(c)) if a != c
+                    );
+                    if turns_over {
+                        continue;
+                    }
+                    if turn_at(k, b, e, f, v)?.is_some_and(|turn| turn < angle) {
+                        chain.push(f);
+                    }
+                }
+            }
+        }
+        let indices = |of: &[EdgeId]| -> Option<Vec<usize>> {
+            of.iter().map(|&e| index_of(&list, e)).collect()
+        };
+        Ok(match (indices(&chain), indices(&undecided)) {
+            (Some(members), Some(undecided)) => Ok(Chain { members, undecided }),
+            _ => Err(Error::Exception),
+        })
+    })?
+}
+
+/// The faces of `body` at record indices `faces` (through `order`), then every face across a
+/// smooth edge from one of them, and so on (module documentation), at the caller's `angle`.
+///
+/// # Errors
+/// [`Error::Argument`] for no faces, an angle as for [`tangent_chain_ordered`], or an index
+/// past the order or naming a face the body does not have; the kernel's refusals as for
+/// [`tangent_chain_ordered`].
+pub fn tangent_face_chain_ordered(
+    body: &Body,
+    order: &Order,
+    faces: &[usize],
+    angle: f64,
+) -> Result<Chain> {
+    if faces.is_empty() || !angle_ok(angle) {
+        return Err(Error::Argument);
+    }
+    let (copy, mapped) = body.copy_with_order(order)?;
+    with_body("tangent_face_chain_ordered", &copy, |k, b| {
+        let face_list = mapped.faces.clone();
+        let edge_list = mapped.edges.clone();
+        let mut chain: Vec<FaceId> = Vec::new();
+        for &i in faces {
+            match face_list.get(i) {
+                Some(&f) if b.face_list().contains(&f) => {
+                    if !chain.contains(&f) {
+                        chain.push(f);
+                    }
+                }
+                _ => return Ok(Err(Error::Argument)),
+            }
+        }
+        let mut smooth = Smooth { known: Vec::new() };
+        let mut undecided: Vec<EdgeId> = Vec::new();
+        let mut next = 0;
+        while let Some(&f) = chain.get(next) {
+            next += 1;
+            for &e in &edge_list {
+                let across = solidcore::query::edge::edge_faces(b, e)?;
+                if !across.contains(&f) {
+                    continue;
+                }
+                match smooth.of(k, b, e, angle)? {
+                    Some(Tangency::Tangent) => {}
+                    Some(Tangency::Undecided { .. }) => {
+                        if !undecided.contains(&e) {
+                            undecided.push(e);
+                        }
+                        continue;
+                    }
+                    None | Some(Tangency::NotTangent) => continue,
+                }
+                for g in across {
+                    if !chain.contains(&g) {
+                        chain.push(g);
+                    }
+                }
+            }
+        }
+        let members: Option<Vec<usize>> = chain.iter().map(|&f| index_of(&face_list, f)).collect();
+        let undecided: Option<Vec<usize>> =
+            undecided.iter().map(|&e| index_of(&edge_list, e)).collect();
+        Ok(match (members, undecided) {
+            (Some(members), Some(undecided)) => Ok(Chain { members, undecided }),
+            _ => Err(Error::Exception),
+        })
+    })?
+}

solidcore/crates/solidcore-ops/tests/boolean.rs

@@ -1,8 +1,12 @@
-//! The boolean family on boxes whose answers are known.
-#![allow(clippy::unwrap_used)]
+//! The boolean family on bodies whose answers are known.
+#![allow(clippy::unwrap_used, clippy::indexing_slicing)] // test
 
+use std::io::Read as _;
+
+use serde_json::Value;
 use solidcore_ops::boolean::{boolean, imprint, union_all};
-use solidcore_ops::{make_box, session, Body, BooleanOp, Error};
+use solidcore_ops::{make_box, session, Body, BooleanOp, CheckLevel, Error};
+use solidcore_record::brep::Brep as Record;
 
 fn all_fixes() {
     session::set_thread_fixes(solidcore::kernel::UpstreamFixes::NAMES.iter().copied()).unwrap();
@@ -76,3 +80,67 @@ fn an_imprint_cuts_the_faces_the_tool_crosses() {
     assert_eq!(r.counts().unwrap(), [6, 12, 8]);
     assert!(near(volume(&r), 1.0), "{}", volume(&r));
 }
+
+/// The kernel rig's case `booleans/<case>`: its entry, and its operand bodies by name, read
+/// under the corpus's fix set.
+fn corpus_case(case: &str) -> (Value, impl Fn(&str) -> Body) {
+    let corpus = format!(
+        "{}/../solidcore/tests/kernel_cases",
+        env!("CARGO_MANIFEST_DIR")
+    );
+    let fixes: Vec<String> =
+        serde_json::from_str(&std::fs::read_to_string(format!("{corpus}/fixes.json")).unwrap())
+            .unwrap();
+    session::set_fixes(fixes.iter().map(String::as_str)).unwrap();
+    let entry: Value = serde_json::from_str(
+        &std::fs::read_to_string(format!("{corpus}/booleans/{case}.json")).unwrap(),
+    )
+    .unwrap();
+    let gz = std::fs::File::open(format!("{corpus}/booleans/{case}.bodies.json.gz")).unwrap();
+    let mut text = String::new();
+    flate2::read::GzDecoder::new(gz)
+        .read_to_string(&mut text)
+        .unwrap();
+    let records: Value = serde_json::from_str(&text).unwrap();
+    let trusted = entry["bodies"].clone();
+    let body = move |name: &str| {
+        let record: Record = serde_json::from_value(records[name].clone()).unwrap();
+        Body::from_record(&record, trusted[name]["trusted"].as_bool().unwrap())
+            .unwrap()
+            .0
+    };
+    (entry, body)
+}
+
+/// A rod cut by two one-turn screw sweeps of one channel profile, one of each hand, from its
+/// top face: the profile's radial walls meet the rod's cylinder, so each sweep's rail there is
+/// a helix on it, and the two rails cross. The crossing is found more than once, a few 1e-12
+/// apart in the rail's parameter; the new edge along the second rail took the interval its
+/// UV curve's trim had snapped onto a knot of its own, 2.4e-12 before the 3D curve's end
+/// (`SmEdge` test 2). Cut in turn and cut by the two sweeps' union, the result is one valid
+/// solid of the case's closed form (its `expected.method`).
+#[test]
+fn a_rod_cut_by_two_counter_wound_channel_sweeps_is_valid() {
+    let (entry, body) = corpus_case("13462-rod-cut-by-two-counter-wound-channel-coils");
+    let want = entry["expected"]["volume_mm3"].as_f64().unwrap();
+    let rel = entry["expected"]["tolerance"]["rel"].as_f64().unwrap();
+    // b6 the rod, b4 and b5 the right- and left-handed sweeps, b14 the rod cut by b4 as the
+    // case's run read it back from its record
+    let in_turn = boolean(body("b14"), body("b5"), BooleanOp::Subtract)
+        .unwrap()
+        .unwrap();
+    let both = union_all(vec![body("b4"), body("b5")]).unwrap();
+    let at_once = boolean(body("b6"), both, BooleanOp::Subtract)
+        .unwrap()
+        .unwrap();
+    for (how, r) in [("in turn", &in_turn), ("by the union", &at_once)] {
+        let report = r.check(CheckLevel::All).unwrap();
+        assert!(report.is_valid(), "cut {how}: {}", report.text);
+        assert_eq!(r.solid_count().unwrap(), 1, "cut {how}");
+        let v = volume(r);
+        assert!(
+            (v - want).abs() <= rel * want,
+            "cut {how}: volume {v}, closed form {want}"
+        );
+    }
+}

solidcore/crates/solidcore-ops/tests/contact.rs

@@ -0,0 +1,95 @@
+//! Contact between bodies on closed forms: meets, meets against several, the boundary
+//! distance, and the refusals.
+#![allow(clippy::unwrap_used)]
+
+use solidcore_ops::session;
+use solidcore_ops::{make_box, make_sphere, Error};
+
+fn all_fixes() {
+    session::set_thread_fixes(solidcore::kernel::UpstreamFixes::NAMES.iter().copied()).unwrap();
+}
+
+#[test]
+fn boxes_sharing_a_face_meet() {
+    all_fixes();
+    let a = make_box([0.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    let b = make_box([1.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    assert!(a.meets(&b, 1e-6).unwrap());
+    assert!(b.meets(&a, 1e-6).unwrap());
+}
+
+#[test]
+fn boxes_one_apart_do_not_meet_and_their_distance_is_one() {
+    all_fixes();
+    let a = make_box([0.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    let b = make_box([2.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    assert!(!a.meets(&b, 1e-3).unwrap());
+    let g = a.boundary_distance(&b, 1e-9).unwrap();
+    assert!(g.lower <= 1.0 && 1.0 <= g.upper, "{g:?}");
+    assert!(g.upper - g.lower <= 1e-9 * g.upper.max(1.0), "{g:?}");
+    let [p, q] = g.witness.unwrap();
+    assert!(
+        (p[0] - 1.0).abs() <= 1e-12 && (q[0] - 2.0).abs() <= 1e-12,
+        "{g:?}"
+    );
+}
+
+#[test]
+fn a_body_meets_itself_and_one_it_encloses() {
+    all_fixes();
+    let a = make_box([0.0, 0.0, 0.0], [3.0, 3.0, 3.0]).unwrap();
+    let inner = make_box([1.0, 1.0, 1.0], [1.0, 1.0, 1.0]).unwrap();
+    assert!(a.meets(&a, 1e-6).unwrap());
+    assert!(a.meets(&inner, 1e-6).unwrap());
+    assert!(inner.meets(&a, 1e-6).unwrap());
+    // neither body changes
+    assert_eq!(a.counts().unwrap(), [6, 12, 8]);
+    assert_eq!(inner.counts().unwrap(), [6, 12, 8]);
+}
+
+#[test]
+fn meets_each_answers_each_with_its_own_tolerance() {
+    all_fixes();
+    let a = make_sphere([0.0, 0.0, 0.0], 1.0).unwrap();
+    let touching = make_box([1.0, -1.0, -1.0], [1.0, 2.0, 2.0]).unwrap();
+    let near = make_sphere([2.5, 0.0, 0.0], 1.0).unwrap(); // 0.5 apart
+    let far = make_box([5.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    let got = a
+        .meets_each(&[(&touching, 1e-6), (&near, 0.1), (&near, 0.6), (&far, 1.0)])
+        .unwrap();
+    assert_eq!(got, vec![true, false, true, false]);
+}
+
+/// The refusal is the kernel's own bracket: a tolerance equal to a gap the kernel brackets
+/// to its rounding is inside the bracket, and neither answer is given.
+#[test]
+fn a_tolerance_inside_the_bracket_is_refused_with_it() {
+    all_fixes();
+    let a = make_box([0.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    let b = make_box([2.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    let far = make_box([5.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    match a.meets(&b, 1.0) {
+        Err(Error::ContactUndecided {
+            other: 0,
+            lower,
+            upper,
+        }) => assert!(lower <= 1.0 && 1.0 <= upper, "[{lower}, {upper}]"),
+        r => panic!("{r:?}"),
+    }
+    match a.meets_each(&[(&far, 1e-3), (&b, 1.0)]) {
+        Err(Error::ContactUndecided { other: 1, .. }) => {}
+        r => panic!("{r:?}"),
+    }
+}
+
+#[test]
+fn a_tolerance_or_width_not_finite_and_positive_is_refused() {
+    all_fixes();
+    let a = make_box([0.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    let b = make_box([2.0, 0.0, 0.0], [1.0, 1.0, 1.0]).unwrap();
+    let invalid = Error::Status(solidcore::error::SM_ERR_INVALID_INPUT);
+    for bad in [0.0, -1.0, f64::NAN, f64::INFINITY] {
+        assert_eq!(a.meets(&b, bad).unwrap_err(), invalid, "{bad}");
+        assert_eq!(a.boundary_distance(&b, bad).unwrap_err(), invalid, "{bad}");
+    }
+}

solidcore/crates/solidcore-ops/tests/kernel_cases.rs

@@ -32,7 +32,9 @@
 //! - `KERNEL_CASES_TIMEOUT_S`: a case's time limit, 180 s by default; one past it is a hang, and
 //!   the cases after it are not run (it holds the process kernel);
 //! - `KERNEL_CASES_REPORT`: a file to write the per-area table and the lists to;
-//! - `KERNEL_CASES_REPORT_ONLY`: set, the test reports without failing.
+//! - `KERNEL_CASES_REPORT_ONLY`: set, the test reports without failing;
+//! - `KERNEL_CASES_SMB`: a directory to write each run case's bodies to as `<case>.smb`, for
+//!   its render (`solidcore-diag`): the final bodies, or the inputs of the refusal that ends it.
 
 #![allow(
     clippy::unwrap_used,
@@ -231,31 +233,38 @@ fn f64s<const N: usize>(v: &Value) -> Option<[f64; N]> {
     (a.len() == N).then_some(out)
 }
 
-/// A pick's record indices, optionally bounded by its record order's length.
+/// A pick's record indices, optionally bounded by its record order's length. Every pick's shape
+/// and range is checked first, so bad data fails wherever it sits; only then is a traced miss
+/// reported as unsupported (#2993).
 fn picked(op: &str, selection: &Value, length: Option<usize>) -> Result<Vec<usize>, Stop> {
     let bad = |what: &str| Stop::Fail(format!("{op}: parameter {what}"));
-    selection["picked"]
+    let picks = selection["picked"]
         .as_array()
-        .ok_or_else(|| bad("picked"))?
-        .iter()
-        .map(|pick| {
-            if let Some(miss) = pick.get("miss") {
-                let why = miss.as_str().ok_or_else(|| bad("miss"))?;
-                if pick.get("index").is_some() {
-                    return Err(bad("pick must hit or miss"));
-                }
-                return Err(Stop::Unsupported(format!("{op}: pick missed: {why}")));
+        .ok_or_else(|| bad("picked"))?;
+    let mut indices = Vec::with_capacity(picks.len());
+    let mut missed = None;
+    for pick in picks {
+        if let Some(miss) = pick.get("miss") {
+            let why = miss.as_str().ok_or_else(|| bad("miss"))?;
+            if pick.get("index").is_some() {
+                return Err(bad("pick must hit or miss"));
             }
-            let index = pick["index"]
-                .as_u64()
-                .and_then(|i| usize::try_from(i).ok())
-                .ok_or_else(|| bad("index"))?;
-            if length.is_some_and(|length| index >= length) {
-                return Err(bad("pick outside record order"));
-            }
-            Ok(index)
-        })
-        .collect()
+            missed.get_or_insert(why);
+            continue;
+        }
+        let index = pick["index"]
+            .as_u64()
+            .and_then(|i| usize::try_from(i).ok())
+            .ok_or_else(|| bad("index"))?;
+        if length.is_some_and(|length| index >= length) {
+            return Err(bad("pick outside record order"));
+        }
+        indices.push(index);
+    }
+    match missed {
+        Some(why) => Err(Stop::Unsupported(format!("{op}: pick missed: {why}"))),
+        None => Ok(indices),
+    }
 }
 
 /// Parses typed record picks without reordering them: misses are unsupported; bad data fails.
@@ -1197,6 +1206,21 @@ fn grade_seams(result: &[Slot], expected: &Value) -> Result<(), Stop> {
     Ok(())
 }
 
+/// With `KERNEL_CASES_SMB` set, writes `bodies` there as `<case>.smb`, `<case>-1.smb`, ...
+fn write_smb(e: &Value, bodies: &[Slot]) {
+    let Some(dir) = std::env::var_os("KERNEL_CASES_SMB") else {
+        return;
+    };
+    let case = e["case"].as_str().unwrap();
+    for (i, s) in bodies.iter().enumerate() {
+        let name = match i {
+            0 => format!("{case}.smb"),
+            _ => format!("{case}-{i}.smb"),
+        };
+        std::fs::write(Path::new(&dir).join(name), s.body.to_smb(true).unwrap()).unwrap();
+    }
+}
+
 /// Runs a case's calls and grades the result against `rig` (or, for a hand-written case
 /// without one, `expected`): `Ok(deviation)` for a match.
 fn run_case(entry: &Path, e: &Value) -> Result<Option<f64>, Stop> {
@@ -1298,7 +1322,10 @@ fn run_case_with_records(
             // A handled refusal is an attempt, not the case's outcome. Keep checking the
             // later operations and final geometry; an unmarked refusal still ends the case.
             (Err(_), Some(_)) if continued => {}
-            (Err(_), Some(_)) => return Ok(None),
+            (Err(_), Some(_)) => {
+                write_smb(e, &ins);
+                return Ok(None);
+            }
             (Err(x), None) => return Err(Stop::Fail(format!("call {i} ({op}) refused: {x}"))),
             (Ok(_), Some(want)) => {
                 return Err(Stop::Fail(format!(
@@ -1321,6 +1348,7 @@ fn run_case_with_records(
                 .ok_or_else(|| Stop::Fail(format!("no final body {n}")))?,
         );
     }
+    write_smb(e, &result);
     let got = measure(&result).map_err(Stop::Fail)?;
     if let Some(seams) = e["expected"].get("seams") {
         grade_seams(&result, seams)?;
@@ -1422,7 +1450,16 @@ fn seam_gaps_are_limited_independently_of_stored_tolerances() {
 
     let body = solidcore_ops::make_box([0.0; 3], [10.0; 3]).unwrap();
     let (mut record, _) = body.to_record().unwrap();
+    // every stored tolerance inflated, not the body's alone: the import keeps each edge's and
+    // vertex's own and takes the body's as the least of them (#3187, as SolidCraft's flat
+    // import does), so a body tolerance alone no longer reaches the edges the grade reads
     record.tolerance = 0.01;
+    for edge in &mut record.edges {
+        edge.tolerance = 0.01;
+    }
+    for vertex in &mut record.vertices {
+        vertex.tolerance = 0.01;
+    }
     for face in &mut record.faces {
         match &mut face.surface {
             Surface::Plane { origin, .. } => {
@@ -3907,6 +3944,36 @@ fn record_picks_preserve_order_and_duplicate_parameter_alignment() {
     ));
 }
 
+/// Bad pick data fails wherever it sits in the list; a traced miss is unsupported only when
+/// every other pick is well formed (#2993).
+#[test]
+fn a_traced_miss_is_unsupported_only_among_well_formed_picks() {
+    let list = |picked: Value| serde_json::json!({"kind": "edge", "picked": picked});
+    for bad in [
+        serde_json::json!([{"miss": "none"}, {"index": 999}]),
+        serde_json::json!([{"index": 999}, {"miss": "none"}]),
+        serde_json::json!([{"miss": "none"}, {}]),
+        serde_json::json!([{"miss": "none"}, {"miss": "none", "index": 0}]),
+    ] {
+        assert!(
+            matches!(
+                record_picks("blend", &list(bad.clone()), "edge", 2),
+                Err(Stop::Fail(_))
+            ),
+            "{bad}"
+        );
+    }
+    assert!(matches!(
+        record_picks(
+            "blend",
+            &list(serde_json::json!([{"index": 0}, {"miss": "none"}])),
+            "edge",
+            2
+        ),
+        Err(Stop::Unsupported(_))
+    ));
+}
+
 /// Captured split followed by merging its redundant faces, with the original grading.
 #[test]
 fn split_body_replays_face_plane() {

solidcore/crates/solidcore-ops/tests/tangent_chain.rs

@@ -0,0 +1,235 @@
+//! `tangent::tangent_chain_ordered` and `tangent_face_chain_ordered` (#3141), on record order.
+//!
+//! A stadium prism: two straight walls and two half-cylinders, 4 high. Its top outline is
+//! four edges each running on tangentially into the next, so a pick of one top edge chains
+//! all four and nothing else (the walls meet each other smoothly, so the vertical edges
+//! between them are smooth, and the bottom outline turns square from the top's). Its walls
+//! meet across smooth edges, so a pick of one wall chains the four walls and not the caps. A
+//! box's edges and faces all meet square: a pick chains itself alone.
+//!
+//! Ported from SolidCraft (`crates/kernel/tests/chamfer_curved_holder.rs`,
+//! `one_chamfer_pick_follows_the_tangent_chain_at_any_part_size`, its #2672): a plate of side
+//! 140, 145 and 250, 10 thick, with a 50 x 10 stadium boss 10 tall on top. One pick on the
+//! boss's top straight edge chains the boss's whole top rim, its four edges at z = 20, at
+//! every plate size (SolidCraft's walk once stopped at the straight edge past a 200 mm part).
+#![allow(
+    clippy::unwrap_used,
+    clippy::expect_used,
+    clippy::panic,
+    clippy::indexing_slicing
+)] // test helpers
+
+use solidcore_ops::boolean::{boolean, BooleanOp};
+use solidcore_ops::sweep::{extrude, Curve, DraftCorner};
+use solidcore_ops::tangent::{tangent_chain_ordered, tangent_face_chain_ordered};
+use solidcore_ops::{make_box, Body};
+use solidcore_record::brep::{Brep as Record, Surface};
+use std::f64::consts::{FRAC_PI_2, PI};
+
+const H: f64 = 4.0;
+/// SolidCraft's smooth-edge angle, the caller's: half a degree.
+const ANGLE: f64 = 0.5 * PI / 180.0;
+
+fn stadium() -> Body {
+    let profile = [
+        Curve::Line {
+            start: [0.0, 0.0, 0.0],
+            end: [20.0, 0.0, 0.0],
+        },
+        Curve::Arc {
+            center: [20.0, 5.0, 0.0],
+            axis: [0.0, 0.0, 1.0],
+            reference: [1.0, 0.0, 0.0],
+            radius: 5.0,
+            start: -FRAC_PI_2,
+            end: FRAC_PI_2,
+        },
+        Curve::Line {
+            start: [20.0, 10.0, 0.0],
+            end: [0.0, 10.0, 0.0],
+        },
+        Curve::Arc {
+            center: [0.0, 5.0, 0.0],
+            axis: [0.0, 0.0, 1.0],
+            reference: [1.0, 0.0, 0.0],
+            radius: 5.0,
+            start: FRAC_PI_2,
+            end: 1.5 * PI,
+        },
+    ];
+    extrude(
+        &profile,
+        [0.0, 0.0, 1.0],
+        H,
+        0.0,
+        DraftCorner::default(),
+        true,
+    )
+    .unwrap()
+}
+
+/// The record index of the edge between the vertices at `a` and `b`.
+fn edge(r: &Record, a: [f64; 3], b: [f64; 3]) -> usize {
+    let near = |i: u32, p: [f64; 3]| {
+        let q = r.vertices[i as usize].point;
+        (0..3).all(|j| (q[j] - p[j]).abs() < 1e-9)
+    };
+    r.edges
+        .iter()
+        .position(|e| {
+            let [s, t] = e.vertices;
+            (near(s, a) && near(t, b)) || (near(s, b) && near(t, a))
+        })
+        .expect("an edge between the points")
+}
+
+/// Whether record edge `i` lies in the top, both its ends at z = H.
+fn on_top(r: &Record, i: usize) -> bool {
+    r.edges[i]
+        .vertices
+        .iter()
+        .all(|&v| (r.vertices[v as usize].point[2] - H).abs() < 1e-9)
+}
+
+/// The record index of the planar face whose normal is along `n` (up to sign).
+fn plane_along(r: &Record, n: [f64; 3]) -> Vec<usize> {
+    let cross = |a: [f64; 3], b: [f64; 3]| {
+        [
+            a[1] * b[2] - a[2] * b[1],
+            a[2] * b[0] - a[0] * b[2],
+            a[0] * b[1] - a[1] * b[0],
+        ]
+    };
+    let along = |m: [f64; 3]| {
+        let c = cross(m, n);
+        c.iter().all(|x| x.abs() < 1e-9) && m.iter().any(|x| x.abs() > 1e-9)
+    };
+    (0..r.faces.len())
+        .filter(|&i| match r.faces[i].surface {
+            Surface::Plane { u_axis, v_axis, .. } => along(cross(u_axis, v_axis)),
+            _ => false,
+        })
+        .collect()
+}
+
+#[test]
+fn a_stadium_s_top_outline_is_one_chain() {
+    let b = stadium();
+    let (r, order) = b.to_record().unwrap();
+    let front = edge(&r, [0.0, 0.0, H], [20.0, 0.0, H]);
+    let chain = tangent_chain_ordered(&b, &order, &[front], &[], ANGLE).unwrap();
+    assert!(chain.undecided.is_empty(), "{chain:?}");
+    assert_eq!(chain.members.len(), 4, "{chain:?}");
+    assert_eq!(chain.members[0], front);
+    assert!(chain.members.iter().all(|&e| on_top(&r, e)), "{chain:?}");
+}
+
+#[test]
+fn a_passed_over_edge_stops_the_chain() {
+    let b = stadium();
+    let (r, order) = b.to_record().unwrap();
+    let front = edge(&r, [0.0, 0.0, H], [20.0, 0.0, H]);
+    let back = edge(&r, [20.0, 10.0, H], [0.0, 10.0, H]);
+    let chain = tangent_chain_ordered(&b, &order, &[front], &[back], ANGLE).unwrap();
+    assert_eq!(chain.members.len(), 3, "{chain:?}");
+    assert!(!chain.members.contains(&back));
+}
+
+#[test]
+fn a_box_edge_chains_alone() {
+    let b = make_box([0.0; 3], [10.0, 6.0, H]).unwrap();
+    let (r, order) = b.to_record().unwrap();
+    let front = edge(&r, [0.0, 0.0, H], [10.0, 0.0, H]);
+    let chain = tangent_chain_ordered(&b, &order, &[front], &[], ANGLE).unwrap();
+    assert_eq!(chain.members, vec![front]);
+    assert!(chain.undecided.is_empty());
+}
+
+#[test]
+fn a_stadium_s_walls_are_one_face_chain() {
+    let b = stadium();
+    let (r, order) = b.to_record().unwrap();
+    let walls = plane_along(&r, [0.0, 1.0, 0.0]);
+    assert_eq!(walls.len(), 2);
+    let chain = tangent_face_chain_ordered(&b, &order, &walls[..1], ANGLE).unwrap();
+    assert!(chain.undecided.is_empty(), "{chain:?}");
+    assert_eq!(chain.members.len(), 4, "{chain:?}");
+    for &f in &chain.members {
+        let caps = plane_along(&r, [0.0, 0.0, 1.0]);
+        assert!(!caps.contains(&f), "a cap joined: {chain:?}");
+    }
+    assert!(walls.iter().all(|w| chain.members.contains(w)), "{chain:?}");
+}
+
+#[test]
+fn a_box_face_chains_alone() {
+    let b = make_box([0.0; 3], [10.0, 6.0, H]).unwrap();
+    let (r, order) = b.to_record().unwrap();
+    let top = plane_along(&r, [0.0, 0.0, 1.0]);
+    let chain = tangent_face_chain_ordered(&b, &order, &top[..1], ANGLE).unwrap();
+    assert_eq!(chain.members, vec![top[0]]);
+}
+
+/// The plate of side `plate` with the stadium boss on top.
+fn plate_with_stadium(plate: f64) -> Body {
+    let base = make_box([-plate / 2.0, -plate / 2.0, 0.0], [plate, plate, 10.0]).unwrap();
+    let z = 10.0;
+    let profile = [
+        Curve::Line {
+            start: [-20.0, -5.0, z],
+            end: [20.0, -5.0, z],
+        },
+        Curve::Arc {
+            center: [20.0, 0.0, z],
+            axis: [0.0, 0.0, 1.0],
+            reference: [1.0, 0.0, 0.0],
+            radius: 5.0,
+            start: -FRAC_PI_2,
+            end: FRAC_PI_2,
+        },
+        Curve::Line {
+            start: [20.0, 5.0, z],
+            end: [-20.0, 5.0, z],
+        },
+        Curve::Arc {
+            center: [-20.0, 0.0, z],
+            axis: [0.0, 0.0, 1.0],
+            reference: [1.0, 0.0, 0.0],
+            radius: 5.0,
+            start: FRAC_PI_2,
+            end: 1.5 * PI,
+        },
+    ];
+    let boss = extrude(
+        &profile,
+        [0.0, 0.0, 1.0],
+        10.0,
+        0.0,
+        DraftCorner::default(),
+        true,
+    )
+    .unwrap();
+    boolean(base, boss, BooleanOp::Union).unwrap().unwrap()
+}
+
+#[test]
+fn one_pick_follows_the_boss_rim_at_any_part_size() {
+    for plate in [140.0, 145.0, 250.0] {
+        let b = plate_with_stadium(plate);
+        let (r, order) = b.to_record().unwrap();
+        let back = edge(&r, [20.0, 5.0, 20.0], [-20.0, 5.0, 20.0]);
+        let chain = tangent_chain_ordered(&b, &order, &[back], &[], ANGLE).unwrap();
+        assert!(chain.undecided.is_empty(), "plate {plate}: {chain:?}");
+        assert_eq!(chain.members.len(), 4, "plate {plate}: {chain:?}");
+        let at_top = |i: usize| {
+            r.edges[i]
+                .vertices
+                .iter()
+                .all(|&v| (r.vertices[v as usize].point[2] - 20.0).abs() < 1e-9)
+        };
+        assert!(
+            chain.members.iter().all(|&e| at_top(e)),
+            "plate {plate}: {chain:?}"
+        );
+    }
+}

solidcore/crates/solidcore-record/src/lib.rs

@@ -2,7 +2,8 @@
 //! and structural validation ([`brep`]), its history and metadata records, the native body
 //! file ([`native`]), and the plain data of vectors ([`Vec2`], [`Vec3`]), sketch planes
 //! ([`Plane`]) and planar profiles ([`Seg2`], [`Loop2`], [`Region2`]), and STEP's Part 21
-//! exchange structure as parsed from a file ([`step`]).
+//! exchange structure as parsed from a file with the units of its representation contexts and
+//! its Part 42 curves and surfaces ([`step`]).
 //!
 //! The record computes no geometric quantity: no square roots, trigonometry, dot or cross
 //! products, normalising or solves (clippy `disallowed-methods`, this crate's `clippy.toml`). It

solidcore/crates/solidcore-record/src/step.rs

@@ -1,3 +1,9 @@
-//! STEP (ISO 10303) as data: the exchange structure a file is read into ([`p21`]). Building
+//! STEP (ISO 10303) as data: the exchange structure a file is read into ([`p21`]), the units
+//! of its representation contexts ([`units`]), its Part 42 curves and surfaces ([`geom`])
+//! as the entity reader ([`read`]) maps them, and its product structure ([`product`]). Building
 //! bodies from it is `solidcore-ops`' job (docs/layers.md §2, "Importers are solidcore's").
+pub mod geom;
 pub mod p21;
+pub mod product;
+pub mod read;
+pub mod units;

solidcore/crates/solidcore-record/src/step/geom.rs

@@ -0,0 +1,444 @@
+//! STEP geometry (ISO 10303-42) as plain data: the curves and surfaces a file defines, exactly
+//! as it defines them, with lengths in millimetres and angles in radians. Nothing is
+//! approximated, bounded, normalised or turned into another kind on the way in: a circle stays a
+//! circle with its placement, an unbounded cylinder stays unbounded, a B-spline keeps its own
+//! knots and form, and a direction keeps the ratios the file writes. Every curve and surface keeps
+//! STEP's own parameterisation, so a 2D curve in a surface's parameter space means the same thing
+//! here as in the file.
+//!
+//! Entities the file shares (one surface under many edges' pcurves) are shared here too, through
+//! `Arc`, so reading is linear in the file however often an entity is referenced.
+//!
+//! The record computes no geometric quantity (docs/layers.md §1, §4): a direction is not made a
+//! unit vector, a placement's reference direction is not made orthogonal to its axis (nor chosen
+//! when the file omits it), its y axis is not formed, a vector's length is not taken, and nothing
+//! is evaluated. Those are the kernel's, on its own types, when it builds from this data (#2578,
+//! slice 4). The formulas on the variants below say what the data means, in ISO 10303-42's
+//! terms; they are not computed here.
+//!
+//! Origin: SolidCraft's `crates/step/src/geom.rs` at `a5b71ca2` (MIT OR Apache-2.0).
+//!
+//! Deviations from SolidCraft: [`Placement`] keeps `axis` and `ref_direction` as the file gives
+//! them (each optional, neither normalised; was: both unit and orthogonal, a missing reference
+//! direction chosen perpendicular to the axis), and [`Axis1::direction`] likewise. A `VECTOR` is
+//! a [`Vector`] of the written orientation, magnitude and unit factors (was: a unit direction
+//! and the vector's length), in [`Curve::Line`] and [`Surface::Extrusion`]. Removed, to come back
+//! as kernel primitives in slice 4: `Placement::y`, `Placement::at` and the vector helpers `add`,
+//! `sub`, `scale`, `dot`, `cross`, `norm`. Doc comments on every public item and field.
+
+use std::sync::Arc;
+
+/// A point or vector: `[x, y, z]` (z = 0 in a 2D parameter space).
+pub type P3 = [f64; 3];
+
+/// `AXIS2_PLACEMENT_3D`, or `AXIS2_PLACEMENT_2D` (no `axis`): an origin and the directions of
+/// its local Z and X axes, as the file writes them.
+///
+/// ISO 10303-42 makes the local axes from these: Z is `axis` (+Z when absent), X is
+/// `ref_direction` made orthogonal to Z (a chosen perpendicular when absent), Y is Z × X. That
+/// construction, with its checks (a zero or parallel reference direction), is the kernel's.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct Placement {
+    /// The location, in millimetres (or the parameter space's units).
+    pub origin: P3,
+    /// Local Z as the file gives it (not normalised); `None` when the file omits it and for an
+    /// `AXIS2_PLACEMENT_2D`, which ISO 10303-42 defines as +Z.
+    pub axis: Option<P3>,
+    /// Local X as the file gives it (not normalised, not made orthogonal to `axis`); `None` when
+    /// the file omits it.
+    pub ref_direction: Option<P3>,
+}
+
+/// `AXIS1_PLACEMENT`: an origin and a direction, as the file writes them.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct Axis1 {
+    /// The location, in millimetres.
+    pub origin: P3,
+    /// The direction as the file gives it (not normalised); `None` when the file omits it, which
+    /// ISO 10303-42 defines as +Z.
+    pub direction: Option<P3>,
+}
+
+/// `VECTOR`: an orientation and a magnitude, as the file writes them, and the unit factors of
+/// the space they are in.
+///
+/// In millimetres and radians, component `i` of the vector is
+/// `scale[i] · magnitude · orientation[i] / |orientation|`. The record does not form it; the
+/// kernel does (slice 4).
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct Vector {
+    /// The direction ratios as written (not normalised; never all zero).
+    pub orientation: P3,
+    /// The magnitude as written, in file units (positive).
+    pub magnitude: f64,
+    /// The unit factor of each component: the length unit in model space, the parameter's unit
+    /// (length, angle, or 1) in a surface's parameter space.
+    pub scale: P3,
+}
+
+/// A STEP LOGICAL.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Logical {
+    /// `.T.`
+    True,
+    /// `.F.`
+    False,
+    /// `.U.`
+    Unknown,
+}
+
+/// `b_spline_curve_form`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum CurveForm {
+    /// `.POLYLINE_FORM.`
+    PolylineForm,
+    /// `.CIRCULAR_ARC.`
+    CircularArc,
+    /// `.ELLIPTIC_ARC.`
+    EllipticArc,
+    /// `.PARABOLIC_ARC.`
+    ParabolicArc,
+    /// `.HYPERBOLIC_ARC.`
+    HyperbolicArc,
+    /// `.UNSPECIFIED.`, or anything else.
+    Unspecified,
+}
+
+/// `b_spline_surface_form`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum SurfaceForm {
+    /// `.PLANE_SURF.`
+    PlaneSurf,
+    /// `.CYLINDRICAL_SURF.`
+    CylindricalSurf,
+    /// `.CONICAL_SURF.`
+    ConicalSurf,
+    /// `.SPHERICAL_SURF.`
+    SphericalSurf,
+    /// `.TOROIDAL_SURF.`
+    ToroidalSurf,
+    /// `.SURF_OF_REVOLUTION.`
+    SurfOfRevolution,
+    /// `.RULED_SURF.`
+    RuledSurf,
+    /// `.GENERALISED_CONE.`
+    GeneralisedCone,
+    /// `.QUADRIC_SURF.`
+    QuadricSurf,
+    /// `.SURF_OF_LINEAR_EXTRUSION.`
+    SurfOfLinearExtrusion,
+    /// `.UNSPECIFIED.`, or anything else.
+    Unspecified,
+}
+
+/// `knot_type`. A B-spline given without knots (`BEZIER_CURVE`, `UNIFORM_CURVE`,
+/// `QUASI_UNIFORM_CURVE` and their surfaces) has them laid out on reading, and keeps the
+/// matching type here.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum KnotSpec {
+    /// `.UNIFORM_KNOTS.`
+    UniformKnots,
+    /// `.QUASI_UNIFORM_KNOTS.`
+    QuasiUniformKnots,
+    /// `.PIECEWISE_BEZIER_KNOTS.`
+    PiecewiseBezierKnots,
+    /// `.UNSPECIFIED.`, or anything else.
+    Unspecified,
+}
+
+/// A B-spline curve: distinct knots with their multiplicities, as STEP writes them.
+#[derive(Clone, Debug, PartialEq)]
+pub struct BSplineCurve {
+    /// The degree (1 to `read::MAX_DEGREE`).
+    pub degree: usize,
+    /// The control points.
+    pub points: Vec<P3>,
+    /// Present for a rational curve: one positive weight per point.
+    pub weights: Option<Vec<f64>>,
+    /// The distinct knots, increasing.
+    pub knots: Vec<f64>,
+    /// Each knot's multiplicity (1 to degree + 1); they add up to points + degree + 1.
+    pub multiplicities: Vec<usize>,
+    /// The curve form.
+    pub form: CurveForm,
+    /// `closed_curve`.
+    pub closed: Logical,
+    /// `self_intersect`.
+    pub self_intersect: Logical,
+    /// The knot type.
+    pub knot_spec: KnotSpec,
+}
+
+/// A B-spline surface; `points[i][j]` runs along u with `i`, along v with `j`.
+#[derive(Clone, Debug, PartialEq)]
+pub struct BSplineSurface {
+    /// The degree in u.
+    pub u_degree: usize,
+    /// The degree in v.
+    pub v_degree: usize,
+    /// The control net, rows along u, every row the same length.
+    pub points: Vec<Vec<P3>>,
+    /// Present for a rational surface: one positive weight per control point.
+    pub weights: Option<Vec<Vec<f64>>>,
+    /// The distinct u knots, increasing.
+    pub u_knots: Vec<f64>,
+    /// Each u knot's multiplicity.
+    pub u_multiplicities: Vec<usize>,
+    /// The distinct v knots, increasing.
+    pub v_knots: Vec<f64>,
+    /// Each v knot's multiplicity.
+    pub v_multiplicities: Vec<usize>,
+    /// The surface form.
+    pub form: SurfaceForm,
+    /// `u_closed`.
+    pub u_closed: Logical,
+    /// `v_closed`.
+    pub v_closed: Logical,
+    /// `self_intersect`.
+    pub self_intersect: Logical,
+    /// The knot type.
+    pub knot_spec: KnotSpec,
+}
+
+/// One end of a `TRIMMED_CURVE`: a point on the basis curve or its parameter (a trim lists one
+/// or both).
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub enum Trim {
+    /// A `CARTESIAN_POINT`.
+    Point(P3),
+    /// A `PARAMETER_VALUE` (radians on a circle or an ellipse).
+    Parameter(f64),
+}
+
+/// `trimming_preference`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum TrimPreference {
+    /// `.CARTESIAN.`
+    Cartesian,
+    /// `.PARAMETER.`
+    Parameter,
+    /// `.UNSPECIFIED.`, or anything else.
+    Unspecified,
+}
+
+/// `preferred_surface_curve_representation`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum PreferredRep {
+    /// `.CURVE_3D.`, or anything else.
+    Curve3d,
+    /// `.PCURVE_S1.`
+    PcurveS1,
+    /// `.PCURVE_S2.`
+    PcurveS2,
+}
+
+/// Which `SURFACE_CURVE` subtype.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum SurfaceCurveKind {
+    /// `SURFACE_CURVE`.
+    Surface,
+    /// `SEAM_CURVE`.
+    Seam,
+    /// `INTERSECTION_CURVE`.
+    Intersection,
+    /// `BOUNDED_SURFACE_CURVE`.
+    BoundedSurface,
+}
+
+/// `PCURVE`: a 2D curve in the parameter space of `surface`. Its coordinates are the surface's
+/// own parameters (lengths in mm, angles in radians).
+#[derive(Clone, Debug, PartialEq)]
+pub struct Pcurve {
+    /// The surface.
+    pub surface: Arc<Surface>,
+    /// A 2D curve: every point and placement has z = 0 and no placement has an axis.
+    pub curve: Arc<Curve>,
+}
+
+/// An item of a `SURFACE_CURVE`'s `associated_geometry`.
+#[derive(Clone, Debug, PartialEq)]
+pub enum Associated {
+    /// A `PCURVE`.
+    Pcurve(Pcurve),
+    /// A surface.
+    Surface(Arc<Surface>),
+}
+
+/// A STEP curve.
+#[derive(Clone, Debug, PartialEq)]
+pub enum Curve {
+    /// `LINE`: `origin + t·v`, with `v` the [`Vector`].
+    Line {
+        /// `pnt`.
+        origin: P3,
+        /// `dir`.
+        vector: Vector,
+    },
+    /// `CIRCLE`. Parameter: the angle from the placement's X axis.
+    Circle {
+        /// The placement.
+        position: Placement,
+        /// The radius (positive).
+        radius: f64,
+    },
+    /// `ELLIPSE`: `origin + a·cos t·X + b·sin t·Y`.
+    Ellipse {
+        /// The placement.
+        position: Placement,
+        /// `a`, along X (positive).
+        semi_axis_1: f64,
+        /// `b`, along Y (positive).
+        semi_axis_2: f64,
+    },
+    /// `HYPERBOLA`: `origin + a·cosh t·X + b·sinh t·Y`.
+    Hyperbola {
+        /// The placement.
+        position: Placement,
+        /// `a` (positive).
+        semi_axis: f64,
+        /// `b` (positive).
+        semi_imag_axis: f64,
+    },
+    /// `PARABOLA`: `origin + f·t²·X + 2f·t·Y`.
+    Parabola {
+        /// The placement.
+        position: Placement,
+        /// `f` (not zero).
+        focal_dist: f64,
+    },
+    /// `B_SPLINE_CURVE` and its subtypes.
+    BSpline(Box<BSplineCurve>),
+    /// `POLYLINE`: segment `i` (from 0) is the parameters `[i, i + 1]`.
+    Polyline(Vec<P3>),
+    /// `TRIMMED_CURVE`.
+    Trimmed {
+        /// `basis_curve`.
+        basis: Arc<Curve>,
+        /// `trim_1` (one or two items).
+        trim_1: Vec<Trim>,
+        /// `trim_2` (one or two items).
+        trim_2: Vec<Trim>,
+        /// `sense_agreement`.
+        sense: bool,
+        /// `master_representation`.
+        preference: TrimPreference,
+    },
+    /// `SURFACE_CURVE`, `SEAM_CURVE`, `INTERSECTION_CURVE`, `BOUNDED_SURFACE_CURVE`.
+    SurfaceCurve {
+        /// Which subtype.
+        kind: SurfaceCurveKind,
+        /// `curve_3d`.
+        curve_3d: Arc<Curve>,
+        /// `associated_geometry` (at most two items).
+        associated: Vec<Associated>,
+        /// `master_representation`.
+        master: PreferredRep,
+    },
+    /// `OFFSET_CURVE_3D`.
+    OffsetCurve3d {
+        /// `basis_curve`.
+        basis: Arc<Curve>,
+        /// `distance`, in millimetres.
+        distance: f64,
+        /// `self_intersect`.
+        self_intersect: Logical,
+        /// `ref_direction` as the file gives it (not normalised).
+        ref_direction: P3,
+    },
+}
+
+/// A STEP surface.
+#[derive(Clone, Debug, PartialEq)]
+pub enum Surface {
+    /// `PLANE`: `origin + u·X + v·Y`.
+    Plane {
+        /// The placement.
+        position: Placement,
+    },
+    /// `CYLINDRICAL_SURFACE`: `origin + r·(cos u·X + sin u·Y) + v·Z`.
+    Cylinder {
+        /// The placement.
+        position: Placement,
+        /// `r` (positive).
+        radius: f64,
+    },
+    /// `CONICAL_SURFACE`: `origin + (r + v·tan a)·(cos u·X + sin u·Y) + v·Z`.
+    Cone {
+        /// The placement.
+        position: Placement,
+        /// `r` (not negative).
+        radius: f64,
+        /// `a`, in radians, its size in (0, π/2).
+        semi_angle: f64,
+    },
+    /// `SPHERICAL_SURFACE`: `origin + r·cos v·(cos u·X + sin u·Y) + r·sin v·Z`.
+    Sphere {
+        /// The placement.
+        position: Placement,
+        /// `r` (positive).
+        radius: f64,
+    },
+    /// `TOROIDAL_SURFACE`: `origin + (R + r·cos v)·(cos u·X + sin u·Y) + r·sin v·Z`.
+    Torus {
+        /// The placement.
+        position: Placement,
+        /// `R` (may be negative: some writers use that for a spindle torus).
+        major_radius: f64,
+        /// `r` (positive).
+        minor_radius: f64,
+    },
+    /// `DEGENERATE_TOROIDAL_SURFACE`: a torus whose minor radius reaches the axis;
+    /// `select_outer` keeps the outer part.
+    DegenerateTorus {
+        /// The placement.
+        position: Placement,
+        /// `R`.
+        major_radius: f64,
+        /// `r` (positive).
+        minor_radius: f64,
+        /// `select_outer`.
+        select_outer: bool,
+    },
+    /// `B_SPLINE_SURFACE` and its subtypes.
+    BSpline(Box<BSplineSurface>),
+    /// `SURFACE_OF_REVOLUTION`: the profile at `v` turned by the angle `u` about the axis.
+    Revolution {
+        /// `swept_curve`.
+        profile: Arc<Curve>,
+        /// `axis_position`.
+        axis: Axis1,
+    },
+    /// `SURFACE_OF_LINEAR_EXTRUSION`: `profile(u) + v·w`, with `w` the [`Vector`].
+    Extrusion {
+        /// `swept_curve`.
+        profile: Arc<Curve>,
+        /// `extrusion_axis`.
+        vector: Vector,
+    },
+    /// `OFFSET_SURFACE`.
+    Offset {
+        /// `basis_surface`.
+        basis: Arc<Surface>,
+        /// `distance`, in millimetres.
+        distance: f64,
+        /// `self_intersect`.
+        self_intersect: Logical,
+    },
+    /// `RECTANGULAR_TRIMMED_SURFACE`, its bounds in the basis surface's parameter units.
+    RectangularTrimmed {
+        /// `basis_surface`.
+        basis: Arc<Surface>,
+        /// `u1`.
+        u1: f64,
+        /// `u2`.
+        u2: f64,
+        /// `v1`.
+        v1: f64,
+        /// `v2`.
+        v2: f64,
+        /// `usense`.
+        u_sense: bool,
+        /// `vsense`.
+        v_sense: bool,
+    },
+}

solidcore/crates/solidcore-record/src/step/product/tests.rs

@@ -0,0 +1,713 @@
+//! The product structure, one case at a time: a part, an assembly with a shared sub-assembly,
+//! mapped items, colours, names with escapes, and what is refused. Lengths are the file's
+//! numbers times the context's unit, written as the same products, so every comparison is
+//! exact.
+//!
+//! Origin: the data cases of SolidCraft's `crates/kernel/src/step_in/tests.rs` at `a5b71ca2`
+//! (`hand_written_part_in_inches_with_colour`, `two_instance_assembly`,
+//! `assembly_cycles_are_bounded`, `exponential_assemblies_are_bounded`), checking the data the
+//! import builds from instead of the bodies it builds.
+
+use std::fmt::Write as _;
+
+use super::{
+    BodyKind, Colour, Definition, Frame, Instance, Item, ItemKind, Link, MAX_ASSEMBLY_DEPTH,
+    MAX_VISITS, Operator, Product, ProductStructure, Representation, RepresentationMap, Side,
+    StyledItem, SurfaceStyle, Transformation, read,
+};
+use crate::step::geom::Placement;
+use crate::step::p21::{self, Exchange};
+use crate::step::units::{Context, Units};
+
+fn file(data: &str) -> Exchange {
+    let t = format!(
+        "ISO-10303-21;\nHEADER;FILE_SCHEMA(('AUTOMOTIVE_DESIGN'));ENDSEC;\nDATA;\n{data}\nENDSEC;\nEND-ISO-10303-21;\n"
+    );
+    match p21::parse(&t) {
+        Ok(ex) if ex.duplicates.is_empty() => ex,
+        Ok(ex) => panic!("ids defined twice: {:?}\n{t}", ex.duplicates),
+        Err(e) => panic!("{e}\n{t}"),
+    }
+}
+
+fn structure(data: &str) -> ProductStructure {
+    read(&file(data)).unwrap_or_else(|e| panic!("{e}"))
+}
+
+fn refused(data: &str) -> String {
+    match read(&file(data)) {
+        Ok(s) => panic!("read: {s:?}"),
+        Err(e) => e,
+    }
+}
+
+/// The application contexts and a body: #8, #9, the solid #101 'Cube' (its shell #100 empty:
+/// the product structure does not read topology).
+const BASE: &str = "#8=PRODUCT_DEFINITION_CONTEXT('part definition',#9,'design');\
+#9=APPLICATION_CONTEXT('');#100=CLOSED_SHELL('',());#101=MANIFOLD_SOLID_BREP('Cube',#100);\n";
+
+/// A geometric context `#id` in the length unit `unit` (#id+2), radians (#id+3) and an
+/// uncertainty of 1e-6 in that unit (#id+1).
+fn context(id: u64, unit: &str) -> String {
+    format!(
+        "#{id}=(GEOMETRIC_REPRESENTATION_CONTEXT(3)GLOBAL_UNCERTAINTY_ASSIGNED_CONTEXT((#{}))GLOBAL_UNIT_ASSIGNED_CONTEXT((#{},#{}))REPRESENTATION_CONTEXT('',''));\n#{}=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(1.E-6),#{},'','');\n#{}={unit};\n#{}=(NAMED_UNIT(*)PLANE_ANGLE_UNIT()SI_UNIT($,.RADIAN.));\n",
+        id + 1,
+        id + 2,
+        id + 3,
+        id + 1,
+        id + 2,
+        id + 2,
+        id + 3
+    )
+}
+
+const MM: &str = "(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.))";
+const CM: &str = "(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.CENTI.,.METRE.))";
+/// Millimetres per centimetre as `units` forms it (prefix times metre).
+const CM_MM: f64 = 1e-2 * 1000.0;
+
+/// A product `name` and its definition `#pd`: `PRODUCT` #pd+1, `PRODUCT_CONTEXT` #pd+2, formation
+/// #pd+3, `PRODUCT_DEFINITION_SHAPE` #pd+4.
+fn product(pd: u64, name: &str) -> String {
+    format!(
+        "#{}=PRODUCT('{name}','{name}','',(#{}));\n#{}=PRODUCT_CONTEXT('',#9,'mechanical');\n#{}=PRODUCT_DEFINITION_FORMATION('','',#{});\n#{pd}=PRODUCT_DEFINITION('design','',#{},#8);\n#{}=PRODUCT_DEFINITION_SHAPE('','',#{pd});\n",
+        pd + 1,
+        pd + 2,
+        pd + 2,
+        pd + 3,
+        pd + 1,
+        pd + 3,
+        pd + 4
+    )
+}
+
+fn mm(len: f64) -> Context {
+    Context {
+        units: Units { len, ang: 1.0 },
+        uncertainty: Some(1.0E-6 * len),
+    }
+}
+
+fn product_of(entity: u64, name: &str) -> Product {
+    Product {
+        entity,
+        id: name.into(),
+        name: name.into(),
+        description: String::new(),
+    }
+}
+
+fn placement(origin: [f64; 3], axis: Option<[f64; 3]>, ref_direction: Option<[f64; 3]>) -> Frame {
+    Frame::Placement(Placement {
+        origin,
+        axis,
+        ref_direction,
+    })
+}
+
+/// A part in inches with a colour: SolidCraft's `hand_written_part_in_inches_with_colour`. The
+/// definition's shape is an empty representation linked to the one with the solid.
+#[test]
+fn a_part() {
+    let mut t = String::from(BASE);
+    t += &context(
+        20,
+        "(CONVERSION_BASED_UNIT('INCH',#30)LENGTH_UNIT()NAMED_UNIT(*));\n#30=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(25.4),#31);\n#31=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.))",
+    );
+    t += &product(50, "Widget");
+    t += "#60=ADVANCED_BREP_SHAPE_REPRESENTATION('brep',(#101,#65),#20);\n#61=SHAPE_DEFINITION_REPRESENTATION(#54,#62);\n#62=SHAPE_REPRESENTATION('',(),#20);\n#63=SHAPE_REPRESENTATION_RELATIONSHIP('','',#62,#60);\n";
+    t += "#65=AXIS2_PLACEMENT_3D('',#66,$,$);\n#66=CARTESIAN_POINT('',(0.,0.,0.));\n";
+    t += "#70=STYLED_ITEM('',(#71),#101);\n#71=PRESENTATION_STYLE_ASSIGNMENT((#72));\n#72=SURFACE_STYLE_USAGE(.BOTH.,#73);\n#73=SURFACE_SIDE_STYLE('',(#74));\n#74=SURFACE_STYLE_FILL_AREA(#75);\n#75=FILL_AREA_STYLE('',(#76));\n#76=FILL_AREA_STYLE_COLOUR('',#77);\n#77=COLOUR_RGB('',1.,0.5,0.);\n";
+    let inch = Context {
+        units: Units {
+            len: 25.4 * 1.0,
+            ang: 1.0,
+        },
+        uncertainty: Some(1.0E-6 * (25.4 * 1.0)),
+    };
+    assert_eq!(
+        structure(&t),
+        ProductStructure {
+            products: vec![product_of(51, "Widget")],
+            definitions: vec![Definition {
+                entity: 50,
+                id: "design".into(),
+                description: String::new(),
+                formation: 53,
+                product: 0,
+                shapes: vec![1],
+            }],
+            representations: vec![
+                Representation {
+                    entity: 60,
+                    kind: "ADVANCED_BREP_SHAPE_REPRESENTATION".into(),
+                    name: "brep".into(),
+                    items: vec![
+                        Item {
+                            entity: 101,
+                            name: "Cube".into(),
+                            kind: ItemKind::Body(BodyKind::ManifoldSolidBrep),
+                        },
+                        Item {
+                            entity: 65,
+                            name: String::new(),
+                            kind: ItemKind::Other("AXIS2_PLACEMENT_3D".into()),
+                        },
+                    ],
+                    context: Some(20),
+                    units: inch,
+                },
+                Representation {
+                    entity: 62,
+                    kind: "SHAPE_REPRESENTATION".into(),
+                    name: String::new(),
+                    items: Vec::new(),
+                    context: Some(20),
+                    units: inch,
+                },
+            ],
+            maps: Vec::new(),
+            links: vec![Link {
+                entity: 63,
+                rep_1: 1,
+                rep_2: 0,
+                transformation: None,
+            }],
+            occurrences: Vec::new(),
+            roots: vec![0],
+            styles: vec![StyledItem {
+                entity: 70,
+                name: String::new(),
+                item: 101,
+                overrides: None,
+                surface: vec![SurfaceStyle {
+                    side: Side::Both,
+                    fill: Some(Colour::Rgb {
+                        name: String::new(),
+                        rgb: [1.0, 0.5, 0.0],
+                    }),
+                    rendering: None,
+                    transparency: None,
+                }],
+                curve: Vec::new(),
+            }],
+        }
+    );
+}
+
+/// A solid outside any product: its representation is still read, and nothing else.
+#[test]
+fn a_loose_solid() {
+    let mut t = String::from(BASE);
+    t += &context(20, MM);
+    t += "#60=MANIFOLD_SURFACE_SHAPE_REPRESENTATION('',(#101),#20);\n";
+    let s = structure(&t);
+    assert_eq!(
+        (s.products.len(), s.definitions.len(), s.roots.len()),
+        (0, 0, 0)
+    );
+    assert_eq!(s.representations.len(), 1);
+    assert_eq!(s.representations[0].entity, 60);
+    assert_eq!(s.representations[0].units, mm(1e-3 * 1000.0));
+}
+
+/// The occurrence `#n` of `child` in `parent` placed by an `ITEM_DEFINED_TRANSFORMATION` of
+/// `item_1` (in `rep_1`) onto `item_2` (in `rep_2`): NAUO #n, its PDS #n+1, the transformation
+/// #n+2, the relationship #n+3, the CDSR #n+4.
+fn occurrence(
+    n: u64,
+    name: &str,
+    parent: u64,
+    child: u64,
+    reps: (u64, u64),
+    items: (u64, u64),
+) -> String {
+    let mut t = String::new();
+    let _ = write!(
+        t,
+        "#{n}=NEXT_ASSEMBLY_USAGE_OCCURRENCE('{n}','{name}','',#{parent},#{child},$);\n\
+#{}=PRODUCT_DEFINITION_SHAPE('','',#{n});\n\
+#{}=ITEM_DEFINED_TRANSFORMATION('','',#{},#{});\n\
+#{}=(REPRESENTATION_RELATIONSHIP('','',#{},#{})REPRESENTATION_RELATIONSHIP_WITH_TRANSFORMATION(#{})SHAPE_REPRESENTATION_RELATIONSHIP());\n\
+#{}=CONTEXT_DEPENDENT_SHAPE_REPRESENTATION(#{},#{});\n",
+        n + 1,
+        n + 2,
+        items.0,
+        items.1,
+        n + 3,
+        reps.0,
+        reps.1,
+        n + 2,
+        n + 4,
+        n + 3,
+        n + 1
+    );
+    t
+}
+
+/// Top uses Sub twice and Part once; Sub uses Part once. Sub's placements are in centimetres,
+/// Top's and Part's in millimetres. Four occurrences, six instances; the transformation is the
+/// two placements as written, each in its representation's unit.
+#[test]
+fn an_assembly_with_a_shared_sub_assembly() {
+    let mut t = String::from(BASE);
+    t += &context(20, CM);
+    t += &context(30, MM);
+    t += &product(50, "Top");
+    t += &product(70, "Sub");
+    t += &product(90, "Part");
+    // Top (mm): its own frame #161 and the places of its three components #163, #165, #167.
+    t += "#160=SHAPE_REPRESENTATION('Top',(#161,#163,#165,#167),#30);\n#162=SHAPE_DEFINITION_REPRESENTATION(#54,#160);\n";
+    t += "#161=AXIS2_PLACEMENT_3D('',#1610,$,$);\n#1610=CARTESIAN_POINT('',(0.,0.,0.));\n";
+    t += "#163=AXIS2_PLACEMENT_3D('',#1630,#1631,#1632);\n#1630=CARTESIAN_POINT('',(100.,0.,0.));\n#1631=DIRECTION('',(0.,0.,1.));\n#1632=DIRECTION('',(0.,2.,0.));\n";
+    t += "#165=AXIS2_PLACEMENT_3D('',#1650,$,$);\n#1650=CARTESIAN_POINT('',(0.,100.,0.));\n";
+    t += "#167=AXIS2_PLACEMENT_3D('',#1670,$,$);\n#1670=CARTESIAN_POINT('',(0.,0.,100.));\n";
+    // Sub (cm): its frame #171 and the place of its part #173.
+    t += "#170=SHAPE_REPRESENTATION('Sub',(#171,#173),#20);\n#172=SHAPE_DEFINITION_REPRESENTATION(#74,#170);\n";
+    t += "#171=AXIS2_PLACEMENT_3D('',#1710,$,$);\n#1710=CARTESIAN_POINT('',(1.,2.,3.));\n";
+    t += "#173=AXIS2_PLACEMENT_3D('',#1730,$,$);\n#1730=CARTESIAN_POINT('',(5.,0.,0.));\n";
+    // Part (mm): the solid and its frame.
+    t += "#180=ADVANCED_BREP_SHAPE_REPRESENTATION('Part',(#101,#181),#30);\n#182=SHAPE_DEFINITION_REPRESENTATION(#94,#180);\n";
+    t += "#181=AXIS2_PLACEMENT_3D('',#1810,$,$);\n#1810=CARTESIAN_POINT('',(0.,0.,0.));\n";
+    t += &occurrence(600, "Sub:1", 50, 70, (170, 160), (171, 163));
+    t += &occurrence(610, "Sub:2", 50, 70, (170, 160), (171, 165));
+    t += &occurrence(620, "Part:1", 70, 90, (180, 170), (181, 173));
+    t += &occurrence(630, "Part:2", 50, 90, (180, 160), (181, 167));
+    let s = structure(&t);
+    assert_eq!(
+        s.products,
+        [
+            product_of(51, "Top"),
+            product_of(71, "Sub"),
+            product_of(91, "Part")
+        ]
+    );
+    // Representations in id order: #160 Top, #170 Sub, #180 Part.
+    let shapes: Vec<_> = s
+        .definitions
+        .iter()
+        .map(|d| (d.entity, d.product, d.shapes.clone()))
+        .collect();
+    assert_eq!(
+        shapes,
+        [(50, 0, vec![0]), (70, 1, vec![1]), (90, 2, vec![2])]
+    );
+    assert_eq!(s.roots, [0]);
+    let occ: Vec<_> = s
+        .occurrences
+        .iter()
+        .map(|o| {
+            (
+                o.entity,
+                o.id.as_str(),
+                o.name.as_str(),
+                o.parent,
+                o.child,
+                o.placements.clone(),
+            )
+        })
+        .collect();
+    assert_eq!(
+        occ,
+        [
+            (600, "600", "Sub:1", 0, 1, vec![0]),
+            (610, "610", "Sub:2", 0, 1, vec![1]),
+            (620, "620", "Part:1", 1, 2, vec![2]),
+            (630, "630", "Part:2", 0, 2, vec![3]),
+        ]
+    );
+    assert_eq!(s.occurrences[0].reference_designator, None);
+    // Sub:1: Sub's frame (cm: 1, 2, 3 → 10, 20, 30 mm) onto Top's place for it, as written.
+    assert_eq!(
+        s.links[0],
+        Link {
+            entity: 603,
+            rep_1: 1,
+            rep_2: 0,
+            transformation: Some(Transformation::Items {
+                entity: 602,
+                item_1: placement([1.0 * CM_MM, 2.0 * CM_MM, 3.0 * CM_MM], None, None),
+                item_2: placement(
+                    [100.0, 0.0, 0.0],
+                    Some([0.0, 0.0, 1.0]),
+                    Some([0.0, 2.0, 0.0])
+                ),
+            }),
+        }
+    );
+    // Part:1: Part's frame (mm) onto Sub's place for it (cm: 5 → 50 mm).
+    assert_eq!(
+        s.links[2].transformation,
+        Some(Transformation::Items {
+            entity: 622,
+            item_1: placement([0.0; 3], None, None),
+            item_2: placement([5.0 * CM_MM, 0.0, 0.0], None, None),
+        })
+    );
+    // Expanded: Top; Sub:1 with its Part:1; Sub:2 with its Part:1; Part:2.
+    let inst = s.instances().unwrap();
+    assert_eq!(
+        inst,
+        [
+            Instance {
+                definition: 0,
+                occurrence: None,
+                parent: None
+            },
+            Instance {
+                definition: 1,
+                occurrence: Some(0),
+                parent: Some(0)
+            },
+            Instance {
+                definition: 2,
+                occurrence: Some(2),
+                parent: Some(1)
+            },
+            Instance {
+                definition: 1,
+                occurrence: Some(1),
+                parent: Some(0)
+            },
+            Instance {
+                definition: 2,
+                occurrence: Some(2),
+                parent: Some(3)
+            },
+            Instance {
+                definition: 2,
+                occurrence: Some(3),
+                parent: Some(0)
+            },
+        ]
+    );
+}
+
+/// SolidCraft's `exponential_assemblies_are_bounded`: P0 uses P1 twice, P1 uses P2 twice, … 30
+/// levels. Reading is linear (31 definitions, 60 occurrences); expanding stops at
+/// [`MAX_VISITS`]. Three levels expand to 1 + 2 + 4 + 8 instances.
+#[test]
+fn a_sub_assembly_shared_at_every_level_is_read_once() {
+    let levels = |n: u64| {
+        let mut t = String::from(BASE);
+        for l in 0..=n {
+            t += &product(1000 + l * 10, &format!("P{l}"));
+            if l < n {
+                for k in 0..2 {
+                    let _ = writeln!(
+                        t,
+                        "#{}=NEXT_ASSEMBLY_USAGE_OCCURRENCE('','','',#{},#{},$);",
+                        2000 + l * 10 + k,
+                        1000 + l * 10,
+                        1000 + (l + 1) * 10
+                    );
+                }
+            }
+        }
+        t
+    };
+    let s = structure(&levels(30));
+    assert_eq!(
+        (s.definitions.len(), s.occurrences.len(), s.roots.clone()),
+        (31, 60, vec![0])
+    );
+    assert_eq!(
+        s.instances(),
+        Err(format!("more than {MAX_VISITS} assembly instances"))
+    );
+    assert_eq!(structure(&levels(3)).instances().map(|i| i.len()), Ok(15));
+}
+
+/// A representation placed twice by `MAPPED_ITEM`s: once by a placement, once by a
+/// non-uniform operator. The map's origin is in the mapped representation's unit (inches), each
+/// target in the unit of the representation that lists it (millimetres).
+#[test]
+fn mapped_items() {
+    let mut t = String::from(BASE);
+    t += &context(20, MM);
+    t += &context(
+        30,
+        "(CONVERSION_BASED_UNIT('INCH',#40)LENGTH_UNIT()NAMED_UNIT(*));\n#40=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(25.4),#41);\n#41=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.))",
+    );
+    t += &product(50, "Holder");
+    t += "#60=SHAPE_REPRESENTATION('',(#110,#115),#20);\n#61=SHAPE_DEFINITION_REPRESENTATION(#54,#60);\n";
+    t += "#110=MAPPED_ITEM('first',#111,#112);\n#111=REPRESENTATION_MAP(#113,#120);\n";
+    t += "#112=AXIS2_PLACEMENT_3D('',#1120,#1121,$);\n#1120=CARTESIAN_POINT('',(5.,0.,0.));\n#1121=DIRECTION('',(0.,0.,-1.));\n";
+    t += "#113=AXIS2_PLACEMENT_3D('',#1130,$,$);\n#1130=CARTESIAN_POINT('',(1.,0.,0.));\n";
+    t += "#115=MAPPED_ITEM('second',#111,#116);\n";
+    t += "#116=CARTESIAN_TRANSFORMATION_OPERATOR_3D_NON_UNIFORM('','',#1161,$,#1160,2.,$,$,3.);\n#1160=CARTESIAN_POINT('',(0.,7.,0.));\n#1161=DIRECTION('',(0.,1.,0.));\n";
+    t += "#120=ADVANCED_BREP_SHAPE_REPRESENTATION('',(#101,#113),#30);\n";
+    let s = structure(&t);
+    assert_eq!(
+        s.representations[0].items,
+        [
+            Item {
+                entity: 110,
+                name: "first".into(),
+                kind: ItemKind::Mapped {
+                    map: 0,
+                    target: placement([5.0, 0.0, 0.0], Some([0.0, 0.0, -1.0]), None),
+                },
+            },
+            Item {
+                entity: 115,
+                name: "second".into(),
+                kind: ItemKind::Mapped {
+                    map: 0,
+                    target: Frame::Operator(Operator {
+                        axis1: Some([0.0, 1.0, 0.0]),
+                        axis2: None,
+                        axis3: None,
+                        origin: [0.0, 7.0, 0.0],
+                        scale: Some(2.0),
+                        scale2: None,
+                        scale3: Some(3.0),
+                    }),
+                },
+            },
+        ]
+    );
+    assert_eq!(
+        s.maps,
+        [RepresentationMap {
+            entity: 111,
+            origin: placement([1.0 * (25.4 * 1.0), 0.0, 0.0], None, None),
+            representation: 1,
+        }]
+    );
+    assert_eq!(s.representations[1].entity, 120);
+    assert_eq!(
+        s.representations[1].items[0].kind,
+        ItemKind::Body(BodyKind::ManifoldSolidBrep)
+    );
+}
+
+/// Colours on a body and on a face: a fill colour, a rendering colour with a transparency, a
+/// pre-defined colour, one ISO 10303-46 does not name, a curve style's colour, and an override.
+#[test]
+fn colours_of_bodies_and_faces() {
+    let mut t = String::from(BASE);
+    t += "#102=ADVANCED_FACE('',(),#103,.T.);\n#103=PLANE('',$);\n";
+    // The body: fill colour and the curve colour of its edges.
+    t += "#70=STYLED_ITEM('body',(#71,#78),#101);\n#71=PRESENTATION_STYLE_ASSIGNMENT((#72));\n#72=SURFACE_STYLE_USAGE(.POSITIVE.,#73);\n#73=SURFACE_SIDE_STYLE('',(#74));\n#74=SURFACE_STYLE_FILL_AREA(#75);\n#75=FILL_AREA_STYLE('',(#76));\n#76=FILL_AREA_STYLE_COLOUR('',#77);\n#77=COLOUR_RGB('steel',0.2,0.25,1.5);\n";
+    t += "#78=PRESENTATION_STYLE_ASSIGNMENT((#79));\n#79=CURVE_STYLE('',#80,POSITIVE_LENGTH_MEASURE(0.1),#81);\n#80=DRAUGHTING_PRE_DEFINED_CURVE_FONT('continuous');\n#81=DRAUGHTING_PRE_DEFINED_COLOUR('black');\n";
+    // The face, over the body's style: rendered red, a quarter transparent, filled 'mauve'.
+    t += "#90=OVER_RIDING_STYLED_ITEM('face',(#91),#102,#70);\n#91=PRESENTATION_STYLE_ASSIGNMENT((#92));\n#92=SURFACE_STYLE_USAGE(.BOTH.,#93);\n#93=SURFACE_SIDE_STYLE('',(#94,#97));\n";
+    t += "#94=SURFACE_STYLE_RENDERING_WITH_PROPERTIES(.NORMAL_SHADING.,#95,(#96));\n#95=DRAUGHTING_PRE_DEFINED_COLOUR('red');\n#96=SURFACE_STYLE_TRANSPARENT(0.25);\n";
+    t += "#97=SURFACE_STYLE_FILL_AREA(#98);\n#98=FILL_AREA_STYLE('',(#99));\n#99=FILL_AREA_STYLE_COLOUR('',#89);\n#89=DRAUGHTING_PRE_DEFINED_COLOUR('mauve');\n";
+    let s = structure(&t);
+    assert_eq!(
+        s.styles,
+        [
+            StyledItem {
+                entity: 70,
+                name: "body".into(),
+                item: 101,
+                overrides: None,
+                surface: vec![SurfaceStyle {
+                    side: Side::Positive,
+                    fill: Some(Colour::Rgb {
+                        name: "steel".into(),
+                        rgb: [0.2, 0.25, 1.5],
+                    }),
+                    rendering: None,
+                    transparency: None,
+                }],
+                curve: vec![Colour::PreDefined {
+                    name: "black".into(),
+                    rgb: Some([0.0, 0.0, 0.0]),
+                }],
+            },
+            StyledItem {
+                entity: 90,
+                name: "face".into(),
+                item: 102,
+                overrides: Some(70),
+                surface: vec![SurfaceStyle {
+                    side: Side::Both,
+                    fill: Some(Colour::PreDefined {
+                        name: "mauve".into(),
+                        rgb: None,
+                    }),
+                    rendering: Some(Colour::PreDefined {
+                        name: "red".into(),
+                        rgb: Some([1.0, 0.0, 0.0]),
+                    }),
+                    transparency: Some(0.25),
+                }],
+                curve: Vec::new(),
+            },
+        ]
+    );
+}
+
+/// ISO 10303-46's eight pre-defined colours.
+#[test]
+fn pre_defined_colours() {
+    let names = [
+        "red", "green", "blue", "yellow", "magenta", "cyan", "black", "white",
+    ];
+    let rgb: Vec<_> = names.iter().map(|n| super::pre_defined_rgb(n)).collect();
+    assert_eq!(
+        rgb,
+        [
+            Some([1.0, 0.0, 0.0]),
+            Some([0.0, 1.0, 0.0]),
+            Some([0.0, 0.0, 1.0]),
+            Some([1.0, 1.0, 0.0]),
+            Some([1.0, 0.0, 1.0]),
+            Some([0.0, 1.0, 1.0]),
+            Some([0.0, 0.0, 0.0]),
+            Some([1.0, 1.0, 1.0]),
+        ]
+    );
+    assert_eq!(super::pre_defined_rgb("Red"), None);
+}
+
+/// Names keep their escapes decoded, and are not trimmed.
+#[test]
+fn names_with_escapes() {
+    let mut t = String::from(BASE);
+    t += "#51=PRODUCT('P-\\X2\\00E9\\X0\\',' B\\X\\E4r ''7'' ','\\X2\\5706\\X0\\',(#52));\n#52=PRODUCT_CONTEXT('',#9,'mechanical');\n#53=PRODUCT_DEFINITION_FORMATION('','',#51);\n#50=PRODUCT_DEFINITION('d\\\\1',$,#53,#8);\n";
+    t += &product(70, "Child");
+    t += "#600=NEXT_ASSEMBLY_USAGE_OCCURRENCE('NAUO1','Gr\\X\\FC\\X\\DFe:1','',#50,#70,'R\\X2\\00E9\\X0\\f');\n";
+    let s = structure(&t);
+    assert_eq!(
+        s.products[0],
+        Product {
+            entity: 51,
+            id: "P-\u{e9}".into(),
+            name: " B\u{e4}r '7' ".into(),
+            description: "\u{5706}".into(),
+        }
+    );
+    assert_eq!(
+        (
+            s.definitions[0].id.as_str(),
+            s.definitions[0].description.as_str()
+        ),
+        ("d\\1", "")
+    );
+    let o = &s.occurrences[0];
+    assert_eq!(
+        (
+            o.id.as_str(),
+            o.name.as_str(),
+            o.reference_designator.as_deref()
+        ),
+        ("NAUO1", "Gr\u{fc}\u{df}e:1", Some("R\u{e9}f"))
+    );
+}
+
+/// A chain of `n` + 1 definitions, each the only component of the one before.
+fn chain(n: u64) -> String {
+    let mut t = String::from(BASE);
+    for l in 0..=n {
+        t += &product(1000 + l * 10, &format!("P{l}"));
+        if l < n {
+            let _ = writeln!(
+                t,
+                "#{}=NEXT_ASSEMBLY_USAGE_OCCURRENCE('','','',#{},#{},$);",
+                5000 + l,
+                1000 + l * 10,
+                1000 + (l + 1) * 10
+            );
+        }
+    }
+    t
+}
+
+#[test]
+fn nesting_is_bounded() {
+    let depth = MAX_ASSEMBLY_DEPTH as u64;
+    let s = structure(&chain(depth));
+    assert_eq!(s.instances().map(|i| i.len()), Ok(MAX_ASSEMBLY_DEPTH + 1));
+    assert_eq!(refused(&chain(depth + 1)), "assembly nested too deeply");
+}
+
+/// What is refused, with its message.
+#[test]
+fn refusals_say_why() {
+    let two = || {
+        let mut t = String::from(BASE);
+        t += &product(50, "A");
+        t += &product(70, "B");
+        t
+    };
+    // A contains B contains A (SolidCraft's `assembly_cycles_are_bounded`).
+    let cycle = two()
+        + "#90=NEXT_ASSEMBLY_USAGE_OCCURRENCE('1','','',#50,#70,$);\n#91=NEXT_ASSEMBLY_USAGE_OCCURRENCE('2','','',#70,#50,$);\n";
+    assert_eq!(refused(&cycle), "assembly cycle");
+    let itself = two() + "#90=NEXT_ASSEMBLY_USAGE_OCCURRENCE('1','','',#50,#50,$);\n";
+    assert_eq!(refused(&itself), "assembly cycle");
+    let missing_child = two() + "#90=NEXT_ASSEMBLY_USAGE_OCCURRENCE('1','','',#50,#999,$);\n";
+    assert_eq!(
+        refused(&missing_child),
+        "occurrence #90: #999: expected a PRODUCT_DEFINITION"
+    );
+    let not_a_definition = two() + "#90=NEXT_ASSEMBLY_USAGE_OCCURRENCE('1','','',#50,#51,$);\n";
+    assert_eq!(
+        refused(&not_a_definition),
+        "occurrence #90: #51: expected a PRODUCT_DEFINITION"
+    );
+    let missing_product = String::from(BASE)
+        + "#53=PRODUCT_DEFINITION_FORMATION('','',#51);\n#50=PRODUCT_DEFINITION('design','',#53,#8);\n";
+    assert_eq!(refused(&missing_product), "#51: expected a PRODUCT");
+    let missing_rep = two() + "#61=SHAPE_DEFINITION_REPRESENTATION(#54,#999);\n";
+    assert_eq!(refused(&missing_rep), "missing entity #999");
+    let not_a_rep = two() + "#61=SHAPE_DEFINITION_REPRESENTATION(#54,#101);\n";
+    assert_eq!(
+        refused(&not_a_rep),
+        "#101: expected a representation, found MANIFOLD_SOLID_BREP"
+    );
+    let missing_item = two()
+        + "#60=SHAPE_REPRESENTATION('',(#101,#999),$);\n#61=SHAPE_DEFINITION_REPRESENTATION(#54,#60);\n";
+    assert_eq!(refused(&missing_item), "missing entity #999");
+    let mapped = |rest: &str| {
+        two()
+            + "#60=SHAPE_REPRESENTATION('',(#110),$);\n#61=SHAPE_DEFINITION_REPRESENTATION(#54,#60);\n#110=MAPPED_ITEM('',#111,#112);\n#112=AXIS2_PLACEMENT_3D('',#113,$,$);\n#113=CARTESIAN_POINT('',(0.,0.,0.));\n"
+            + rest
+    };
+    assert_eq!(
+        refused(&mapped("#111=REPRESENTATION_MAP(#112,#60);\n")),
+        "mapped item cycle"
+    );
+    assert_eq!(
+        refused(&mapped("#111=SHAPE_REPRESENTATION('',(),$);\n")),
+        "#110: mapping source #111 is a SHAPE_REPRESENTATION, not a REPRESENTATION_MAP"
+    );
+    assert_eq!(
+        refused(&mapped("#111=REPRESENTATION_MAP(#112,#999);\n")),
+        "missing entity #999"
+    );
+    assert_eq!(
+        refused(&mapped(
+            "#111=REPRESENTATION_MAP(#112,#120);\n#120=SHAPE_REPRESENTATION('',(#101),$);\n"
+        )
+        .replace(
+            "#110=MAPPED_ITEM('',#111,#112);",
+            "#110=MAPPED_ITEM('',#111,#114);#114=CARTESIAN_TRANSFORMATION_OPERATOR_3D('','',$,$,#113,0.,$);"
+        )),
+        "mapped item #110: operator scale: expected a number other than zero"
+    );
+    assert_eq!(
+        refused(&mapped(
+            "#111=REPRESENTATION_MAP(#113,#120);\n#120=SHAPE_REPRESENTATION('',(#101),$);\n"
+        )),
+        "representation map #111: #113: expected a placement, found CARTESIAN_POINT"
+    );
+    let styled = |rest: &str| two() + rest;
+    assert_eq!(
+        refused(&styled("#170=STYLED_ITEM('',(),#999);\n")),
+        "styled item #170: missing entity #999"
+    );
+    assert_eq!(
+        refused(&styled(
+            "#170=STYLED_ITEM('',(#171),#101);\n#171=PRESENTATION_STYLE_ASSIGNMENT((#172));\n#172=SURFACE_STYLE_USAGE(.BOTH.,#173);\n#173=SURFACE_SIDE_STYLE('',(#174));\n#174=SURFACE_STYLE_RENDERING(.NORMAL_SHADING.,#175);\n#175=COLOUR_RGB('',1.,$,0.);\n"
+        )),
+        "styled item #170: green: expected a number"
+    );
+    let placed = two()
+        + "#60=SHAPE_REPRESENTATION('',(),$);\n#80=SHAPE_REPRESENTATION('',(),$);\n#90=NEXT_ASSEMBLY_USAGE_OCCURRENCE('1','','',#50,#70,$);\n#91=PRODUCT_DEFINITION_SHAPE('','',#90);\n#93=(REPRESENTATION_RELATIONSHIP('','',#60,#80)REPRESENTATION_RELATIONSHIP_WITH_TRANSFORMATION(#92)SHAPE_REPRESENTATION_RELATIONSHIP());\n#94=CONTEXT_DEPENDENT_SHAPE_REPRESENTATION(#93,#91);\n";
+    assert_eq!(refused(&placed), "relationship #93: missing entity #92");
+}

solidcore/crates/solidcore-record/src/step/units.rs

@@ -0,0 +1,466 @@
+//! The units of a representation context (ISO 10303-41 measures and units, ISO 10303-43
+//! representation contexts): `GLOBAL_UNIT_ASSIGNED_CONTEXT`'s length and plane angle units and
+//! `GLOBAL_UNCERTAINTY_ASSIGNED_CONTEXT`'s distance uncertainty, read from a parsed
+//! [`Exchange`]. Missing or malformed units read as millimetres and radians; nothing here fails.
+//!
+//! A unit is a factor: millimetres per file length unit, radians per file plane angle unit. An
+//! SI unit is its prefix times its base (`METRE` = 1000 mm, `RADIAN` = 1 rad); a
+//! `CONVERSION_BASED_UNIT` is the value of its measure times the factor of the measure's own unit
+//! (an inch is `LENGTH_MEASURE(25.4)` of millimetres, a degree `PLANE_ANGLE_MEASURE(0.01745…)`
+//! of radians). Only multiplications: the factor of a degree is the number the file writes, not
+//! a π computed here (the record computes no geometric quantity, docs/layers.md §4).
+//!
+//! Origin: SolidCraft's `crates/step/src/units.rs` and the `Units` type of
+//! `crates/step/src/read.rs` at `a5b71ca2` (MIT OR Apache-2.0), carried over with their
+//! behaviour unchanged.
+//!
+//! Deviations from SolidCraft: [`Units`] lives here (it was in `read.rs`, which is not carried
+//! over yet). The nesting bound of a `CONVERSION_BASED_UNIT` chain is the named
+//! `MAX_CONVERSION_DEPTH` (was the literal 4). Otherwise only formatting and doc comments on every
+//! public item.
+
+use super::p21::{Exchange, Param};
+
+/// Most `CONVERSION_BASED_UNIT` links followed from one unit (a unit defined from a unit defined
+/// from …); a deeper chain, or a cycle, reads as no unit.
+const MAX_CONVERSION_DEPTH: usize = 4;
+
+/// The units of a representation context.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct Units {
+    /// Millimetres per file length unit.
+    pub len: f64,
+    /// Radians per file plane angle unit.
+    pub ang: f64,
+}
+
+impl Default for Units {
+    /// Millimetres and radians.
+    fn default() -> Self {
+        Units { len: 1.0, ang: 1.0 }
+    }
+}
+
+/// What a representation context says about its numbers.
+#[derive(Clone, Copy, Debug, Default, PartialEq)]
+pub struct Context {
+    /// The length and plane angle units (millimetres and radians where the context names none
+    /// that can be read).
+    pub units: Units,
+    /// The context's distance uncertainty in millimetres (the last `UNCERTAINTY_MEASURE_WITH_UNIT`
+    /// it lists), if any.
+    pub uncertainty: Option<f64>,
+}
+
+/// The factor of an SI prefix (`$` or an unknown prefix: 1).
+fn si_prefix(p: Option<&Param>) -> f64 {
+    match p.and_then(Param::as_enum) {
+        Some("EXA") => 1e18,
+        Some("PETA") => 1e15,
+        Some("TERA") => 1e12,
+        Some("GIGA") => 1e9,
+        Some("MEGA") => 1e6,
+        Some("KILO") => 1e3,
+        Some("HECTO") => 1e2,
+        Some("DECA") => 1e1,
+        Some("DECI") => 1e-1,
+        Some("CENTI") => 1e-2,
+        Some("MILLI") => 1e-3,
+        Some("MICRO") => 1e-6,
+        Some("NANO") => 1e-9,
+        Some("PICO") => 1e-12,
+        Some("FEMTO") => 1e-15,
+        Some("ATTO") => 1e-18,
+        _ => 1.0,
+    }
+}
+
+/// What a unit measures.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum UnitKind {
+    /// A `LENGTH_UNIT`.
+    Length,
+    /// A `PLANE_ANGLE_UNIT`.
+    Angle,
+    /// Any other unit (solid angle, mass, …).
+    Other,
+}
+
+/// A unit's kind and size: millimetres for lengths, radians for plane angles (1 for anything
+/// else, or a unit that cannot be read). `None` when `#id` is not an entity, or is a
+/// `CONVERSION_BASED_UNIT` whose measure cannot be read or is not finite and positive.
+pub fn unit_factor(ex: &Exchange, id: u64) -> Option<(UnitKind, f64)> {
+    factor(ex, id, 0)
+}
+
+fn factor(ex: &Exchange, id: u64, depth: usize) -> Option<(UnitKind, f64)> {
+    if depth > MAX_CONVERSION_DEPTH {
+        return None;
+    }
+    let e = ex.get(id)?;
+    let kind = if e.has("LENGTH_UNIT") {
+        UnitKind::Length
+    } else if e.has("PLANE_ANGLE_UNIT") {
+        UnitKind::Angle
+    } else {
+        UnitKind::Other
+    };
+    if let Some(si) = e.record("SI_UNIT") {
+        let base = match si.get(1).and_then(Param::as_enum) {
+            Some("METRE") => 1000.0,
+            Some("RADIAN") => 1.0,
+            _ => return Some((kind, 1.0)),
+        };
+        return Some((kind, si_prefix(si.first()) * base));
+    }
+    if let Some(cb) = e.record("CONVERSION_BASED_UNIT") {
+        let m = ex.get(cb.get(1)?.as_ref_id()?)?;
+        let mp = m.params();
+        let v = mp.first()?.as_f64()?;
+        let (_, f) = factor(ex, mp.get(1)?.as_ref_id()?, depth + 1)?;
+        let x = v * f;
+        return (x.is_finite() && x > 0.0).then_some((kind, x));
+    }
+    Some((kind, 1.0))
+}
+
+/// The units and uncertainty of the representation context `#id` (the defaults when `#id` is
+/// not an entity or lists no readable unit).
+///
+/// Each unit `GLOBAL_UNIT_ASSIGNED_CONTEXT` lists that reads as a finite, positive length or
+/// plane angle factor sets that unit; a later one wins. Each `UNCERTAINTY_MEASURE_WITH_UNIT` that
+/// `GLOBAL_UNCERTAINTY_ASSIGNED_CONTEXT` lists sets the uncertainty to its value times the factor
+/// of its unit (the context's length unit when that cannot be read), or clears it when the
+/// product is not finite and positive; the last one wins.
+pub fn context(ex: &Exchange, id: u64) -> Context {
+    let mut c = Context::default();
+    let Some(e) = ex.get(id) else { return c };
+    if let Some(units) = e
+        .record("GLOBAL_UNIT_ASSIGNED_CONTEXT")
+        .and_then(<[Param]>::first)
+        .and_then(Param::as_list)
+    {
+        for uid in units.iter().filter_map(Param::as_ref_id) {
+            match unit_factor(ex, uid) {
+                Some((UnitKind::Length, f)) if f.is_finite() && f > 0.0 => c.units.len = f,
+                Some((UnitKind::Angle, f)) if f.is_finite() && f > 0.0 => c.units.ang = f,
+                _ => {}
+            }
+        }
+    }
+    if let Some(unc) = e
+        .record("GLOBAL_UNCERTAINTY_ASSIGNED_CONTEXT")
+        .and_then(<[Param]>::first)
+        .and_then(Param::as_list)
+    {
+        for uid in unc.iter().filter_map(Param::as_ref_id) {
+            if let Some(m) = ex.get(uid)
+                && let Some(v) = m.params().first().and_then(Param::as_f64)
+            {
+                let f = m
+                    .params()
+                    .get(1)
+                    .and_then(Param::as_ref_id)
+                    .and_then(|x| unit_factor(ex, x))
+                    .map(|x| x.1);
+                c.uncertainty =
+                    Some(v * f.unwrap_or(c.units.len)).filter(|t| t.is_finite() && *t > 0.0);
+            }
+        }
+    }
+    c
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::step::p21;
+    use std::f64::consts::PI;
+    use std::fmt::Write as _;
+
+    /// Millimetres, radians and steradians as SolidCraft's writer and its topology tests
+    /// (`crates/step/src/topology_tests.rs`, `file`) write them.
+    const MM: &str = "#1=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.));\
+         #2=(NAMED_UNIT(*)PLANE_ANGLE_UNIT()SI_UNIT($,.RADIAN.));\
+         #3=(NAMED_UNIT(*)SI_UNIT($,.STERADIAN.)SOLID_ANGLE_UNIT());";
+
+    fn parse(data: &str) -> Exchange {
+        let t = format!(
+            "ISO-10303-21;\nHEADER;FILE_SCHEMA(('AUTOMOTIVE_DESIGN'));ENDSEC;\nDATA;\n{data}\nENDSEC;\nEND-ISO-10303-21;\n"
+        );
+        match p21::parse(&t) {
+            Ok(ex) => ex,
+            Err(e) => panic!("{e}\n{t}"),
+        }
+    }
+
+    /// A context `#100` with the units `units` and the uncertainties `unc` (entity ids).
+    fn ctx(data: &str, units: &str, unc: &str) -> Context {
+        let c = format!(
+            "#100=(GEOMETRIC_REPRESENTATION_CONTEXT(3)GLOBAL_UNCERTAINTY_ASSIGNED_CONTEXT(({unc}))\
+             GLOBAL_UNIT_ASSIGNED_CONTEXT(({units}))REPRESENTATION_CONTEXT('',''));"
+        );
+        context(&parse(&format!("{data}{c}")), 100)
+    }
+
+    #[test]
+    fn solidcraft_file_context() {
+        // SolidCraft's topology test file: mm, rad, sr and an uncertainty of 1e-7 mm.
+        let c = ctx(
+            &format!(
+                "{MM}#4=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(1.E-07),#1,'distance_accuracy_value','');"
+            ),
+            "#1,#2,#3",
+            "#4",
+        );
+        assert_eq!(c.units, Units { len: 1.0, ang: 1.0 });
+        // 1e-7 times MILLI (1e-3) times METRE (1000 mm).
+        assert_eq!(c.uncertainty, Some(1e-7 * (1e-3 * 1000.0)));
+    }
+
+    #[test]
+    fn si_prefixes() {
+        for (prefix, mm) in [
+            (".MILLI.", 1e-3 * 1000.0),
+            ("$", 1000.0),
+            (".MICRO.", 1e-6 * 1000.0),
+            (".CENTI.", 1e-2 * 1000.0),
+            (".KILO.", 1e3 * 1000.0),
+        ] {
+            let c = ctx(
+                &format!("#1=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT({prefix},.METRE.));"),
+                "#1",
+                "",
+            );
+            assert_eq!(c.units.len, mm, "{prefix}");
+            assert_eq!(c.units.ang, 1.0, "{prefix}");
+            assert_eq!(c.uncertainty, None, "{prefix}");
+        }
+        // The products the table defines: a millimetre is exactly 1, a metre 1000.
+        assert_eq!(1e-3 * 1000.0, 1.0);
+        let ex = parse("#1=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MICRO.,.METRE.));");
+        assert_eq!(unit_factor(&ex, 1), Some((UnitKind::Length, 1e-6 * 1000.0)));
+        // A milliradian.
+        let ex = parse("#1=(NAMED_UNIT(*)PLANE_ANGLE_UNIT()SI_UNIT(.MILLI.,.RADIAN.));");
+        assert_eq!(unit_factor(&ex, 1), Some((UnitKind::Angle, 1e-3)));
+    }
+
+    #[test]
+    fn inches_and_degrees() {
+        // An inch as 25.4 mm, a degree as π/180 rad (written as the shortest decimal of
+        // PI / 180, so it reads as exactly that double).
+        let data = format!(
+            "{MM}#10=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(25.4),#1);\
+             #11=(CONVERSION_BASED_UNIT('INCH',#10)LENGTH_UNIT()NAMED_UNIT(#12));\
+             #12=DIMENSIONAL_EXPONENTS(1.,0.,0.,0.,0.,0.,0.);\
+             #13=PLANE_ANGLE_MEASURE_WITH_UNIT(PLANE_ANGLE_MEASURE(0.017453292519943295),#2);\
+             #14=(CONVERSION_BASED_UNIT('DEGREE',#13)NAMED_UNIT(#15)PLANE_ANGLE_UNIT());\
+             #15=DIMENSIONAL_EXPONENTS(0.,0.,0.,0.,0.,0.,0.);"
+        );
+        let c = ctx(&data, "#11,#14,#3", "");
+        assert_eq!(
+            c.units,
+            Units {
+                len: 25.4,
+                ang: PI / 180.0
+            }
+        );
+        // An inch defined from metres: 0.0254 times 1000 mm.
+        let c = ctx(
+            "#1=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT($,.METRE.));\
+             #10=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(0.0254),#1);\
+             #11=(CONVERSION_BASED_UNIT('INCH',#10)LENGTH_UNIT()NAMED_UNIT(*));",
+            "#11",
+            "",
+        );
+        assert_eq!(c.units.len, 0.0254 * 1000.0);
+        // A foot defined from the inch: a chain of two conversions, 12 times 25.4 mm.
+        let c = ctx(
+            &format!(
+                "{data}#20=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(12.),#11);\
+                 #21=(CONVERSION_BASED_UNIT('FOOT',#20)LENGTH_UNIT()NAMED_UNIT(*));"
+            ),
+            "#21",
+            "",
+        );
+        assert_eq!(c.units.len, 12.0 * 25.4);
+    }
+
+    #[test]
+    fn missing_or_broken_units_read_as_mm_and_rad() {
+        let mm_rad = Units { len: 1.0, ang: 1.0 };
+        // No such context, or a context without units.
+        assert_eq!(context(&parse(MM), 100), Context::default());
+        assert_eq!(context(&parse(MM), 1), Context::default());
+        assert_eq!(Context::default().units, mm_rad);
+        for (data, units) in [
+            // Dangling references.
+            ("", "#7,#8"),
+            // An SI unit with an unknown base: factor 1.
+            (
+                "#1=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.FURLONG.));",
+                "#1",
+            ),
+            // A conversion whose measure is missing, unreadable, zero, negative or infinite.
+            (
+                "#1=(CONVERSION_BASED_UNIT('INCH',#9)LENGTH_UNIT()NAMED_UNIT(*));",
+                "#1",
+            ),
+            (
+                "#2=(NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.)LENGTH_UNIT());\
+                 #3=LENGTH_MEASURE_WITH_UNIT($,#2);\
+                 #1=(CONVERSION_BASED_UNIT('INCH',#3)LENGTH_UNIT()NAMED_UNIT(*));",
+                "#1",
+            ),
+            (
+                "#2=(NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.)LENGTH_UNIT());\
+                 #3=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(0.),#2);\
+                 #1=(CONVERSION_BASED_UNIT('INCH',#3)LENGTH_UNIT()NAMED_UNIT(*));",
+                "#1",
+            ),
+            (
+                "#2=(NAMED_UNIT(*)PLANE_ANGLE_UNIT()SI_UNIT($,.RADIAN.));\
+                 #3=PLANE_ANGLE_MEASURE_WITH_UNIT(PLANE_ANGLE_MEASURE(-1.),#2);\
+                 #1=(CONVERSION_BASED_UNIT('DEGREE',#3)PLANE_ANGLE_UNIT()NAMED_UNIT(*));",
+                "#1",
+            ),
+            (
+                "#2=(NAMED_UNIT(*)SI_UNIT(.EXA.,.METRE.)LENGTH_UNIT());\
+                 #3=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(1.E300),#2);\
+                 #1=(CONVERSION_BASED_UNIT('BIG',#3)LENGTH_UNIT()NAMED_UNIT(*));",
+                "#1",
+            ),
+            // A conversion that refers to itself: the depth bound ends it.
+            (
+                "#3=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(2.),#1);\
+                 #1=(CONVERSION_BASED_UNIT('LOOP',#3)LENGTH_UNIT()NAMED_UNIT(*));",
+                "#1",
+            ),
+            // Units that are neither lengths nor plane angles.
+            (MM, "#3"),
+            // An empty list.
+            (MM, ""),
+        ] {
+            let c = ctx(data, units, "");
+            assert_eq!(c.units, mm_rad, "{data} / {units}");
+        }
+        // A unit list that is not a list.
+        let ex = parse(&format!(
+            "{MM}#100=(GEOMETRIC_REPRESENTATION_CONTEXT(3)GLOBAL_UNIT_ASSIGNED_CONTEXT(#1)REPRESENTATION_CONTEXT('',''));"
+        ));
+        assert_eq!(context(&ex, 100), Context::default());
+        // A broken length unit leaves the readable angle unit in place.
+        let c = ctx(
+            "#2=(NAMED_UNIT(*)PLANE_ANGLE_UNIT()SI_UNIT(.MILLI.,.RADIAN.));\
+             #1=(CONVERSION_BASED_UNIT('INCH',#9)LENGTH_UNIT()NAMED_UNIT(*));",
+            "#1,#2",
+            "",
+        );
+        assert_eq!(
+            c.units,
+            Units {
+                len: 1.0,
+                ang: 1e-3
+            }
+        );
+    }
+
+    #[test]
+    fn conversion_depth_is_bounded() {
+        // #1 is millimetres; #2..=#7 each 2 of the one before, so #(1+k) is 2^k mm and
+        // MAX_CONVERSION_DEPTH links are followed from the unit asked for.
+        let mut data = String::from("#1=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.MILLI.,.METRE.));");
+        for k in 2..=7 {
+            write!(
+                data,
+                "#{m}=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(2.),#{p});\
+                 #{k}=(CONVERSION_BASED_UNIT('U',#{m})LENGTH_UNIT()NAMED_UNIT(*));",
+                m = 100 + k,
+                p = k - 1
+            )
+            .unwrap();
+        }
+        let ex = parse(&data);
+        assert_eq!(unit_factor(&ex, 5), Some((UnitKind::Length, 16.0)));
+        assert_eq!(unit_factor(&ex, 6), None);
+    }
+
+    #[test]
+    fn uncertainty_in_file_units() {
+        let inch = format!(
+            "{MM}#10=LENGTH_MEASURE_WITH_UNIT(LENGTH_MEASURE(25.4),#1);\
+             #11=(CONVERSION_BASED_UNIT('INCH',#10)LENGTH_UNIT()NAMED_UNIT(*));"
+        );
+        // 1e-4 inch is 1e-4 * 25.4 mm.
+        let c = ctx(
+            &format!("{inch}#20=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(1.E-04),#11,'d','');"),
+            "#11,#2",
+            "#20",
+        );
+        assert_eq!(c.units.len, 25.4);
+        assert_eq!(c.uncertainty, Some(1e-4 * 25.4));
+        // A measure in metres in an inch context: its own unit, 1e-6 * 1000 mm.
+        let c = ctx(
+            &format!(
+                "{inch}#12=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT($,.METRE.));\
+                 #20=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(1.E-06),#12,'d','');"
+            ),
+            "#11",
+            "#20",
+        );
+        assert_eq!(c.uncertainty, Some(1e-6 * 1000.0));
+        // A measure whose unit cannot be read is in the context's length unit.
+        let c = ctx(
+            &format!("{inch}#20=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(1.E-04),$,'d','');"),
+            "#11",
+            "#20",
+        );
+        assert_eq!(c.uncertainty, Some(1e-4 * 25.4));
+        // The last one listed wins.
+        let c = ctx(
+            &format!(
+                "{MM}#20=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(1.E-04),#1,'d','');\
+                 #21=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(2.E-04),#1,'d','');"
+            ),
+            "#1",
+            "#20,#21",
+        );
+        assert_eq!(c.uncertainty, Some(2e-4 * (1e-3 * 1000.0)));
+    }
+
+    #[test]
+    fn uncertainty_zero_negative_or_infinite_is_none() {
+        for v in ["0.", "-1.E-04", "1.E300"] {
+            // In exametres (1e21 mm): 0, negative, and 1e300 * 1e21 mm, which is infinite.
+            let c = ctx(
+                &format!(
+                    "{MM}#12=(LENGTH_UNIT()NAMED_UNIT(*)SI_UNIT(.EXA.,.METRE.));\
+                     #20=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE({v}),#12,'d','');"
+                ),
+                "#1",
+                "#20",
+            );
+            assert_eq!(c.uncertainty, None, "{v}");
+        }
+        // A bad one after a good one clears it (the last one wins).
+        let c = ctx(
+            &format!(
+                "{MM}#20=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(1.E-04),#1,'d','');\
+                 #21=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(0.),#1,'d','');"
+            ),
+            "#1",
+            "#20,#21",
+        );
+        assert_eq!(c.uncertainty, None);
+        // One without a readable value, or a dangling reference, is skipped.
+        let c = ctx(
+            &format!(
+                "{MM}#20=UNCERTAINTY_MEASURE_WITH_UNIT(LENGTH_MEASURE(1.E-04),#1,'d','');\
+                 #21=UNCERTAINTY_MEASURE_WITH_UNIT($,#1,'d','');"
+            ),
+            "#1",
+            "#20,#21,#99",
+        );
+        assert_eq!(c.uncertainty, Some(1e-4 * (1e-3 * 1000.0)));
+    }
+}

solidcore/crates/solidcore-record/tests/step_p21_corpus.rs

@@ -1,4 +1,5 @@
-//! The Part 21 parser over a STEP corpus: every file parses.
+//! The Part 21 parser over a STEP corpus: every file parses, the units of its representation
+//! contexts, and its Part 42 curves and surfaces.
 //!
 //! Ignored by default; the corpus is not in the repository. Run it with the directory of
 //! `.stp` / `.step` files (read in place, recursively) in `SOLIDCORE_STEP_CORPUS`:
@@ -13,6 +14,31 @@
 //! caller holding the file's bytes would. The test fails when any file does not parse. The
 //! STEP files committed to the repository are parsed by `repository_files_parse`, which always
 //! runs.
+//!
+//! `corpus_units` (ignored too, same variable and command with `corpus_units` as the filter)
+//! reads every geometric representation context with assigned units in each file and prints
+//! one line per file and a table of how often each length and plane angle unit occurs, and
+//! how many contexts state an uncertainty. It fails when a file does not parse. Files with no
+//! context whose length unit can be read are listed and counted, not failed: a file written
+//! with Part 21 short names (`SUNT`, `LNGUNT`, `GMRPCN`, …) or one without geometry has none.
+//!
+//! `corpus_geometry` (ignored too, same variable, `corpus_geometry` as the filter) reads every
+//! curve and surface entity of each file with `step::read::Reader`, in the units of the file's
+//! first geometric context: curves in model space with `curve`, the curves of a parameter space
+//! through their `PCURVE` with `pcurve`, surfaces with `surface`. It prints one line per file
+//! and, per group and entity kind, how many were read and how many refused, with the reasons.
+//! It also lists the entities where a check the record no longer makes (a direction shorter than
+//! 1e-12, unit factors equal within 1e-12) would have decided otherwise. It fails when a file
+//! does not parse; refusals are counted, not failed.
+//!
+//! `corpus_product` (ignored too, same variable, `corpus_product` as the filter) reads the
+//! product structure of each file with `step::product::read` and expands its assembly tree. It
+//! prints one line per file and the files with assemblies, and checks the structure against the
+//! file's own entity counts: products, definitions, occurrences, body items (every solid the
+//! file has is an item of a representation the structure holds), relationships with a
+//! transformation and styled items must all be there; a mapped item it does not hold must be
+//! listed only by representations it does not reach (counted by the kind that lists them). It
+//! fails when a file does not parse, is refused, or a count differs.
 
 #![allow(
     clippy::unwrap_used,
@@ -21,9 +47,11 @@
     clippy::indexing_slicing
 )] // test
 
+use std::collections::BTreeMap;
 use std::path::{Path, PathBuf};
 
 use solidcore_record::step::p21;
+use solidcore_record::step::units::{self, UnitKind};
 
 fn files(dir: &Path, out: &mut Vec<PathBuf>) {
     let Ok(entries) = std::fs::read_dir(dir) else {
@@ -109,6 +137,116 @@ fn corpus_parses() {
     );
 }
 
+/// A length factor's name (millimetres per unit).
+fn length_name(f: f64) -> String {
+    match f {
+        1.0 => "mm".into(),
+        25.4 => "inch".into(),
+        1000.0 => "m".into(),
+        10.0 => "cm".into(),
+        304.8 => "foot".into(),
+        _ => format!("{f} mm"),
+    }
+}
+
+/// A plane angle factor's name (radians per unit). A degree is the number the file writes:
+/// `degree` when it is π/180 to 12 digits or more, else the written factor, so a file that
+/// rounds π/180 shorter (`0.0174532925`) shows in the table as what it is.
+fn angle_name(f: f64) -> String {
+    if f == 1.0 {
+        "rad".into()
+    } else if (f - std::f64::consts::PI / 180.0).abs() <= 1e-14 {
+        "degree".into()
+    } else {
+        format!("{f} rad")
+    }
+}
+
+#[test]
+#[ignore = "needs a STEP corpus in SOLIDCORE_STEP_CORPUS"]
+fn corpus_units() {
+    let Some(dir) = std::env::var_os("SOLIDCORE_STEP_CORPUS") else {
+        eprintln!("SOLIDCORE_STEP_CORPUS is not set");
+        return;
+    };
+    let root = Path::new(&dir);
+    let mut paths = Vec::new();
+    files(root, &mut paths);
+    assert!(!paths.is_empty(), "no STEP files under {dir:?}");
+    let mut failures = Vec::new();
+    let mut unread = Vec::new();
+    let mut lengths: BTreeMap<String, usize> = BTreeMap::new();
+    let mut angles: BTreeMap<String, usize> = BTreeMap::new();
+    let (mut contexts, mut with_uncertainty, mut files_read) = (0usize, 0usize, 0usize);
+    for path in &paths {
+        let name = path
+            .strip_prefix(root)
+            .unwrap_or(path)
+            .display()
+            .to_string();
+        let ex = match std::fs::read(path)
+            .map_err(|e| e.to_string())
+            .and_then(|b| p21::parse(&String::from_utf8_lossy(&b)).map_err(|e| e.to_string()))
+        {
+            Ok(ex) => ex,
+            Err(e) => {
+                println!("{name}: ERROR {e}");
+                failures.push(format!("{name}: {e}"));
+                continue;
+            }
+        };
+        let mut here = Vec::new();
+        let mut readable = false;
+        for (&id, e) in &ex.entities {
+            if !(e.has("GEOMETRIC_REPRESENTATION_CONTEXT") && e.has("GLOBAL_UNIT_ASSIGNED_CONTEXT"))
+            {
+                continue;
+            }
+            // Whether the context names a length unit that reads as a factor, rather than
+            // falling back to millimetres.
+            readable |= e
+                .record("GLOBAL_UNIT_ASSIGNED_CONTEXT")
+                .and_then(<[p21::Param]>::first)
+                .and_then(p21::Param::as_list)
+                .is_some_and(|l| {
+                    l.iter().filter_map(p21::Param::as_ref_id).any(|u| {
+                        matches!(units::unit_factor(&ex, u),
+                            Some((UnitKind::Length, f)) if f.is_finite() && f > 0.0)
+                    })
+                });
+            let c = units::context(&ex, id);
+            contexts += 1;
+            with_uncertainty += usize::from(c.uncertainty.is_some());
+            let (l, a) = (length_name(c.units.len), angle_name(c.units.ang));
+            *lengths.entry(l.clone()).or_default() += 1;
+            *angles.entry(a.clone()).or_default() += 1;
+            here.push(format!("#{id} {l}/{a} uncertainty {:?}", c.uncertainty));
+        }
+        println!("{name}: {} contexts: {}", here.len(), here.join(", "));
+        if readable {
+            files_read += 1;
+        } else {
+            println!("{name}: no context with a readable length unit");
+            unread.push(name);
+        }
+    }
+    println!(
+        "{files_read} of {} files have a context with a readable length unit; {contexts} contexts, {with_uncertainty} with an uncertainty",
+        paths.len()
+    );
+    println!("length units (contexts): {lengths:?}");
+    println!("plane angle units (contexts): {angles:?}");
+    println!(
+        "no context with a readable length unit: {} files {unread:?}",
+        unread.len()
+    );
+    assert!(
+        failures.is_empty(),
+        "files that did not parse:\n{}",
+        failures.join("\n")
+    );
+}
+
 /// The STEP files in the repository parse to every instance they hold, each id once: a parser
 /// that dropped or merged instances would change the counts (the instance lines in the files).
 #[test]
@@ -130,3 +268,508 @@ fn repository_files_parse() {
         assert!(ex.duplicates.is_empty(), "{path}: {:?}", ex.duplicates);
     }
 }
+
+/// Curve entity names (simple instances) the corpus count looks at: every one the reader maps,
+/// and the other ISO 10303-42 curves a file may hold, which it refuses.
+const CURVES: &[&str] = &[
+    "B_SPLINE_CURVE",
+    "B_SPLINE_CURVE_WITH_KNOTS",
+    "BEZIER_CURVE",
+    "BOUNDED_SURFACE_CURVE",
+    "CIRCLE",
+    "CLOTHOID",
+    "COMPOSITE_CURVE",
+    "COMPOSITE_CURVE_ON_SURFACE",
+    "CURVE_REPLICA",
+    "ELLIPSE",
+    "HYPERBOLA",
+    "INTERSECTION_CURVE",
+    "LINE",
+    "OFFSET_CURVE_2D",
+    "OFFSET_CURVE_3D",
+    "PARABOLA",
+    "POLYLINE",
+    "QUASI_UNIFORM_CURVE",
+    "SEAM_CURVE",
+    "SURFACE_CURVE",
+    "TRIMMED_CURVE",
+    "UNIFORM_CURVE",
+];
+
+/// Surface entity names, likewise.
+const SURFACES: &[&str] = &[
+    "B_SPLINE_SURFACE",
+    "B_SPLINE_SURFACE_WITH_KNOTS",
+    "BEZIER_SURFACE",
+    "CONICAL_SURFACE",
+    "CURVE_BOUNDED_SURFACE",
+    "CYLINDRICAL_SURFACE",
+    "DEGENERATE_TOROIDAL_SURFACE",
+    "OFFSET_SURFACE",
+    "ORIENTED_SURFACE",
+    "PLANE",
+    "QUASI_UNIFORM_SURFACE",
+    "RECTANGULAR_COMPOSITE_SURFACE",
+    "RECTANGULAR_TRIMMED_SURFACE",
+    "SPHERICAL_SURFACE",
+    "SURFACE_OF_LINEAR_EXTRUSION",
+    "SURFACE_OF_REVOLUTION",
+    "SURFACE_REPLICA",
+    "TOROIDAL_SURFACE",
+    "UNIFORM_SURFACE",
+];
+
+/// Whether `e` is a curve or a surface for the count, and its kind: the entity name, or for a
+/// complex instance `(B_SPLINE_CURVE …)` with `rational` when it is.
+fn geometry_kind(e: &p21::Entity) -> Option<(bool, String)> {
+    if e.is_complex() {
+        let rational = if e.has("RATIONAL_B_SPLINE_CURVE") || e.has("RATIONAL_B_SPLINE_SURFACE") {
+            " rational"
+        } else {
+            ""
+        };
+        let is_curve =
+            e.has("B_SPLINE_CURVE") || e.records.iter().any(|r| CURVES.contains(&r.name.as_str()));
+        let is_surface = e.has("B_SPLINE_SURFACE")
+            || e.records
+                .iter()
+                .any(|r| SURFACES.contains(&r.name.as_str()));
+        let names: Vec<&str> = e
+            .records
+            .iter()
+            .map(|r| r.name.as_str())
+            .filter(|n| CURVES.contains(n) || SURFACES.contains(n))
+            .collect();
+        let kind = format!("({}){rational}", names.join(" "));
+        return match (is_curve, is_surface) {
+            (true, false) => Some((true, kind)),
+            (false, true) => Some((false, kind)),
+            _ => None,
+        };
+    }
+    let n = e.name();
+    if CURVES.contains(&n) {
+        Some((true, n.to_string()))
+    } else if SURFACES.contains(&n) {
+        Some((false, n.to_string()))
+    } else {
+        None
+    }
+}
+
+/// An error message with its entity ids replaced by `#n`, so equal reasons count together.
+fn reason(e: &str) -> String {
+    let mut out = String::new();
+    let mut chars = e.chars().peekable();
+    while let Some(c) = chars.next() {
+        out.push(c);
+        if c == '#' && chars.peek().is_some_and(char::is_ascii_digit) {
+            out.push('n');
+            while chars.peek().is_some_and(char::is_ascii_digit) {
+                chars.next();
+            }
+        }
+    }
+    out
+}
+
+/// The curves of a file that lie in a parameter space: the items of its
+/// `DEFINITIONAL_REPRESENTATION`s and the curves they refer to (a 2D trimmed curve's basis …).
+fn curves_2d(ex: &p21::Exchange) -> std::collections::BTreeSet<u64> {
+    fn refs(p: &p21::Param, out: &mut Vec<u64>) {
+        match p {
+            p21::Param::Ref(r) => out.push(*r),
+            p21::Param::List(l) | p21::Param::Typed(_, l) => l.iter().for_each(|x| refs(x, out)),
+            _ => {}
+        }
+    }
+    let mut stack = Vec::new();
+    for e in ex.entities.values() {
+        if e.name() == "DEFINITIONAL_REPRESENTATION"
+            && let Some(items) = e.params().get(1)
+        {
+            refs(items, &mut stack);
+        }
+    }
+    let mut seen = std::collections::BTreeSet::new();
+    while let Some(id) = stack.pop() {
+        let Some(e) = ex.get(id) else { continue };
+        if !matches!(geometry_kind(e), Some((true, _))) || !seen.insert(id) {
+            continue;
+        }
+        for r in &e.records {
+            r.params.iter().for_each(|p| refs(p, &mut stack));
+        }
+    }
+    seen
+}
+
+/// Read or refused, by reason.
+#[derive(Default)]
+struct Tally {
+    read: usize,
+    refused: BTreeMap<String, usize>,
+}
+
+impl Tally {
+    fn add<T>(&mut self, r: &Result<T, String>) {
+        match r {
+            Ok(_) => self.read += 1,
+            Err(e) => *self.refused.entry(reason(e)).or_default() += 1,
+        }
+    }
+    fn refused(&self) -> usize {
+        self.refused.values().sum()
+    }
+}
+
+#[test]
+#[ignore = "needs a STEP corpus in SOLIDCORE_STEP_CORPUS"]
+fn corpus_geometry() {
+    use solidcore_record::step::read::Reader;
+    let Some(dir) = std::env::var_os("SOLIDCORE_STEP_CORPUS") else {
+        eprintln!("SOLIDCORE_STEP_CORPUS is not set");
+        return;
+    };
+    let root = Path::new(&dir);
+    let mut paths = Vec::new();
+    files(root, &mut paths);
+    assert!(!paths.is_empty(), "no STEP files under {dir:?}");
+    let mut failures = Vec::new();
+    // (group, kind) -> tally, groups "curve", "surface", "pcurve" (by its 2D curve's kind).
+    let mut kinds: BTreeMap<(&str, String), Tally> = BTreeMap::new();
+    let mut mixed_units = Vec::new();
+    let mut removed = Vec::new();
+    for path in &paths {
+        let name = path
+            .strip_prefix(root)
+            .unwrap_or(path)
+            .display()
+            .to_string();
+        let ex = match std::fs::read(path)
+            .map_err(|e| e.to_string())
+            .and_then(|b| p21::parse(&String::from_utf8_lossy(&b)).map_err(|e| e.to_string()))
+        {
+            Ok(ex) => ex,
+            Err(e) => {
+                println!("{name}: ERROR {e}");
+                failures.push(format!("{name}: {e}"));
+                continue;
+            }
+        };
+        // The units of the file's first geometric context (the topology reader, which comes
+        // later, reads each representation in its own context).
+        let contexts: Vec<units::Units> = ex
+            .entities
+            .iter()
+            .filter(|(_, e)| {
+                e.has("GEOMETRIC_REPRESENTATION_CONTEXT") && e.has("GLOBAL_UNIT_ASSIGNED_CONTEXT")
+            })
+            .map(|(&id, _)| units::context(&ex, id).units)
+            .collect();
+        let u = contexts.first().copied().unwrap_or_default();
+        if contexts.iter().any(|c| *c != u) {
+            mixed_units.push(name.clone());
+        }
+        // Where a removed check would have decided otherwise: SolidCraft refused a direction
+        // whose length is at most 1e-12 (here: only one that is exactly zero), and took the two
+        // unit factors of a conic's parameter space as equal within 1e-12 relative (here: only
+        // when equal).
+        for (&id, e) in &ex.entities {
+            if e.name() == "DIRECTION"
+                && let Some(r) = e.params().get(1).and_then(p21::Param::as_list)
+            {
+                let sq: f64 = r.iter().filter_map(p21::Param::as_f64).map(|x| x * x).sum();
+                if sq > 0.0 && sq <= 1e-24 {
+                    removed.push(format!("{name}: #{id} a direction of length at most 1e-12"));
+                }
+            }
+        }
+        if u.len != u.ang && (u.len - u.ang).abs() <= 1e-12 * u.len.abs().max(u.ang.abs()) {
+            removed.push(format!(
+                "{name}: length and angle factors equal within 1e-12"
+            ));
+        }
+        let flat = curves_2d(&ex);
+        let mut reader = Reader::new(&ex, u);
+        let mut here = (Tally::default(), Tally::default(), Tally::default());
+        for (&id, e) in &ex.entities {
+            if e.name() == "PCURVE" {
+                let kind = e
+                    .params()
+                    .get(2)
+                    .and_then(p21::Param::as_ref_id)
+                    .and_then(|r| ex.get(r))
+                    .and_then(|r| r.params().get(1)?.as_list()?.first()?.as_ref_id())
+                    .and_then(|c| ex.get(c))
+                    .and_then(geometry_kind)
+                    .map_or_else(|| "?".to_string(), |k| k.1);
+                let r = reader.pcurve(id);
+                here.2.add(&r);
+                kinds.entry(("pcurve", kind)).or_default().add(&r);
+                continue;
+            }
+            let Some((is_curve, kind)) = geometry_kind(e) else {
+                continue;
+            };
+            if is_curve {
+                if flat.contains(&id) {
+                    continue;
+                }
+                let r = reader.curve(id);
+                here.0.add(&r);
+                kinds.entry(("curve", kind)).or_default().add(&r);
+            } else {
+                let r = reader.surface(id);
+                here.1.add(&r);
+                kinds.entry(("surface", kind)).or_default().add(&r);
+            }
+        }
+        println!(
+            "{name}: curves {} read, {} refused; surfaces {} read, {} refused; pcurves {} read, {} refused",
+            here.0.read,
+            here.0.refused(),
+            here.1.read,
+            here.1.refused(),
+            here.2.read,
+            here.2.refused()
+        );
+    }
+    println!("by kind (group, kind: read / refused, with reasons):");
+    let mut totals: BTreeMap<&str, (usize, usize)> = BTreeMap::new();
+    for ((group, kind), t) in &kinds {
+        println!("  {group} {kind}: {} / {}", t.read, t.refused());
+        for (why, n) in &t.refused {
+            println!("      {n} x {why}");
+        }
+        let g = totals.entry(group).or_default();
+        g.0 += t.read;
+        g.1 += t.refused();
+    }
+    println!("totals (read / refused): {totals:?}");
+    println!(
+        "files whose contexts have different units (read in the first): {} {mixed_units:?}",
+        mixed_units.len()
+    );
+    println!(
+        "entities a removed check would have decided otherwise: {} {removed:?}",
+        removed.len()
+    );
+    assert!(
+        failures.is_empty(),
+        "files that did not parse:\n{}",
+        failures.join("\n")
+    );
+}
+
+/// The entity types counted by `corpus_product` against what the product structure holds.
+const BODY_KINDS: [&str; 4] = [
+    "MANIFOLD_SOLID_BREP",
+    "BREP_WITH_VOIDS",
+    "FACETED_BREP",
+    "SHELL_BASED_SURFACE_MODEL",
+];
+const OCCURRENCE_KINDS: [&str; 3] = [
+    "NEXT_ASSEMBLY_USAGE_OCCURRENCE",
+    "ASSEMBLY_COMPONENT_USAGE",
+    "SPECIFIED_HIGHER_USAGE_OCCURRENCE",
+];
+const STYLED_KINDS: [&str; 3] = [
+    "STYLED_ITEM",
+    "OVER_RIDING_STYLED_ITEM",
+    "CONTEXT_DEPENDENT_OVER_RIDING_STYLED_ITEM",
+];
+
+#[test]
+#[ignore = "needs a STEP corpus in SOLIDCORE_STEP_CORPUS"]
+fn corpus_product() {
+    use solidcore_record::step::product::{self, ItemKind};
+    let Some(dir) = std::env::var_os("SOLIDCORE_STEP_CORPUS") else {
+        eprintln!("SOLIDCORE_STEP_CORPUS is not set");
+        return;
+    };
+    let root = Path::new(&dir);
+    let mut paths = Vec::new();
+    files(root, &mut paths);
+    assert!(!paths.is_empty(), "no STEP files under {dir:?}");
+    let mut failures = Vec::new();
+    let mut assemblies = Vec::new();
+    // Totals: name -> (held, census).
+    let mut totals: BTreeMap<&str, (usize, usize)> = BTreeMap::new();
+    let mut coloured_by_kind: BTreeMap<String, usize> = BTreeMap::new();
+    let mut instances_total = 0usize;
+    let mut unreached_mapped: BTreeMap<String, usize> = BTreeMap::new();
+    for path in &paths {
+        let name = path
+            .strip_prefix(root)
+            .unwrap_or(path)
+            .display()
+            .to_string();
+        let ex = match std::fs::read(path)
+            .map_err(|e| e.to_string())
+            .and_then(|b| p21::parse(&String::from_utf8_lossy(&b)).map_err(|e| e.to_string()))
+        {
+            Ok(ex) => ex,
+            Err(e) => {
+                println!("{name}: ERROR {e}");
+                failures.push(format!("{name}: {e}"));
+                continue;
+            }
+        };
+        let census = |names: &[&str]| {
+            ex.entities
+                .values()
+                .filter(|e| names.contains(&e.name()))
+                .count()
+        };
+        let s = match product::read(&ex) {
+            Ok(s) => s,
+            Err(e) => {
+                println!("{name}: REFUSED {e}");
+                failures.push(format!("{name}: refused: {e}"));
+                continue;
+            }
+        };
+        let mut bodies = std::collections::BTreeSet::new();
+        let mut mapped = std::collections::BTreeSet::new();
+        for r in &s.representations {
+            for i in &r.items {
+                match i.kind {
+                    ItemKind::Body(_) => {
+                        bodies.insert(i.entity);
+                    }
+                    ItemKind::Mapped { .. } => {
+                        mapped.insert(i.entity);
+                    }
+                    ItemKind::Other(_) => {}
+                }
+            }
+        }
+        let placed = s
+            .links
+            .iter()
+            .filter(|l| l.transformation.is_some())
+            .count();
+        let coloured: Vec<_> = s
+            .styles
+            .iter()
+            .filter(|st| {
+                !st.curve.is_empty()
+                    || st
+                        .surface
+                        .iter()
+                        .any(|f| f.fill.is_some() || f.rendering.is_some())
+            })
+            .collect();
+        for st in &coloured {
+            let kind = ex.get(st.item).map_or("?", p21::Entity::name);
+            *coloured_by_kind.entry(kind.to_string()).or_default() += 1;
+        }
+        let instances = match s.instances() {
+            Ok(i) => i.len(),
+            Err(e) => {
+                failures.push(format!("{name}: instances: {e}"));
+                0
+            }
+        };
+        instances_total += instances;
+        let rows = [
+            ("products", s.products.len(), census(&["PRODUCT"])),
+            (
+                "definitions",
+                s.definitions.len(),
+                census(&[
+                    "PRODUCT_DEFINITION",
+                    "PRODUCT_DEFINITION_WITH_ASSOCIATED_DOCUMENTS",
+                ]),
+            ),
+            (
+                "occurrences",
+                s.occurrences.len(),
+                census(&OCCURRENCE_KINDS),
+            ),
+            ("body items", bodies.len(), census(&BODY_KINDS)),
+            (
+                "placed links",
+                placed,
+                ex.entities
+                    .values()
+                    .filter(|e| e.has("REPRESENTATION_RELATIONSHIP_WITH_TRANSFORMATION"))
+                    .count(),
+            ),
+            ("styled items", s.styles.len(), census(&STYLED_KINDS)),
+        ];
+        // A mapped item the structure does not hold is listed only by representations it does
+        // not reach (the draughting models of PMI views): checked, and counted apart.
+        let reached: std::collections::BTreeSet<u64> =
+            s.representations.iter().map(|r| r.entity).collect();
+        let mut listers: BTreeMap<u64, Vec<(u64, &str)>> = BTreeMap::new();
+        for (&id, e) in &ex.entities {
+            for r in &e.records {
+                for p in &r.params {
+                    for m in p
+                        .as_list()
+                        .unwrap_or_default()
+                        .iter()
+                        .filter_map(p21::Param::as_ref_id)
+                    {
+                        if ex.get(m).is_some_and(|m| m.name() == "MAPPED_ITEM") {
+                            listers.entry(m).or_default().push((id, e.name()));
+                        }
+                    }
+                }
+            }
+        }
+        let all_mapped = census(&["MAPPED_ITEM"]);
+        for (&id, e) in &ex.entities {
+            if e.name() != "MAPPED_ITEM" || mapped.contains(&id) {
+                continue;
+            }
+            let by = listers.get(&id).cloned().unwrap_or_default();
+            if by.iter().any(|(l, _)| reached.contains(l)) {
+                failures.push(format!(
+                    "{name}: mapped item #{id} of a reached representation not held"
+                ));
+            }
+            for (_, kind) in by {
+                *unreached_mapped.entry(kind.to_string()).or_default() += 1;
+            }
+        }
+        let t = totals.entry("mapped items").or_default();
+        t.0 += mapped.len();
+        t.1 += all_mapped;
+        let mut line = format!("{name}: mapped items {}/{all_mapped};", mapped.len());
+        for (what, held, n) in rows {
+            let _ = std::fmt::Write::write_fmt(&mut line, format_args!(" {what} {held}/{n};"));
+            let t = totals.entry(what).or_default();
+            t.0 += held;
+            t.1 += n;
+            if held != n {
+                failures.push(format!("{name}: {what}: {held} held, {n} in the file"));
+            }
+        }
+        println!(
+            "{line} coloured items {}; roots {}; instances {instances}",
+            coloured.len(),
+            s.roots.len()
+        );
+        if !s.occurrences.is_empty() {
+            assemblies.push(format!(
+                "{name}: {} definitions, {} occurrences, {} roots, {instances} instances, {} mapped items",
+                s.definitions.len(),
+                s.occurrences.len(),
+                s.roots.len(),
+                mapped.len()
+            ));
+        }
+    }
+    println!("totals (held / in the files): {totals:?}");
+    println!("coloured items by kind: {coloured_by_kind:?}");
+    println!("mapped items not held, by the kind of entity listing them: {unreached_mapped:?}");
+    println!("instances: {instances_total}");
+    println!("files with assemblies: {}", assemblies.len());
+    for a in &assemblies {
+        println!("  {a}");
+    }
+    assert!(failures.is_empty(), "{}", failures.join("\n"));
+}

solidcore/crates/solidcore-tess/src/planner/mod.rs

@@ -2298,16 +2298,26 @@ fn plan_face(
     }
     // Whatever the layout, no triangle leaves the surface by more than the tolerance.
     if !planar {
-        if sag::refine(s, tol, reach, &fixed, &mut all, &mut triangles, MAX_REFINE)
-            .map_err(|e| sag_stop(e, all.len()))?
+        // The kernel's classifier is asked once per node over the three passes.
+        let mut poles = sag::Poles::new(s, reach);
+        if sag::refine(
+            s,
+            tol,
+            &mut poles,
+            &fixed,
+            &mut all,
+            &mut triangles,
+            MAX_REFINE,
+        )
+        .map_err(|e| sag_stop(e, all.len()))?
         {
             caps.push(Cap::Refine);
         }
-        sag::flip(s, tol, reach, &fixed, &all, &mut triangles)
+        sag::flip(s, tol, &mut poles, &fixed, &all, &mut triangles)
             .map_err(|e| sag_stop(e, all.len()))?;
         // A face a bound limited is named with the sag its triangles reach.
         if !caps.is_empty() {
-            let (sag, unmeasured) = sag::worst(s, reach, &fixed, &all, &triangles)
+            let (sag, unmeasured) = sag::worst(s, &mut poles, &fixed, &all, &triangles)
                 .map_err(|e| sag_stop(e, all.len()))?;
             stats.over_tolerance.push(OverTolerance {
                 face: fi as usize,

solidcore/crates/solidcore-tess/src/planner/refusals.rs

@@ -379,7 +379,14 @@ fn the_flips_name_a_middle_the_surface_does_not_evaluate_at() {
     let uv = vec![[0.0, 0.0], [0.75, -0.5], [0.75, 0.5], [0.0, 1.0]];
     let fixed: Vec<Vec3> = uv.iter().map(|q| point(&s, *q)).collect();
     let mut tris = vec![[0, 1, 2], [0, 2, 3]];
-    match super::sag::flip(&s, 0.01, 1e-9, &fixed, &uv, &mut tris) {
+    match super::sag::flip(
+        &s,
+        0.01,
+        &mut super::sag::Poles::new(&s, 1e-9),
+        &fixed,
+        &uv,
+        &mut tris,
+    ) {
         Err(super::sag::Stop::NoValue(NoValue(q))) => assert_eq!(q[0], 0.5, "{q:?}"),
         other => panic!("{other:?}, flipped to {tris:?}"),
     }
@@ -544,7 +551,13 @@ fn a_step_inwards_the_surface_has_no_point_at_refuses_the_face() {
 fn the_worst_sag_is_measured_where_the_surface_evaluates() {
     let s = cylinder_without(0.5);
     let uv = [[0.0, 0.0], [0.75, -0.5], [0.75, 0.5]];
-    let got = super::sag::worst(&s, 1e-9, &[], &uv, &[[0, 1, 2]]);
+    let got = super::sag::worst(
+        &s,
+        &mut super::sag::Poles::new(&s, 1e-9),
+        &[],
+        &uv,
+        &[[0, 1, 2]],
+    );
     // Measured at its three sides' middles; its middle, unmeasured, is counted, so the face is
     // never taken as within its tolerance over it.
     assert!(

solidcore/crates/solidcore-tess/src/planner/sag.rs

@@ -18,8 +18,9 @@ use super::{NoValue, Unclassified};
 
 /// Split the triangles `tris` of a face (indices into `uv`; the first `fixed.len()` points sit
 /// at `fixed`, the rest on the surface at their parameters) until none of them lies farther
-/// than `tol` from the surface `s`, adding at most `max_points` points to `uv`. `reach`: how near
-/// a pole a point is taken as one (see [`solidcore::eval::uv::degenerate_within`]).
+/// than `tol` from the surface `s`, adding at most `max_points` points to `uv`. `poles`: the
+/// classifier of the face's nodes, shared by [`refine`], [`flip`] and [`worst`] (how near a pole a
+/// point is taken as one: see [`solidcore::eval::uv::degenerate_within`]).
 ///
 /// A point the surface does not evaluate at (a node, or a middle the check needs) is the
 /// evaluator refusing the face: the error names it, and the caller leaves the face out whole.
@@ -50,7 +51,7 @@ impl From<Unclassified> for Stop {
 pub(crate) fn refine(
     s: &EvalSurface,
     tol: f64,
-    reach: f64,
+    poles: &mut Poles,
     fixed: &[Vec3],
     uv: &mut Vec<[f64; 2]>,
     tris: &mut Vec<[u32; 3]>,
@@ -64,7 +65,6 @@ pub(crate) fn refine(
             .map(|d| kernel::record_vec3(d.0))
             .ok_or(NoValue(q))
     };
-    let mean = |qs: &[[f64; 2]]| mean(s, reach, qs);
     // How far the flat point `c` lies from the surface, measured along the normal at the surface
     // point of the same parameters: those parameters need not be the nearest (a straight line in
     // the parameters is no geodesic near a pole), and only the departure across the surface
@@ -103,10 +103,7 @@ pub(crate) fn refine(
             continue;
         };
         let p = |i: u32| pos.get(i as usize).copied();
-        let q = |i: u32| uv.get(i as usize).copied();
-        let (Some(pa), Some(pb), Some(pc), Some(qa), Some(qb), Some(qc)) =
-            (p(t[0]), p(t[1]), p(t[2]), q(t[0]), q(t[1]), q(t[2]))
-        else {
+        let (Some(pa), Some(pb), Some(pc)) = (p(t[0]), p(t[1]), p(t[2])) else {
             continue;
         };
         // Sides inside the face (two triangles on them), long enough to split, with their sag.
@@ -117,7 +114,7 @@ pub(crate) fn refine(
             if sides.get(&e).is_none_or(|ts| ts.len() != 2) {
                 continue;
             }
-            let (Some(xa), Some(xb), Some(ua), Some(ub)) = (p(a), p(b), q(a), q(b)) else {
+            let (Some(xa), Some(xb)) = (p(a), p(b)) else {
                 continue;
             };
             let len = xa.dist(xb);
@@ -127,7 +124,7 @@ pub(crate) fn refine(
             let sag = if let Some(&sag) = sag_of.get(&e) {
                 sag
             } else {
-                let sag = off(mean(&[ua, ub])?, (xa + xb) * 0.5)?;
+                let sag = off(poles.mean(uv, &[a, b])?, (xa + xb) * 0.5)?;
                 sag_of.insert(e, sag);
                 sag
             };
@@ -138,7 +135,7 @@ pub(crate) fn refine(
         // inside the face divides by four. A triangle whose middle is off splits its side inside
         // the face that sags most, while that side still contributes; what is left comes from
         // its boundary sides, which the edges' own sampling keeps within the tolerance.
-        let centroid = mean(&[qa, qb, qc])?;
+        let centroid = poles.mean(uv, &t)?;
         let worst = inner.iter().max_by(|x, y| x.0.total_cmp(&y.0)).copied();
         let split = match worst {
             Some((sag, _, e)) if sag > tol => e,
@@ -174,14 +171,11 @@ pub(crate) fn refine(
         if from != ti {
             queue.push(ti);
         }
-        let (Some(ua), Some(ub)) = (q(split.0), q(split.1)) else {
-            continue;
-        };
         // A split is wanted and there is no room for its point.
         if uv.len() >= limit {
             return Ok(true);
         }
-        let m = mean(&[ua, ub])?;
+        let m = poles.mean(uv, &[split.0, split.1])?;
         let pm = at(m)?;
         // Proven: `plan_face` checks its nodes and the MAX_REFINE more it lets this add are at most
         // MAX_FACE_NODES, so the index fits a u32.
@@ -194,29 +188,82 @@ pub(crate) fn refine(
     Ok(false)
 }
 
-/// The mean of parameter points, as the surface point between them: at a pole the parameter
-/// along the degenerate direction is free (the pole copy carries a neighbour's), so there the
-/// mean takes it from the other points alone.
-/// A point whose poles the kernel's classifier cannot tell is the error.
-fn mean(s: &EvalSurface, reach: f64, qs: &[[f64; 2]]) -> Result<[f64; 2], Unclassified> {
-    let mut out = [0.0; 2];
-    // Proven: `d` < 2 enumerates `out` and indexes the `[f64; 2]` parameters `qs`.
-    #[allow(clippy::indexing_slicing)]
-    for (d, slot) in out.iter_mut().enumerate() {
-        let mut free: Vec<f64> = Vec::new();
-        for q in qs {
-            if !super::pole_at(s, *q, d, reach)? {
-                free.push(q[d]);
+/// Which parameter directions the surface is collapsed along at each node of a face's
+/// triangulation, as the kernel's classifier says (within `reach`): a property of the node's
+/// parameters, so it is asked once per node however many triangles and rounds look at it.
+pub(crate) struct Poles<'a> {
+    s: &'a EvalSurface,
+    reach: f64,
+    /// Per node index; `None` until asked.
+    flags: Vec<Option<[bool; 2]>>,
+    /// Calls of the kernel's classifier made, for the tests.
+    #[cfg(test)]
+    asked: usize,
+}
+
+impl<'a> Poles<'a> {
+    pub(crate) fn new(s: &'a EvalSurface, reach: f64) -> Self {
+        Poles {
+            s,
+            reach,
+            flags: Vec::new(),
+            #[cfg(test)]
+            asked: 0,
+        }
+    }
+
+    /// Whether each direction is collapsed at node `i`, whose parameters are `q`.
+    fn at(&mut self, i: u32, q: [f64; 2]) -> Result<[bool; 2], Unclassified> {
+        let i = i as usize;
+        if let Some(Some(f)) = self.flags.get(i) {
+            return Ok(*f);
+        }
+        #[cfg(test)]
+        {
+            self.asked += 2;
+        }
+        let f = [
+            super::pole_at(self.s, q, 0, self.reach)?,
+            super::pole_at(self.s, q, 1, self.reach)?,
+        ];
+        if self.flags.len() <= i {
+            self.flags.resize(i + 1, None);
+        }
+        if let Some(slot) = self.flags.get_mut(i) {
+            *slot = Some(f);
+        }
+        Ok(f)
+    }
+
+    /// The mean of nodes' parameters, as the surface point between them: at a pole the
+    /// parameter along the degenerate direction is free (the pole copy carries a neighbour's),
+    /// so there the mean takes it from the other nodes alone. A node whose poles the kernel's
+    /// classifier cannot tell is the error.
+    fn mean(&mut self, uv: &[[f64; 2]], nodes: &[u32]) -> Result<[f64; 2], Unclassified> {
+        let mut qs: Vec<([f64; 2], [bool; 2])> = Vec::new();
+        for &i in nodes {
+            if let Some(&q) = uv.get(i as usize) {
+                qs.push((q, self.at(i, q)?));
             }
         }
-        let pick: Vec<f64> = if free.is_empty() {
-            qs.iter().map(|q| q[d]).collect()
-        } else {
-            free
-        };
-        *slot = pick.iter().sum::<f64>() / pick.len().max(1) as f64;
+        let mut out = [0.0; 2];
+        // Proven: `d` < 2 enumerates `out` and indexes the `[f64; 2]` parameters and flags.
+        #[allow(clippy::indexing_slicing)]
+        for (d, slot) in out.iter_mut().enumerate() {
+            let free: Vec<f64> = qs
+                .iter()
+                .filter(|(_, f)| !f[d])
+                .map(|(q, _)| q[d])
+                .collect();
+            let pick: Vec<f64> = if free.is_empty() {
+                qs.iter().map(|(q, _)| q[d]).collect()
+            } else {
+                free
+            };
+            *slot = pick.iter().sum::<f64>() / pick.len().max(1) as f64;
+        }
+        Ok(out)
     }
-    Ok(out)
 }
 
 /// The farthest the triangles `tris` (as for [`refine`]) lie from the surface, measured as
@@ -229,7 +276,7 @@ fn mean(s: &EvalSurface, reach: f64, qs: &[[f64; 2]]) -> Result<[f64; 2], Unclas
 /// classifier cannot tell.
 pub(crate) fn worst(
     s: &EvalSurface,
-    reach: f64,
+    poles: &mut Poles,
     fixed: &[Vec3],
     uv: &[[f64; 2]],
     tris: &[[u32; 3]],
@@ -245,8 +292,8 @@ pub(crate) fn worst(
         })
         .collect();
     // How far the flat point `c` lies from the surface at the mean of `qs`, as `refine`'s `off`.
-    let off = |qs: &[[f64; 2]], c: Vec3| -> Result<Option<f64>, Unclassified> {
-        let m = mean(s, reach, qs)?;
+    let mut off = |nodes: &[u32], c: Vec3| -> Result<Option<f64>, Unclassified> {
+        let m = poles.mean(uv, nodes)?;
         let Some((x, su, sv)) = s.derivs(m[0], m[1]).map(kernel::record_triple) else {
             return Ok(None);
         };
@@ -259,7 +306,7 @@ pub(crate) fn worst(
     let (mut worst, mut unmeasured) = (0.0f64, 0usize);
     for (k, t) in tris.iter().enumerate() {
         let corner = |i: u32| Some((*uv.get(i as usize)?, *pos.get(i as usize)?));
-        let (Some((qa, pa)), Some((qb, pb)), Some((qc, pc))) =
+        let (Some((_, pa)), Some((_, pb)), Some((_, pc))) =
             (corner(t[0]), corner(t[1]), corner(t[2]))
         else {
             return Err(Stop::Corner(k));
@@ -268,16 +315,16 @@ pub(crate) fn worst(
         // corner they need).
         let mut measured: Vec<Option<f64>> = Vec::new();
         measured.push(match (pa, pb, pc) {
-            (Some(a), Some(b), Some(c)) => off(&[qa, qb, qc], (a + b + c) * (1.0 / 3.0))?,
+            (Some(a), Some(b), Some(c)) => off(t, (a + b + c) * (1.0 / 3.0))?,
             _ => None,
         });
-        for ((qx, px), (qy, py)) in [
-            ((qa, pa), (qb, pb)),
-            ((qb, pb), (qc, pc)),
-            ((qc, pc), (qa, pa)),
+        for ((nx, px), (ny, py)) in [
+            ((t[0], pa), (t[1], pb)),
+            ((t[1], pb), (t[2], pc)),
+            ((t[2], pc), (t[0], pa)),
         ] {
             measured.push(match (px, py) {
-                (Some(x), Some(y)) => off(&[qx, qy], (x + y) * 0.5)?,
+                (Some(x), Some(y)) => off(&[nx, ny], (x + y) * 0.5)?,
                 _ => None,
             });
         }
@@ -388,7 +435,7 @@ const MIN_FLIP_ANGLE: f64 = 1e-3;
 pub(crate) fn flip(
     s: &EvalSurface,
     tol: f64,
-    reach: f64,
+    poles: &mut Poles,
     fixed: &[Vec3],
     uv: &[[f64; 2]],
     tris: &mut [[u32; 3]],
@@ -396,7 +443,6 @@ pub(crate) fn flip(
     if !(tol.is_finite() && tol > 0.0) || tris.len() < 2 {
         return Ok(());
     }
-    let mean = |qs: &[[f64; 2]]| mean(s, reach, qs);
     let derivs = |q: [f64; 2]| {
         s.derivs(q[0], q[1])
             .map(kernel::record_triple)
@@ -441,13 +487,11 @@ pub(crate) fn flip(
         angle(a, b, c).min(angle(b, c, a)).min(angle(c, a, b))
     };
     // How far a facet's normal turns from the surface normal at its middle (radians, 0 to pi/2).
-    let deviation = |t: [u32; 3]| -> Result<f64, Stop> {
-        let (Some(a), Some(b), Some(c), Some(qa), Some(qb), Some(qc)) =
-            (p(t[0]), p(t[1]), p(t[2]), q(t[0]), q(t[1]), q(t[2]))
-        else {
+    let deviation = |poles: &mut Poles, t: [u32; 3]| -> Result<f64, Stop> {
+        let (Some(a), Some(b), Some(c)) = (p(t[0]), p(t[1]), p(t[2])) else {
             return Ok(0.0);
         };
-        let m = mean(&[qa, qb, qc])?;
+        let m = poles.mean(uv, &t)?;
         let facet = (b - a).cross(c - a).normalized();
         let (_, su, sv) = derivs(m)?;
         Ok(match (facet, su.cross(sv).normalized()) {
@@ -458,20 +502,16 @@ pub(crate) fn flip(
     };
     // Whether the facet's normal lies on the side of the surface normal that its (u, v)
     // orientation `sign` says.
-    let upright = |t: [u32; 3], sign: f64| -> Result<bool, Stop> {
-        let (Some(a), Some(b), Some(c), Some(qa), Some(qb), Some(qc)) =
-            (p(t[0]), p(t[1]), p(t[2]), q(t[0]), q(t[1]), q(t[2]))
-        else {
+    let upright = |poles: &mut Poles, t: [u32; 3], sign: f64| -> Result<bool, Stop> {
+        let (Some(a), Some(b), Some(c)) = (p(t[0]), p(t[1]), p(t[2])) else {
             return Ok(false);
         };
-        let (_, su, sv) = derivs(mean(&[qa, qb, qc])?)?;
+        let (_, su, sv) = derivs(poles.mean(uv, &t)?)?;
         Ok((b - a).cross(c - a).dot(su.cross(sv)) * sign > 0.0)
     };
-    let centroid_off = |t: [u32; 3]| -> Result<f64, Stop> {
-        match (p(t[0]), p(t[1]), p(t[2]), q(t[0]), q(t[1]), q(t[2])) {
-            (Some(a), Some(b), Some(c), Some(qa), Some(qb), Some(qc)) => {
-                Ok(off(mean(&[qa, qb, qc])?, (a + b + c) * (1.0 / 3.0))?)
-            }
+    let centroid_off = |poles: &mut Poles, t: [u32; 3]| -> Result<f64, Stop> {
+        match (p(t[0]), p(t[1]), p(t[2])) {
+            (Some(a), Some(b), Some(c)) => Ok(off(poles.mean(uv, &t)?, (a + b + c) * (1.0 / 3.0))?),
             _ => Ok(f64::INFINITY),
         }
     };
@@ -523,20 +563,20 @@ pub(crate) fn flip(
         // The pair the other way must lie closer along the surface (its facets turn less from
         // the surface normal), by more than a degree: a pair within a degree of the surface is
         // left as the layout made it.
-        let mut cached = |ti: u32, t: [u32; 3]| -> Result<f64, Stop> {
+        let mut cached = |poles: &mut Poles, ti: u32, t: [u32; 3]| -> Result<f64, Stop> {
             if let Some(d) = dev_of.get(ti as usize).copied().flatten() {
                 Ok(d)
             } else {
-                let d = deviation(t)?;
+                let d = deviation(poles, t)?;
                 if let Some(slot) = dev_of.get_mut(ti as usize) {
                     *slot = Some(d);
                 }
                 Ok(d)
             }
         };
-        let worse = cached(t1, ta)?.max(cached(t2, tb)?);
+        let worse = cached(poles, t1, ta)?.max(cached(poles, t2, tb)?);
         let degree = 1f64.to_radians();
-        if worse < degree || deviation(n1)?.max(deviation(n2)?) >= worse - degree {
+        if worse < degree || deviation(poles, n1)?.max(deviation(poles, n2)?) >= worse - degree {
             continue;
         }
         // ... and have area in 3D (three corners on one line of a cone have none, however they
@@ -544,21 +584,19 @@ pub(crate) fn flip(
         if min_angle(n1).min(min_angle(n2)) < MIN_FLIP_ANGLE {
             continue;
         }
-        if !(upright(n1, sign)? && upright(n2, sign)?) {
+        if !(upright(poles, n1, sign)? && upright(poles, n2, sign)?) {
             continue;
         }
-        let (Some(pa), Some(pb), Some(pc), Some(pd), Some(qa), Some(qb), Some(qc), Some(qd)) =
-            (p(a), p(b), p(c), p(d), q(a), q(b), q(c), q(d))
-        else {
+        let (Some(pa), Some(pb), Some(pc), Some(pd)) = (p(a), p(b), p(c), p(d)) else {
             continue;
         };
         let allowed = tol
-            .max(off(mean(&[qa, qb])?, (pa + pb) * 0.5)?)
-            .max(centroid_off(ta)?)
-            .max(centroid_off(tb)?);
-        if off(mean(&[qc, qd])?, (pc + pd) * 0.5)? > allowed
-            || centroid_off(n1)? > allowed
-            || centroid_off(n2)? > allowed
+            .max(off(poles.mean(uv, &[a, b])?, (pa + pb) * 0.5)?)
+            .max(centroid_off(poles, ta)?)
+            .max(centroid_off(poles, tb)?);
+        if off(poles.mean(uv, &[c, d])?, (pc + pd) * 0.5)? > allowed
+            || centroid_off(poles, n1)? > allowed
+            || centroid_off(poles, n2)? > allowed
         {
             continue;
         }
@@ -607,7 +645,15 @@ mod tests {
         assert_eq!(fixed.len(), 4);
         let mut tris = vec![[0, 1, 2], [0, 2, 3]];
         assert_eq!(
-            refine(&s, 0.01, 1e-9, &fixed, &mut uv, &mut tris, 1000),
+            refine(
+                &s,
+                0.01,
+                &mut Poles::new(&s, 1e-9),
+                &fixed,
+                &mut uv,
+                &mut tris,
+                1000
+            ),
             Err(Stop::NoValue(NoValue([0.5, 0.5])))
         );
         assert_eq!(tris, vec![[0, 1, 2], [0, 2, 3]]);
@@ -628,11 +674,19 @@ mod tests {
         assert_eq!(fixed.len(), 4);
         let mut tris = vec![[0, 1, 4], [1, 2, 4], [2, 3, 4], [3, 0, 4]];
         assert_eq!(
-            refine(&s, 0.01, 1e-9, &fixed, &mut uv, &mut tris, 1000),
+            refine(
+                &s,
+                0.01,
+                &mut Poles::new(&s, 1e-9),
+                &fixed,
+                &mut uv,
+                &mut tris,
+                1000
+            ),
             Err(Stop::NoValue(NoValue([0.5, 0.5])))
         );
         assert_eq!(
-            flip(&s, 0.01, 1e-9, &fixed, &uv, &mut tris),
+            flip(&s, 0.01, &mut Poles::new(&s, 1e-9), &fixed, &uv, &mut tris),
             Err(Stop::NoValue(NoValue([0.5, 0.5])))
         );
     }
@@ -661,7 +715,7 @@ mod tests {
         };
         let uv = [[0.5, -0.1], [0.5, 0.1], [0.6, 0.0]];
         let side = 3.0 * (1.0 - 0.1f64.cos());
-        let got = worst(&s, 0.0, &[], &uv, &[[0, 1, 2]]);
+        let got = worst(&s, &mut Poles::new(&s, 0.0), &[], &uv, &[[0, 1, 2]]);
         assert!(
             got.as_ref()
                 .is_ok_and(|(w, unmeasured)| (w - side).abs() < 1e-9 * side && *unmeasured == 0),
@@ -669,8 +723,70 @@ mod tests {
         );
         // A corner past the nodes is the triangle's index.
         assert_eq!(
-            worst(&s, 0.0, &[], &uv, &[[0, 1, 2], [0, 1, 3]]),
+            worst(
+                &s,
+                &mut Poles::new(&s, 0.0),
+                &[],
+                &uv,
+                &[[0, 1, 2], [0, 1, 3]]
+            ),
             Err(Stop::Corner(1))
         );
     }
+
+    /// Refining, flipping and measuring a coarse patch of a cylinder (every sag over the
+    /// tolerance, so the nodes are looked at by many triangles, sides and rounds) asks the
+    /// kernel's classifier once per node and direction, not once per look.
+    #[test]
+    fn the_classifier_is_asked_once_per_node() {
+        use solidcore::eval::EvalCurve;
+        let s = EvalSurface::Revolved {
+            profile: EvalCurve::new(
+                1,
+                vec![0.0, 0.0, 1.0, 1.0],
+                vec![[3.0, 0.0, 0.0, 1.0], [3.0, 0.0, 4.0, 1.0]],
+            ),
+            origin: solidcore::Vec3::ZERO,
+            axis: solidcore::Vec3::Z,
+            transform: [
+                [1.0, 0.0, 0.0, 0.0],
+                [0.0, 1.0, 0.0, 0.0],
+                [0.0, 0.0, 1.0, 0.0],
+            ],
+            swap: false,
+        };
+        let n = 6u32;
+        let mut uv: Vec<[f64; 2]> = Vec::new();
+        for i in 0..=n {
+            for j in 0..=n {
+                uv.push([
+                    f64::from(i) / f64::from(n),
+                    3.0 * f64::from(j) / f64::from(n),
+                ]);
+            }
+        }
+        let mut tris: Vec<[u32; 3]> = Vec::new();
+        for i in 0..n {
+            for j in 0..n {
+                let a = i * (n + 1) + j;
+                let (b, c, d) = (a + 1, a + n + 1, a + n + 2);
+                tris.push([a, c, d]);
+                tris.push([a, d, b]);
+            }
+        }
+        let mut poles = Poles::new(&s, 1e-9);
+        let start = uv.len();
+        // Refinement is capped (it may or may not run out of room): the count holds either way.
+        refine(&s, 5e-2, &mut poles, &[], &mut uv, &mut tris, 300).unwrap();
+        flip(&s, 5e-2, &mut poles, &[], &uv, &mut tris).unwrap();
+        worst(&s, &mut poles, &[], &uv, &tris).unwrap();
+        assert!(uv.len() > 2 * start, "{} nodes: not refined", uv.len());
+        assert!(poles.asked > 0);
+        assert!(
+            poles.asked <= 2 * uv.len(),
+            "{} calls for {} nodes",
+            poles.asked,
+            uv.len()
+        );
+    }
 }

solidcore/crates/solidcore-tess/src/planner/tangle.rs

@@ -61,12 +61,28 @@ pub(crate) fn crossing(
         if n < 3 {
             continue;
         }
+        // Each node is on a pole or not whichever two chords it ends: asked once.
+        let mut on_pole: Vec<Option<bool>> = vec![None; n];
+        let mut node_pole = |k: usize, q: [f64; 2]| -> Result<bool, super::Unclassified> {
+            if let Some(p) = on_pole.get(k).copied().flatten() {
+                return Ok(p);
+            }
+            let p = pole(q)?;
+            if let Some(slot) = on_pole.get_mut(k) {
+                *slot = Some(p);
+            }
+            Ok(p)
+        };
         for k in 0..n {
             // Proven: n = l.uv.len() >= 3, checked above
-            let (Some(&a), Some(&b)) = (l.uv.get(k), l.uv.get((k + 1) % n)) else {
+            let next = (k + 1) % n;
+            let (Some(&a), Some(&b)) = (l.uv.get(k), l.uv.get(next)) else {
                 continue;
             };
-            if !(a.iter().chain(&b).all(|x| x.is_finite())) || pole(a)? || pole(b)? {
+            if !(a.iter().chain(&b).all(|x| x.is_finite()))
+                || node_pole(k, a)?
+                || node_pole(next, b)?
+            {
                 continue;
             }
             // The loop's closing chord of a loop that winds round the surface ends at the copy of

solidcore/crates/solidcore-tess/src/planner/tests.rs

@@ -1345,7 +1345,16 @@ fn sag_refinement_across_an_inflection_ends_without_slivers() {
     let fixed: Vec<Vec3> = Vec::new();
     let tol = 0.5;
     let start = uv.len();
-    sag::refine(&s, tol, 1e-9, &fixed, &mut uv, &mut tris, 20_000).unwrap();
+    sag::refine(
+        &s,
+        tol,
+        &mut sag::Poles::new(&s, 1e-9),
+        &fixed,
+        &mut uv,
+        &mut tris,
+        20_000,
+    )
+    .unwrap();
     assert!(
         uv.len() - start < 1_000,
         "{} points added: refinement ran to its budget",
@@ -1400,7 +1409,7 @@ fn triangles_standing_across_a_curved_sheet_are_flipped_along_it() {
             .sum()
     };
     let before = area(&tris);
-    sag::flip(&s, 0.1, 1e-9, &[], &uv, &mut tris).unwrap();
+    sag::flip(&s, 0.1, &mut sag::Poles::new(&s, 1e-9), &[], &uv, &mut tris).unwrap();
     let after = area(&tris);
     let sides: Vec<(u32, u32)> = tris
         .iter()
@@ -2138,3 +2147,19 @@ fn an_edge_stopped_at_its_depth_bound_is_named_within_its_tolerance() {
     assert!(capped.within && capped.sag <= capped.tol, "{capped:?}");
     assert!(capped.excess > 1.0, "{capped:?}");
 }
+
+/// Refining a spline face moves no triangle count: the memo of the pole classifier only drops the
+/// repeated question (the coil took 1,089,434 / 1,091,452 calls at display / export before it).
+#[test]
+fn the_spline_coil_keeps_its_triangles() {
+    let name = "smlib_coil_lower_half";
+    let (b, size) = (fixture(name), size_of(name));
+    for (t, want) in [
+        (MeshTolerance::display_of(size), 30_776),
+        (MeshTolerance::export_of(size), 30_808),
+    ] {
+        let (p, _) = plan(&b, &t, size).unwrap();
+        let (m, _) = p.evaluate();
+        assert_eq!(m.triangles.len(), want);
+    }
+}

solidcore/crates/solidcore/src/blend/blend_corner.rs

@@ -25,6 +25,7 @@
 //! | `FilletBrep::calc_join_section` | `SmFilletVertex::CalcJoinSection` (543d25a) |
 //! | `FilletBrep::calc_rail_int_end_surface` | `SmFilletVertex::CalcRailIntEndSurface` (`SmBlendCornerEnd.cpp`, 3e26f76) |
 //! | [`mixed`]                    | the Mixed corner (`ClassifyMixed`, `MakeMixedTopology`, `CalcMixedVertGeom`, `CalcMixedEdgeGeom`, `CreateMixedPatches`; 6fd0411, 6e79de5, e1a2153) |
+//! | [`on_face`]                  | none: a Setback's spring curve kept inside its trimmed face (solidcore#2343 (d)) |
 //! | [`setback`]                  | the Setback (`ClassifySetBack`, `MakeSetBackTopology`, `BuildSetBackFill`, `CreateSetBackPatches`; 61547af, 1506e2f, f1d81f4) |
 //! | [`swept`]                    | the Swept turn (`Classify`'s Swept part, `BuildSweptSurface`, `CreateSweptPatch`) |
 //! | [`BlendChamferCorner`], [`chamfer`] | not the fork's: chamfers meeting at a vertex, closed by their planes (WR-716, #2345) |
@@ -69,6 +70,7 @@ pub mod ball;
 pub mod chamfer;
 pub mod end;
 pub mod mixed;
+pub mod on_face;
 pub mod setback;
 pub mod swept;
 

solidcore/crates/solidcore/src/blend/blend_corner/mixed.rs

@@ -1423,7 +1423,8 @@ pub fn calc_mixed_edge_geom(
                 Point3::new(to.0, to.1, 0.0),
             )?;
             let side_i = *nth(if turn { &which_t } else { &which }, kk, OP_EDGE)?;
-            *nth_mut(of2m(&mut side_curves, f), side_i, OP_EDGE)? = Some(iso.clone());
+            *nth_mut(of2m(&mut side_curves, f).as_mut_slice(), side_i, OP_EDGE)? =
+                Some(iso.clone());
             of2m(&mut state.curves_3d, f).push(Curve::from(iso));
             of2m(&mut state.uv_curves, f).push(Curve::from(uv));
             of2m(&mut state.orients, f).push(*nth(&orients, kk, OP_EDGE)?);

solidcore/crates/solidcore/src/blend/blend_corner/on_face.rs

@@ -0,0 +1,383 @@
+//! Whether a Setback's spring curve stays inside its trimmed face: it comes within no gap of
+//! any of the face's other edges (solidcore#2343 (d), the owner's ruling B there).
+//!
+//! Upstream: none. The fork's ruling on smlib#85 part C asked that the spring curve's
+//! parameter-plane control triangle `(P^, X^, Q^)` lie inside the trimmed face; that is the
+//! convex-hull bound for the curve itself, sound but loose (it refuses setbacks whose spring
+//! curve stays on the face). Ruling B on solidcore#2343 checks the curve.
+//!
+//! | Rust              | Upstream |
+//! |-------------------|----------|
+//! | [`Clearance`]     | none     |
+//! | [`bezier_pieces`] | none     |
+//! | [`clear_of`]      | none     |
+//!
+//! Decided on control points, never at sample points (`docs/definitions-and-certificates.md`
+//! §1): a rational Bézier piece with positive weights lies in the convex hull of its
+//! control points (Farin, *Curves and Surfaces for CAGD*). Two pieces whose hulls are
+//! proved farther apart than the gap and both pieces' rounding (their boxes', or their gap
+//! along the line between their centroids: `apart`) come no nearer than the gap. Otherwise the wider of the two is halved (de Casteljau on its
+//! homogeneous points) and the halves are tried in turn. A piece halved [`DEPTH`] times is
+//! halved no further, and a pair still undecided then, or once [`PAIRS`] pairs have been
+//! tried, is [`Clearance::Near`]: an undecided spring curve is not taken as clear. The
+//! rounding is Higham's `gamma` of the operations each point has been through, as
+//! `blend_setback::containment` bounds its patches.
+//!
+//! Deviations: no recursion: the pairs are kept on an explicit stack, each piece halved at
+//! most [`DEPTH`] times, at most [`PAIRS`] pairs per curve and piece list.
+
+use std::borrow::Cow;
+
+use crate::curve::curve::{Curve, CurveKind};
+use crate::error::Result;
+use crate::geom::vector3d::sqrt;
+use crate::kernel::Kernel;
+use crate::math::Vec3;
+use crate::nurbs::b_spline_curve::BSplineCurve;
+use crate::nurbs::math::{gamma, NOW, NOZ};
+
+const OP: &str = "blend::blend_corner::on_face::clear_of";
+
+/// A homogeneous point `(x w, y w, z w, w)`.
+pub type Hom = [f64; 4];
+
+/// How many times a piece is halved at most: a piece of a part's size, tens of millimetres,
+/// is then under 1e-10 long, the rounding of the part's coordinates (§4.4 of the
+/// definitions doc).
+pub const DEPTH: usize = 40;
+
+/// How many pairs of pieces [`clear_of`] tries at most for one curve against one list of
+/// pieces. Near a closest approach a few pairs stay at each halving, so a decided case needs
+/// a few hundred.
+pub const PAIRS: usize = 4096;
+
+/// Whether one curve comes within a gap of another ([`clear_of`]).
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub enum Clearance {
+    /// Proved to stay farther than the gap from the other everywhere.
+    Clear,
+    /// Within the gap somewhere, or not shown not to be within [`DEPTH`] and [`PAIRS`].
+    Near,
+}
+
+/// The rational Bézier pieces of `curve` as homogeneous points, one piece per knot span: of
+/// the B-spline a line, a conic or a B-spline curve is built on (the whole of it, which holds
+/// an edge it is trimmed to; a line's or an ellipse's made on a copy where it holds none
+/// yet). `None` for a curve of another kind, a planar (2D) one, one whose B-spline is not
+/// made, or one whose weights are not all positive and finite: such a curve has no hull to
+/// bound it by.
+///
+/// # Errors
+///
+/// Those of the B-spline's decomposition into its Bézier pieces; a cancellation while an
+/// ellipse's is made.
+pub fn bezier_pieces(k: &Kernel, curve: &Curve) -> Result<Option<Vec<Vec<Hom>>>> {
+    let base: Cow<'_, BSplineCurve> = match curve.kind() {
+        CurveKind::BSpline(c) => Cow::Borrowed(c),
+        CurveKind::Line(c) => c.base_with_nurb()?,
+        CurveKind::Ellipse(c) if c.base().nurb.is_none() => {
+            let mut copy = c.clone();
+            match copy.make_nurb(k) {
+                Err(e) if e.is_unported_or_cancelled() => return Err(e),
+                Err(_) => return Ok(None),
+                Ok(()) => Cow::Owned(copy.base().clone()),
+            }
+        }
+        CurveKind::Ellipse(c) => Cow::Borrowed(c.base()),
+        CurveKind::Hyperbola(c) => Cow::Borrowed(&c.base),
+        CurveKind::Parabola(c) => Cow::Borrowed(c.base()),
+        _ => return Ok(None),
+    };
+    let Some(nurb) = base.nurb.as_ref() else {
+        return Ok(None);
+    };
+    let mut pieces = Vec::new();
+    for bez in nurb.decompose_bez()? {
+        let mut piece = Vec::new();
+        for cp in bez.cpts() {
+            if cp.z == NOZ {
+                return Ok(None);
+            }
+            let h = if cp.w == NOW {
+                [cp.x, cp.y, cp.z, 1.0]
+            } else {
+                [cp.x, cp.y, cp.z, cp.w]
+            };
+            if !h.iter().all(|c| c.is_finite()) || h[3] <= 0.0 {
+                return Ok(None);
+            }
+            piece.push(h);
+        }
+        pieces.push(piece);
+    }
+    Ok(Some(pieces))
+}
+
+/// A piece on the stack: its homogeneous points, how many more times it may be halved, and
+/// the rounding bound of its Euclidean points (that of the piece it was halved from).
+#[derive(Clone)]
+struct Piece {
+    points: Vec<Hom>,
+    depth: usize,
+    rounding: f64,
+}
+
+impl Piece {
+    /// A piece as given: its Euclidean points are within `rounding` of the exact ones after
+    /// [`DEPTH`] halvings of `degree` averaging steps each and the division by the weight:
+    /// `3 gamma(ops + 2)` of its largest homogeneous coordinate over its least weight (shrunk
+    /// by the weights' own rounding), `ops = 8 + DEPTH degree` (the 8 for the knot insertions
+    /// that cut a B-spline into its pieces and the division). `None` where a weight is not
+    /// positive or a coordinate not finite.
+    fn new(points: &[Hom]) -> Option<Self> {
+        let degree = points.len().checked_sub(1)?;
+        let (mut most, mut w_min) = (0.0f64, f64::INFINITY);
+        for h in points {
+            if !h.iter().all(|c| c.is_finite()) {
+                return None;
+            }
+            most = most.max(h[0].abs()).max(h[1].abs()).max(h[2].abs());
+            w_min = w_min.min(h[3]);
+        }
+        let ops = 8 + DEPTH * degree;
+        let shrink = 1.0 - gamma(ops);
+        if !(w_min > 0.0 && shrink > 0.0) {
+            return None;
+        }
+        Some(Self {
+            points: points.to_vec(),
+            depth: DEPTH,
+            rounding: 3.0 * gamma(ops + 2) * most / (w_min * shrink),
+        })
+    }
+
+    /// Its Euclidean points; `None` where a weight is not positive.
+    fn euclidean(&self) -> Option<Vec<Vec3>> {
+        let mut out = Vec::new();
+        for h in &self.points {
+            if h[3].is_nan() || h[3] <= 0.0 {
+                return None;
+            }
+            out.push(Vec3::new(h[0] / h[3], h[1] / h[3], h[2] / h[3]));
+        }
+        Some(out)
+    }
+
+    /// Its two halves at the middle of its parameter (de Casteljau), each halvable once less.
+    fn halves(&self) -> (Self, Self) {
+        let d = self.points.len().saturating_sub(1);
+        let mut work = self.points.clone();
+        let mut left = Vec::new();
+        let mut right = Vec::new();
+        for k in 0..=d {
+            if let Some(&h) = work.first() {
+                left.push(h);
+            }
+            if let Some(&h) = work.get(d - k) {
+                right.push(h);
+            }
+            for i in 0..d - k {
+                if let (Some(&a), Some(&b)) = (work.get(i), work.get(i + 1)) {
+                    if let Some(w) = work.get_mut(i) {
+                        *w = [
+                            0.5 * (a[0] + b[0]),
+                            0.5 * (a[1] + b[1]),
+                            0.5 * (a[2] + b[2]),
+                            0.5 * (a[3] + b[3]),
+                        ];
+                    }
+                }
+            }
+        }
+        right.reverse();
+        let depth = self.depth.saturating_sub(1);
+        (
+            Self {
+                points: left,
+                depth,
+                rounding: self.rounding,
+            },
+            Self {
+                points: right,
+                depth,
+                rounding: self.rounding,
+            },
+        )
+    }
+}
+
+/// The widest extent of `points` along an axis.
+fn width(points: &[Vec3]) -> f64 {
+    let (lo, hi) = extent(points);
+    (hi.x - lo.x).max(hi.y - lo.y).max(hi.z - lo.z)
+}
+
+/// The box of `points`, its least and greatest corners.
+fn extent(points: &[Vec3]) -> (Vec3, Vec3) {
+    let mut lo = Vec3::new(f64::INFINITY, f64::INFINITY, f64::INFINITY);
+    let mut hi = Vec3::new(f64::NEG_INFINITY, f64::NEG_INFINITY, f64::NEG_INFINITY);
+    for p in points {
+        lo = Vec3::new(lo.x.min(p.x), lo.y.min(p.y), lo.z.min(p.z));
+        hi = Vec3::new(hi.x.max(p.x), hi.y.max(p.y), hi.z.max(p.z));
+    }
+    (lo, hi)
+}
+
+/// A lower bound on the distance between the convex hulls of `a` and `b`, less its own
+/// rounding: the larger of the distance between their boxes and their gap along the line
+/// between their centroids (any unit direction `u` separates them by `min u . b - max u . a`;
+/// that one closes on the hulls' distance as near-parallel pieces shrink, where the boxes'
+/// does not). The boxes' gaps are rounded by `2 gamma(1)` of the largest coordinate `s`, their
+/// sum of squares by `gamma(6)`; each projection by `gamma(3) sqrt 3 s |u|`, and the quotient
+/// by `|u|` by `gamma(4)`.
+fn apart(a: &[Vec3], b: &[Vec3]) -> f64 {
+    let ((alo, ahi), (blo, bhi)) = (extent(a), extent(b));
+    let size = [alo, ahi, blo, bhi].iter().fold(0.0f64, |m, c| {
+        m.max(c.x.abs()).max(c.y.abs()).max(c.z.abs())
+    });
+    let gap = |l: f64, h: f64| l - h;
+    let mut squares = 0.0;
+    for d in [
+        gap(blo.x, ahi.x).max(gap(alo.x, bhi.x)),
+        gap(blo.y, ahi.y).max(gap(alo.y, bhi.y)),
+        gap(blo.z, ahi.z).max(gap(alo.z, bhi.z)),
+    ] {
+        let d = (d - 2.0 * gamma(1) * size).max(0.0);
+        squares += d * d;
+    }
+    let boxes = sqrt(squares * (1.0 - gamma(6))) * (1.0 - gamma(2));
+    let centroid = |p: &[Vec3]| {
+        let (sum, count) = p
+            .iter()
+            .fold((Vec3::ZERO, 0.0), |(s, c), &q| (s + q, c + 1.0));
+        sum * (1.0 / count)
+    };
+    let w = centroid(b) - centroid(a);
+    // the line between the centroids, and its parts square to each piece's chord (for
+    // near-parallel pieces side by side, whatever their shift along each other)
+    let square_to = |p: &[Vec3]| match (p.first(), p.last()) {
+        (Some(&first), Some(&last)) => {
+            let t = last - first;
+            let tt = t.dot(t);
+            if tt > 0.0 {
+                w - t * (w.dot(t) / tt)
+            } else {
+                w
+            }
+        }
+        _ => w,
+    };
+    let mut best = boxes;
+    for u in [w, square_to(a), square_to(b)] {
+        let length = u.length();
+        if length.is_nan() || length <= 0.0 {
+            continue;
+        }
+        let reach_a = a.iter().fold(f64::NEG_INFINITY, |m, p| m.max(u.dot(*p)));
+        let reach_b = b.iter().fold(f64::INFINITY, |m, p| m.min(u.dot(*p)));
+        let along = (reach_b - reach_a) / length * (1.0 - gamma(4))
+            - 2.0 * gamma(3) * sqrt(3.0) * size * (1.0 + gamma(4));
+        best = best.max(along);
+    }
+    best
+}
+
+/// Whether the rational Bézier curve `curve` (its homogeneous Bernstein coefficients) comes
+/// within `gap` of any of `pieces` (each such a curve too): [`Clearance::Clear`] only where
+/// that is proved on the pieces' control points (module docs).
+///
+/// # Errors
+///
+/// The kernel's cancellation.
+pub fn clear_of(k: &Kernel, curve: &[Hom], pieces: &[Vec<Hom>], gap: f64) -> Result<Clearance> {
+    let Some(a) = Piece::new(curve) else {
+        return Ok(Clearance::Near);
+    };
+    let mut stack = Vec::new();
+    for p in pieces {
+        let Some(b) = Piece::new(p) else {
+            return Ok(Clearance::Near);
+        };
+        stack.push((a.clone(), b));
+    }
+    let mut tried = 0;
+    while let Some((a, b)) = stack.pop() {
+        k.check_cancelled(OP)?;
+        tried += 1;
+        if tried > PAIRS {
+            return Ok(Clearance::Near);
+        }
+        let (Some(pa), Some(pb)) = (a.euclidean(), b.euclidean()) else {
+            return Ok(Clearance::Near);
+        };
+        if apart(&pa, &pb) > gap + a.rounding + b.rounding {
+            continue;
+        }
+        let (wa, wb) = (width(&pa), width(&pb));
+        // the wider is halved, where it may be; neither: undecided
+        let halve_a = a.depth > 0 && (wa >= wb || b.depth == 0);
+        if halve_a {
+            let (a0, a1) = a.halves();
+            stack.push((a1, b.clone()));
+            stack.push((a0, b));
+        } else if b.depth > 0 {
+            let (b0, b1) = b.halves();
+            stack.push((a.clone(), b1));
+            stack.push((a, b0));
+        } else {
+            return Ok(Clearance::Near);
+        }
+    }
+    Ok(Clearance::Clear)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    /// A quarter circle of radius `r` about `(cx, cy)` in z = 0, from angle 0 to 90 degrees:
+    /// the rational quadratic with middle weight `cos 45`.
+    fn quarter(cx: f64, cy: f64, r: f64) -> Vec<Hom> {
+        let w = 0.5f64.sqrt();
+        vec![
+            [cx + r, cy, 0.0, 1.0],
+            [(cx + r) * w, (cy + r) * w, 0.0, w],
+            [cx, cy + r, 0.0, 1.0],
+        ]
+    }
+
+    /// A segment from `a` to `b`, degree 1.
+    fn segment(a: [f64; 3], b: [f64; 3]) -> Vec<Hom> {
+        vec![[a[0], a[1], a[2], 1.0], [b[0], b[1], b[2], 1.0]]
+    }
+
+    #[test]
+    fn a_segment_near_a_circle_is_clear_by_more_than_the_gap_and_near_within_it() {
+        let k = Kernel::default();
+        let arc = vec![quarter(0.0, 0.0, 10.0)];
+        // the line x + y = c outside the circle is closest to the arc at 45 degrees, c / sqrt 2
+        // - 10 away, and runs along it within twice that for a hundredth of a turn
+        let c = 2.0f64.sqrt() * (10.0 + 1e-3);
+        let chord = segment([c, 0.0, 0.0], [0.0, c, 0.0]);
+        assert_eq!(
+            clear_of(&k, &chord, &arc, 0.9e-3).unwrap(),
+            Clearance::Clear
+        );
+        assert_eq!(clear_of(&k, &chord, &arc, 1.1e-3).unwrap(), Clearance::Near);
+        // inside it, crossing it twice: near at any gap
+        let c = 2.0f64.sqrt() * (10.0 - 1e-3);
+        let chord = segment([c, 0.0, 0.0], [0.0, c, 0.0]);
+        assert_eq!(clear_of(&k, &chord, &arc, 0.0).unwrap(), Clearance::Near);
+    }
+
+    #[test]
+    fn pieces_far_apart_are_clear_at_once_and_a_bad_weight_is_near() {
+        let k = Kernel::default();
+        let far = vec![quarter(100.0, 0.0, 1.0)];
+        let chord = segment([0.0, 0.0, 0.0], [1.0, 1.0, 0.0]);
+        assert_eq!(clear_of(&k, &chord, &far, 1e-6).unwrap(), Clearance::Clear);
+        let mut bad = quarter(100.0, 0.0, 1.0);
+        bad[1][3] = 0.0;
+        assert_eq!(clear_of(&k, &chord, &[bad], 1e-6).unwrap(), Clearance::Near);
+    }
+}

solidcore/crates/solidcore/src/blend/blend_corner/setback.rs

@@ -44,6 +44,7 @@
 //! | `curved_least` (private)     | `sm_SbCurvedLeast` (37c9e1d)                          |
 //! | `gather_ends` (private)      | `BuildSetBackFill`'s `gather`                         |
 //! | `grow_curved` (private)      | `BuildSetBackFill`'s growth beside curved faces (37c9e1d) |
+//! | `springs_on_faces`, `springs_refusal` (private) | none (solidcore#2343 (d))          |
 //!
 //! Deviations: the Setback's own members are kept in [`SetbackCorner`] on the corner
 //! ([`FilletCorner::setback`]) from its creation (`SetFillOrder`) until its patches are
@@ -60,19 +61,26 @@
 //! the vertex there, from the edge's direction at the setback, not the end of its rails
 //! nearer the vertex as the fork's `gather` takes it: a round on an arc, extended past a far
 //! corner that does not blend, comes back round nearer the vertex than a long setback's end
-//! section (solidcore#2835).
+//! section (solidcore#2835). Beside a curved face each spring curve is checked to stay inside
+//! its trimmed face before the fill is made, and again at setbacks the growth finds; a
+//! setback that takes one off its face is refused, naming the largest that keeps every one
+//! on its face, or none where none down to the rails' crossing does or the growth's
+//! setbacks take one off (solidcore#2343 (d); the fork's ruling checked the curve's parameter-plane
+//! control triangle instead, and built no check).
 //!
 //! [`FilletCorner::setback`]: crate::blend::fillet_corner::p3::FilletCorner::setback
 
 use std::sync::Arc;
 
 use crate::blend::blend_corner::ball::{solver_of_edgeuse_or_mate, BallSolvers};
+use crate::blend::blend_corner::on_face::{self, Clearance};
 use crate::blend::blend_corner::swept::fmt_g;
 use crate::blend::blend_corner::{BlendCorner, BlendCornerEvent};
 use crate::blend::blend_refusal::BlendRefusal;
 use crate::blend::blend_setback::{
     bisect_thousandths, certified_scale, containment, distances, fill_hole_counted,
-    fill_hole_probe, Edge, Face, FaceKind, Fill, FillStats, Probe, Round,
+    fill_hole_probe, spring_curve, Edge, Face, FaceKind, Fill, FillStats, Probe, Round,
+    SpringCurve,
 };
 use crate::blend::fillet_corner::p1::{face_by_two_edgeuses, test_g1_continuity};
 use crate::blend::fillet_corner::p3::{CornerPatchEnv, FilletCorner, FilletCornerKind};
@@ -92,6 +100,7 @@ use crate::error::{EntityRef, Result, SolidError};
 use crate::geom::extent1d::Extent1d;
 use crate::geom::extent2d::Extent2d;
 use crate::geom::global_solver::SolverOperation;
+use crate::geom::vector3d::sqrt;
 use crate::intersect::point_class::PointClassType;
 use crate::kernel::Kernel;
 use crate::math::{Point2, Point3, Vec3, BIG_DOUBLE, EFF_ZERO, EFF_ZERO_SQRT};
@@ -105,6 +114,7 @@ use crate::surface::surface::Surface;
 use crate::topology::brep::p7::{make_face_with_curves, FaceCurvesInput};
 use crate::topology::edgeuse::p1 as eu1;
 use crate::topology::face::p2 as face2;
+use crate::topology::face::p4 as face4;
 use crate::topology::{edge, vertex, Brep, EdgeId, EdgeuseId, FaceId, VertexId};
 
 const OP_CLASSIFY: &str = "blend::blend_corner::setback::classify_setback";
@@ -129,6 +139,10 @@ pub struct SetbackCorner {
     /// curved face the length is the edge's arc length, as the setbacks are measured along
     /// it; between planes (straight edges) the distance between its ends.
     pub room: Vec<f64>,
+    /// Not the fork (solidcore#2343 (d)): each blended edge's least setback, where the
+    /// rails of the rounds beside it cross (`sm_SbSetBacks`'s `rvLeast`); a setback below it
+    /// is too short.
+    pub least: Vec<f64>,
     /// `m_pFill`: the fill, from the edge geometry until the patches take it.
     pub fill: Option<Fill>,
     /// `m_bSetBackOpen` (the fork's ef57570, smlib#125): an open G1 corner, its spring
@@ -149,6 +163,7 @@ impl Default for SetbackCorner {
             convex: true,
             overflows: false,
             room: Vec::new(),
+            least: Vec::new(),
             fill: None,
             open: false,
             definition: None,
@@ -1234,6 +1249,7 @@ pub fn make_setback_topology(
     }
     sb.overflows = !fits;
     sb.room.clone_from(&room);
+    sb.least.clone_from(&least);
     // a G1 fill is taken only certified convex: the least scale of the setbacks at which it
     // is (CertifiedScale). The rule's grow to it, each held at its room less the rule's
     // quarter radius (the others growing on); refused, naming them, where none within the
@@ -1783,6 +1799,27 @@ fn grow_curved<S: SetbackSolvers>(
     let Some(ends) = growth.place(pseudo, corner, solvers, hi)? else {
         return Err(err());
     };
+    // the setbacks the fill needs keep every spring curve on its face, or none is taken
+    // (#2343 (d)): the growth finds no smaller one certified, and a spring curve off its face
+    // at these is taken to stay off it at every larger one (as the growth takes
+    // certification, checked on the cases, not proved)
+    let springs = springs_on_faces(
+        growth.k,
+        growth.target,
+        pseudo,
+        corner,
+        growth.planes,
+        growth.tol,
+    )?;
+    if springs == Springs::Leave {
+        return Ok(Err(SetbackRefusal::no_room(
+            format!(
+                "Fillet Error: the setback corner's fill stays no more concave than its faces only from {} times its setbacks, where a spring curve is not shown to stay on its face: no setback builds",
+                fmt_g(hi)
+            ),
+            Some(0.0),
+        )));
+    }
     if let Some(a) = asked {
         let room = &corner.setback.as_ref().ok_or_else(err)?.room;
         let fits_room = room.iter().all(|&r| hi * a.setback + a.ease < r);
@@ -1805,6 +1842,292 @@ fn grow_curved<S: SetbackSolvers>(
     Ok(Ok(ends))
 }
 
+/// Where a Setback's spring curves stand on its faces ([`springs_on_faces`]).
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+enum Springs {
+    /// Each proved to keep clear of every other edge of its face.
+    Clear,
+    /// One comes within its gap of another edge of its face, or is not shown not to.
+    Leave,
+    /// One is not made: [`spring_curve`] refuses the rails' ends (the fill, which makes it
+    /// from the same ends, says why).
+    Unmade,
+}
+
+/// The derivative along `v` of `face`'s unit normal field ([`Face::distance`]'s normal, out
+/// of the material, at any point) at `x`: zero on a plane; a sphere's `side (v - (v . u) u) /
+/// |x - c|` (u the unit direction from its centre); a cylinder's or cone's `side cos v_t /
+/// rho`, `v_t` the part of `v` along the circle about the axis through `x`, rho that circle's
+/// radius and `cos` that of the cone's half angle (1 on a cylinder). `None` on a quadric's
+/// centre or axis.
+fn normal_turn(face: &Face, x: Point3, v: Vec3) -> Option<Vec3> {
+    let u = x - face.point;
+    match face.kind {
+        FaceKind::Plane => Some(Vec3::ZERO),
+        FaceKind::Sphere => {
+            let len = u.length();
+            let d = u.unitize().ok()?;
+            Some((v - d * v.dot(d)) * (face.side / len))
+        }
+        FaceKind::Cylinder | FaceKind::Cone => {
+            let r = u - face.axis * u.dot(face.axis);
+            let rho = r.length();
+            let d = r.unitize().ok()?;
+            let along = v - d * v.dot(d) - face.axis * v.dot(face.axis);
+            let cos = 1.0 / sqrt(1.0 + face.slope * face.slope);
+            Some(along * (face.side * cos / rho))
+        }
+    }
+}
+
+/// The unit direction of the rail on `face` of the round of radius `r` along `edge_id`, at
+/// its end `p` on `face` whose other end is `q` on `other` (the round's two contact points in
+/// one section), turned toward the corner's vertex (`sign` `+1` at a convex corner, `-1` at a
+/// concave one). In closed form, not from the rail as traced, which runs only from the
+/// setback the corner was made at outward: the ball's centre is `c = p - sign r n(p)` and
+/// runs along `n(p) x m(q)` (n, m the faces' normals, constant along their normal lines), the
+/// rail is `c + sign r n(c)`, so its direction is that of the centre's plus `sign r` times the
+/// normal's turn along it ([`normal_turn`]). Toward the vertex: the side the edge runs on to
+/// the vertex at its setback (as `gather_ends` takes the corner's side of an end section).
+/// `None` where the faces' normals are parallel there, or a normal's turn is not defined.
+#[allow(clippy::too_many_arguments)]
+fn rail_toward_vertex(
+    k: &Kernel,
+    target: &Brep,
+    corner: &FilletCorner,
+    edge_id: EdgeId,
+    face: &Face,
+    p: Point3,
+    other: &Face,
+    q: Point3,
+    r: f64,
+    sign: f64,
+) -> Result<Option<Vec3>> {
+    let nul = || SolidError::null_pointer(OP_FILL);
+    let vtx = corner.vertex.ok_or_else(nul)?;
+    let (_, n) = face.distance(p);
+    let (_, m) = other.distance(q);
+    let centre = p - n * (sign * r);
+    let along = n.cross(m);
+    let Some(turn) = normal_turn(face, centre, along) else {
+        return Ok(None);
+    };
+    let Ok(t) = (along + turn * (sign * r)).unitize() else {
+        return Ok(None);
+    };
+    let setback = corner.set_back_dist_along(target, edge_id)?;
+    let (_, edge_dir) = set_back_frame(k, target, edge_id, Some(vtx), setback, OP_FILL)?;
+    let from_start = edge::start_vertex(target, edge_id)? == Some(vtx);
+    let side = t.dot(if from_start { -edge_dir } else { edge_dir });
+    if !side.is_finite() || side.abs() <= 0.0 {
+        return Ok(None);
+    }
+    Ok(Some(if side > 0.0 { t } else { -t }))
+}
+
+/// The corner's spring curves, one per face, at the setbacks its vertices are placed at, as
+/// the fill makes them ([`spring_curve`]): on face `F_i`, from `S_i`, the end of the blend
+/// after `F_i`, leaving its rail toward the vertex, to `M_i`, the end of the blend before,
+/// tangent to both rails ([`rail_toward_vertex`], each with the blend's other end, on its
+/// other face, the mate of its end on `F_i`). [`Springs::Leave`] where a rail's direction is
+/// not found (not shown to stay on its face); [`Springs::Unmade`] where [`spring_curve`]
+/// refuses the rails' ends.
+fn corner_springs(
+    k: &Kernel,
+    target: &Brep,
+    pseudo: &FilletBrep,
+    corner: &FilletCorner,
+    planes: &CornerPlanes,
+) -> Result<core::result::Result<Vec<SpringCurve>, Springs>> {
+    let nul = || SolidError::null_pointer(OP_FILL);
+    let all = corner.all_eus.as_ref().ok_or_else(nul)?;
+    let sign = if corner.setback.as_ref().ok_or_else(nul)?.convex {
+        1.0
+    } else {
+        -1.0
+    };
+    let n = planes.faces.len();
+    let point = |i: usize| -> Result<Point3> {
+        pseudo.vertex_point(*corner.vertices.get(i).ok_or_else(nul)?)
+    };
+    let mut springs = Vec::new();
+    for (f, plane) in planes.planes.iter().enumerate() {
+        // (no face: no corner, refused by the checked remainders)
+        let before = (f + n - 1).checked_rem(n).ok_or_else(nul)?;
+        let after = (f + 1).checked_rem(n).ok_or_else(nul)?;
+        let mut ends = [(Point3::ZERO, None); 2];
+        // S_f with its mate M_(f+1) on F_(f+1); M_f with its mate S_(f-1) on F_(f-1)
+        for (slot, (blend, at, mate, other)) in ends.iter_mut().zip([
+            (f, 3 * f + 2, 3 * after, after),
+            (before, 3 * f, 3 * before + 2, before),
+        ]) {
+            let e = eu1::edge(target, *all.get(blend).ok_or_else(nul)?)?.ok_or_else(nul)?;
+            let p = point(at)?;
+            let tangent = rail_toward_vertex(
+                k,
+                target,
+                corner,
+                e,
+                plane,
+                p,
+                planes.planes.get(other).ok_or_else(nul)?,
+                point(mate)?,
+                planes.edges.get(blend).ok_or_else(nul)?.radius,
+                sign,
+            )?;
+            *slot = (p, tangent);
+        }
+        let [(p, Some(tp)), (q, Some(tq))] = ends else {
+            return Ok(Err(Springs::Leave));
+        };
+        let Ok(spring) = spring_curve(plane, p, tp, q, -tq) else {
+            return Ok(Err(Springs::Unmade));
+        };
+        springs.push(spring);
+    }
+    Ok(Ok(springs))
+}
+
+/// solidcore#2343 (d), the owner's ruling B there: whether the corner's spring curves
+/// ([`corner_springs`]) stay inside their trimmed faces. Each starts inside its face, so it
+/// stays inside where it keeps clear of every edge of the face but the two blended edges at
+/// the vertex ([`on_face::clear_of`]: by more than the corner's tolerance and the edge's). The
+/// two blended edges are left out whole: between them the spring curve lies past the rails of
+/// their rounds, which run inside the face along them. An edge without a curve, or whose
+/// curve is not built on a B-spline, gives no hull to bound it by: the spring curve is not
+/// shown clear of it.
+fn springs_on_faces(
+    k: &Kernel,
+    target: &Brep,
+    pseudo: &FilletBrep,
+    corner: &FilletCorner,
+    planes: &CornerPlanes,
+    tol: f64,
+) -> Result<Springs> {
+    let nul = || SolidError::null_pointer(OP_FILL);
+    let vtx = corner.vertex.ok_or_else(nul)?;
+    let springs = match corner_springs(k, target, pseudo, corner, planes)? {
+        Ok(springs) => springs,
+        Err(verdict) => return Ok(verdict),
+    };
+    for (&face, spring) in planes.faces.iter().zip(&springs) {
+        let mut seen = Vec::new();
+        for e in face4::edges(target, face, None, false, None)? {
+            if seen.contains(&e) {
+                continue;
+            }
+            seen.push(e);
+            if edge::start_vertex(target, e)? == Some(vtx)
+                || edge::end_vertex(target, e)? == Some(vtx)
+            {
+                continue;
+            }
+            let Some(curve) = edge::curve(target, e)? else {
+                return Ok(Springs::Leave);
+            };
+            let Some(pieces) = on_face::bezier_pieces(k, curve)? else {
+                return Ok(Springs::Leave);
+            };
+            let gap = tol + edge::tolerance(target, e)?;
+            for half in [&spring.from_p.curve, &spring.from_q.curve] {
+                if on_face::clear_of(k, half, &pieces, gap)? == Clearance::Near {
+                    return Ok(Springs::Leave);
+                }
+            }
+        }
+    }
+    Ok(Springs::Clear)
+}
+
+/// What a setback that takes a spring curve off its face does, for [`setback_too_long`].
+const SPRING_LEAVES: &str =
+    "takes a setback corner's spring curve off its face (it comes within the tolerances of another edge of the face, or is not shown not to)";
+
+/// solidcore#2343 (d): where a spring curve leaves its face at the corner's setbacks
+/// ([`springs_on_faces`]), the refusal naming the largest common scale of them on the grid of
+/// thousandths at which every spring curve stays inside its face. It is found by the growth's
+/// bisection ([`bisect_thousandths`], each trial placing the setback vertices again as the
+/// growth does), between 1 and the least scale at which every setback reaches its edge's
+/// least, where the rails cross; the search assumes a spring curve on its face at a scale
+/// stays on it at every smaller one (the curve shrinks toward the vertex with its setbacks),
+/// as the growth assumes certification monotone: checked on the cases, not proved. One asked
+/// for is refused as [`BlendRefusal::SetbackTooLong`] naming that scale times it; the
+/// rule's, naming those setbacks. None at or above the least: no setback builds. A trial
+/// whose vertices are not placed counts as off its face, so the scale named is at worst
+/// smaller than need be, never one off its face; whether the fill certifies there is the
+/// fill's to say when that setback is asked. `None` where every spring curve stays on its
+/// face, or one is not made (the fill says why).
+#[allow(clippy::too_many_arguments)]
+fn springs_refusal<S: SetbackSolvers>(
+    k: &Kernel,
+    target: &Brep,
+    pseudo: &mut FilletBrep,
+    corner: &mut FilletCorner,
+    solvers: &mut S,
+    planes: &CornerPlanes,
+    fills: &[SetBackFill],
+    tol: f64,
+) -> Result<Option<SetbackRefusal>> {
+    let err = || SolidError::sm_err(OP_FILL);
+    let at_base = springs_on_faces(k, target, pseudo, corner, planes, tol)?;
+    if at_base != Springs::Leave {
+        return Ok(None);
+    }
+    let vtx = corner.vertex.ok_or_else(err)?;
+    let asked = set_back_fill_of(fills, vtx);
+    let sb = corner.setback.as_ref().ok_or_else(err)?;
+    let base = sb.setbacks.clone();
+    if sb.least.len() != base.len() {
+        return Err(err());
+    }
+    let mut least_scale: f64 = 0.0;
+    for (&l, &s) in sb.least.iter().zip(&base) {
+        least_scale = smax(least_scale, l / s);
+    }
+    let growth = Growth {
+        k,
+        target,
+        planes,
+        tol,
+        most: vec![BIG_DOUBLE; base.len()],
+        base,
+    };
+    let mut leaves = |i: i32| -> Result<bool> {
+        Ok(
+            match growth.place(pseudo, corner, solvers, f64::from(i) / 1000.0)? {
+                Some(_) => {
+                    springs_on_faces(k, target, pseudo, corner, planes, tol)? != Springs::Clear
+                }
+                None => true,
+            },
+        )
+    };
+    let lo = (1..1000).find(|&i| f64::from(i) >= 1000.0 * least_scale);
+    let fit = match lo {
+        Some(lo) if !leaves(lo)? => Some(bisect_thousandths(lo, 1000, &mut leaves)? - 1),
+        _ => None,
+    };
+    let Some(fit) = fit.map(|i| f64::from(i) / 1000.0) else {
+        return Ok(Some(SetbackRefusal::no_room(
+            "Fillet Error: no setback at or above where the rails cross keeps the setback corner's spring curves on their faces",
+            Some(0.0),
+        )));
+    };
+    if let Some(a) = asked {
+        return Ok(Some(setback_too_long(
+            a,
+            vtx,
+            fit * a.setback,
+            SPRING_LEAVES,
+        )));
+    }
+    let list: Vec<String> = growth.base.iter().map(|&s| fmt_g(fit * s)).collect();
+    Ok(Some(SetbackRefusal::not_built(format!(
+        "Fillet Error: the rule's setbacks take a setback corner's spring curve off its face (it comes within the tolerances of another edge of the face, or is not shown not to): setbacks of {} keep every spring curve on its face",
+        list.join(", ")
+    ))))
+}
+
 /// A setback asked at `vtx` that, with its ease, does not fit (`why`): refused, naming
 /// `largest`, below which one fits ([`BlendRefusal::SetbackTooLong`]).
 fn setback_too_long(a: SetBackFill, vtx: VertexId, largest: f64, why: &str) -> SetbackRefusal {
@@ -1907,6 +2230,14 @@ pub fn build_setback_fill<S: SetbackSolvers>(
     if open && order == 1 {
         return open_setback_springs(pseudo, corner, &planes.planes, &planes.edges);
     }
+    // beside a curved face, the spring curves stay inside their trimmed faces (#2343 (d))
+    if curved {
+        if let Some(refusal) =
+            springs_refusal(k, target, pseudo, corner, solvers, &planes, fills, tol)?
+        {
+            return Ok(Err(refusal));
+        }
+    }
     let mut stats = FillStats::default();
     let first = fill_hole_counted(
         k,

solidcore/crates/solidcore/src/blend/fillet_corner/p1.rs

@@ -1229,10 +1229,15 @@ pub fn check_nx1_degeneracy_status(
                 | SolidError::Cancelled { .. }
                 | SolidError::NotFound { .. }),
             ) => Err(e),
-            Err(
-                e @ (SolidError::InvalidInput { reason, .. }
-                | SolidError::PortInvariant { reason, .. }),
-            ) if reason == NULL_DEREF => Err(e),
+            Err(e)
+                if matches!(
+                    &e,
+                    SolidError::InvalidInput { reason, .. }
+                    | SolidError::PortInvariant { reason, .. } if *reason == NULL_DEREF
+                ) =>
+            {
+                Err(e)
+            }
             Err(e) => Ok(Err(e)),
         }
     };

solidcore/crates/solidcore/src/blend/fillet_exact.rs

@@ -2521,46 +2521,11 @@ fn keep_definition(
     let Some(surface) = pseudo.geom_mut(g)?.fillet_surface_mut(None)? else {
         return Err(SolidError::null_pointer(OP));
     };
-    keep_round_if_proved(k, surface, round, inputs.tol)?;
+    round.recertify(k, surface)?;
+    surface.set_exact_round(Some(round));
     Ok(())
 }
 
-/// `round` kept on `net` where it is proved ([`ExactRound::recertify`]), returning whether it
-/// was. The class is read within `tol`, the body's tolerance, and the certificate to rounding.
-/// Supports only that close to the class (a cylinder's axis 1e-13 off square to a plane, as
-/// read from a record) make a net that is the round but not provably on the class's surface:
-/// no bound of 0, so it keeps no definition. A net further off the
-/// class than `tol` ([`ExactRound::miss`]) is built wrongly, and stays an error.
-///
-/// # Errors
-///
-/// The certificate's refusal of a net more than `tol` off the class, or of supports that
-/// give the class no surface; those of the certificate and of [`ExactRound::miss`].
-pub fn keep_round_if_proved(
-    k: &Kernel,
-    net: &mut Surface,
-    round: ExactRound,
-    tol: f64,
-) -> Result<bool> {
-    match round.recertify(k, net) {
-        Ok(_) => {
-            net.set_exact_round(Some(round));
-            Ok(true)
-        }
-        Err(e) => {
-            let off = matches!(
-                &e,
-                SolidError::InvalidInput { operation, .. }
-                    if *operation == crate::surface::implicit::OP_EXACT
-            );
-            match off.then(|| round.miss(k, net)).transpose()?.flatten() {
-                Some(miss) if miss <= tol => Ok(false),
-                _ => Err(e),
-            }
-        }
-    }
-}
-
 /// [`calc_exact_fillet_geom`]'s build by the class (`CalcExactFilletGeom`), without the
 /// definition kept.
 #[allow(clippy::too_many_arguments)]
@@ -2719,7 +2684,8 @@ fn exact_fillet_geom_of_class(
 mod tests {
     use super::*;
 
-    /// A box's edge rounded 2: the round's net, without its definition, and the definition.
+    /// A cylinder R 10, 20 high, its top rim rounded 2 (a round of the circle class): the
+    /// round's net, without its definition, and the definition.
     fn kept_round() -> (Kernel, Surface, ExactRound) {
         use crate::blend::fillet_executive::session::FilletSession;
         use crate::kernel::UpstreamFixes;
@@ -2729,24 +2695,51 @@ mod tests {
             fixes: UpstreamFixes::all(),
             ..Kernel::default()
         };
-        let mut b = crate::primitive::api_primitives::create_box(
+        let mut b = crate::primitive::api_primitives::create_cylinder(
             &mut k,
             Point3::new(0.0, 0.0, 0.0),
-            30.0,
-            20.0,
             10.0,
+            20.0,
         )
         .unwrap();
-        let edge = b.edge_list()[0];
+        // the top rim: the edge through (10, 0, 20)
+        let rim = *b
+            .edge_list()
+            .iter()
+            .min_by(|&&x, &&y| {
+                let d = |e| {
+                    crate::query::api_queries::edge_closest_point(
+                        &k,
+                        &b,
+                        e,
+                        Point3::new(10.0, 0.0, 20.0),
+                    )
+                    .unwrap()
+                    .closest
+                    .distance
+                        + crate::query::api_queries::edge_closest_point(
+                            &k,
+                            &b,
+                            e,
+                            Point3::new(-10.0, 0.0, 20.0),
+                        )
+                        .unwrap()
+                        .closest
+                        .distance
+                };
+                d(x).total_cmp(&d(y))
+            })
+            .unwrap();
         {
             let mut s = FilletSession::new(&mut k, &mut b).unwrap();
-            s.prepare_constant_radius_edges(&mut k, &[edge], 2.0, 1, 1, 1.0)
+            s.prepare_constant_radius_edges(&mut k, &[rim], 2.0, 1, 1, 1.0)
                 .unwrap();
             s.do_fillet(&mut k).unwrap();
         }
         for &f in b.face_list() {
             let s = face::surface(&b, f).unwrap().unwrap();
             if let Some(BlendRef::Exact { round, .. }) = s.procedural_blend() {
+                assert_eq!(round.class, ExactClass::Circle);
                 let round = round.clone();
                 let mut net = s.clone();
                 net.set_exact_round(None);
@@ -2769,23 +2762,21 @@ mod tests {
         net
     }
 
-    /// The class is read within 2e-5 here. A net on it keeps its definition; one off it by
-    /// less keeps none (the round of supports that close to the class); one further off is
-    /// built wrongly, and stays an error.
+    /// A circle-class round's definition is the torus its net is on, a stated distance from
+    /// the supports' class torus within the tolerance the class was read at (2e-5 here): the
+    /// net as built is at 0, the net moved by (1, 1, 1) 1e-7 is at sqrt 3 1e-7, and the net
+    /// moved by (1, 1, 1) 1e-3 is refused.
     #[test]
-    fn a_net_off_its_class_keeps_no_definition_within_the_tolerance_only() {
-        let tol = 2e-5;
+    fn a_circle_rounds_net_is_certified_on_its_own_torus_near_the_class() {
         let (k, net, round) = kept_round();
-        let mut on = net.clone();
-        assert!(keep_round_if_proved(&k, &mut on, round.clone(), tol).unwrap());
-        assert!(on.procedural_blend().is_some());
-
-        let mut near = moved(&k, &net, 1e-7);
-        assert!(!keep_round_if_proved(&k, &mut near, round.clone(), tol).unwrap());
-        assert!(near.procedural_blend().is_none());
-
-        let mut far = moved(&k, &net, 1e-3);
-        let refused = keep_round_if_proved(&k, &mut far, round, tol);
+        assert_eq!(round.recertify(&k, &net).unwrap(), 0.0);
+        assert!(round.supports_distance(&k, &net).unwrap() < 1e-12);
+        let near = moved(&k, &net, 1e-7);
+        assert_eq!(round.recertify(&k, &near).unwrap(), 0.0);
+        let d = round.supports_distance(&k, &near).unwrap();
+        assert!((d - 3.0_f64.sqrt() * 1e-7).abs() < 1e-12, "{d}");
+        let far = moved(&k, &net, 1e-3);
+        let refused = round.recertify(&k, &far);
         assert!(
             matches!(refused, Err(SolidError::InvalidInput { .. })),
             "{refused:?}"

solidcore/crates/solidcore/src/blend/fillet_exact/rational.rs

@@ -1304,7 +1304,7 @@ fn rational_spine_parts(
 #[cfg(test)]
 mod tests {
     use super::*;
-    use crate::blend::fillet_exact::{classify_supports, keep_round_if_proved, ClassInputs};
+    use crate::blend::fillet_exact::{classify_supports, ClassInputs};
     use crate::curve::curve::CurveKind;
     use crate::geom::axis2_placement::Axis2Placement;
     use crate::surface::cone::Cone;
@@ -1779,10 +1779,10 @@ mod tests {
                             inputs,
                         )
                         .unwrap();
-                        assert!(
-                            keep_round_if_proved(&k, &mut net, round, inputs.tol).unwrap(),
-                            "{offsets:?}, {contact:?}"
-                        );
+                        if let Err(e) = round.recertify(&k, &net) {
+                            panic!("{offsets:?}, {contact:?}: {e}");
+                        }
+                        net.set_exact_round(Some(round));
                         assert_eq!(
                             net.procedural_blend().unwrap().exact().unwrap().bound(),
                             0.0

solidcore/crates/solidcore/src/blend/fillet_section/certificate.rs

@@ -308,6 +308,61 @@ pub fn nurbs_partials_over_piece(
     va: f64,
     vb: f64,
     lk: usize,
+) -> Result<Partials<Ivl>> {
+    partials_over_piece(cn, ku, kv, ua, ub, va, vb, lk, None)
+}
+
+/// [`nurbs_partials_over_piece`] for a box inside the piece's closed knot span (not the
+/// fork's): there the weight is a convex combination of the piece's control weights, so it
+/// lies between their least and greatest, and its enclosure is cut to that range before
+/// the quotient. Where the Taylor enclosure of the weight alone holds 0 (a rational piece of
+/// high degree over a large box) this proves it positive. A box past the span is enclosed
+/// as [`nurbs_partials_over_piece`] encloses it.
+///
+/// # Errors
+///
+/// As [`nurbs_partials_over_piece`].
+#[allow(clippy::too_many_arguments)]
+pub fn nurbs_partials_within_span(
+    cn: &Nurbs,
+    ku: usize,
+    kv: usize,
+    ua: f64,
+    ub: f64,
+    va: f64,
+    vb: f64,
+    lk: usize,
+) -> Result<Partials<Ivl>> {
+    let inside = |u: &[f64], k: usize, a: f64, b: f64| {
+        knot(u, k as isize) <= a && b <= knot(u, k as isize + 1)
+    };
+    let hull = if inside(&cn.u, ku, ua, ub) && inside(&cn.v, kv, va, vb) {
+        let mut h: Option<Ivl> = None;
+        for i in (ku + 1).saturating_sub(cn.p + 1)..=ku {
+            for j in (kv + 1).saturating_sub(cn.q + 1)..=kv {
+                let w = Ivl::from(pw_at(&cn.pw, 4 * (i * cn.nv + j) + 3));
+                h = Some(h.map_or(w, |x| x.hull(w)));
+            }
+        }
+        h
+    } else {
+        None
+    };
+    partials_over_piece(cn, ku, kv, ua, ub, va, vb, lk, hull)
+}
+
+/// [`nurbs_partials_over_piece`], the weight's enclosure cut to `weights` where given.
+#[allow(clippy::too_many_arguments)]
+fn partials_over_piece(
+    cn: &Nurbs,
+    ku: usize,
+    kv: usize,
+    ua: f64,
+    ub: f64,
+    va: f64,
+    vb: f64,
+    lk: usize,
+    weights: Option<Ivl>,
 ) -> Result<Partials<Ivl>> {
     let um = 0.5 * (ua + ub);
     let vm = 0.5 * (va + vb);
@@ -377,6 +432,10 @@ pub fn nurbs_partials_over_piece(
         }
     }
     let w00 = at2(&wv, 0, 0, IZ);
+    let w00 = match weights {
+        Some(h) => Ivl::new(w00.lo.max(h.lo), w00.hi.min(h.hi)),
+        None => w00,
+    };
     let positive = w00.lo > 0.0;
     if !positive {
         // "SmGnSectionFSG: a face's weights are not positive over a box"
@@ -2160,6 +2219,23 @@ mod tests {
     /// A box across a knot line: the piecewise enclosure holds every partial of the face on
     /// both sides (the third u-partial jumps at the knot), which one piece continued over the
     /// box does not; a knot of too low a continuity, and a box past the knots, are refused.
+    #[test]
+    fn a_box_past_its_span_keeps_the_unclipped_weight() {
+        // the control weights bound the weight only inside the span: a box across the knot at
+        // u = 1 is enclosed as `nurbs_partials_over_piece` encloses it
+        let mut n = cubic_with_knot(1);
+        // weights from 1 to 4.5: the weight continued past the span leaves their range
+        for (i, w) in n.pw.chunks_mut(4).enumerate() {
+            let k = 1.0 + 0.5 * i as f64;
+            for c in w.iter_mut() {
+                *c *= k;
+            }
+        }
+        let a = nurbs_partials_within_span(&n, 3, 1, 0.9, 1.1, 0.2, 0.3, 3).unwrap();
+        let b = nurbs_partials_over_piece(&n, 3, 1, 0.9, 1.1, 0.2, 0.3, 3).unwrap();
+        assert_eq!(a, b);
+    }
+
     #[test]
     fn a_box_across_a_knot_line_is_enclosed_piece_by_piece() {
         let n = cubic_with_knot(1);

solidcore/crates/solidcore/src/curve/curve/p5.rs

@@ -81,7 +81,14 @@
 //! - **Length.** Spans of degree above 1 use the ported `SmIntegrator` (unit
 //!   `mass.integrator`; with `Kernel::fixes.integrator_propagates_failure`, WR-94,
 //!   failed span integrals propagate instead of contributing zero). `Length` needs the
-//!   kernel (the cache tessellation reads its tolerances).
+//!   kernel (the cache tessellation reads its tolerances). Not upstream: the accuracy
+//!   is held over the whole curve, not per span. Upstream integrates each span to
+//!   `dDesiredAccuracy / span count` relative to that span's integral so far, so each of
+//!   a span's steps may err by nearly that and the steps together by up to their number
+//!   times it; here each step is held to half the accuracy relative to its share of the
+//!   estimated length plus its own increment (`OdeOptions::rate`), shares that add up to
+//!   at most twice the length ([`Curve::length`];
+//!   `plan/findings/curve.curve_p5--curve-length-global-error-moves-cases-2026-11-08.md`).
 //! - **Out-params.** Flags with outputs are `Option`s (`IsLine`: point and vector;
 //!   `IsArc`: frame, radius, start and end angle; the guesses); `IsLinear`'s
 //!   optional outputs are the fields of [`Linearity`] (`want_deviation` stands for a

solidcore/crates/solidcore/src/curve/ellipse/p2.rs

@@ -2330,6 +2330,40 @@ mod tests {
         assert_eq!(c.base().form(), BSplineCurveForm::EllipticArc);
     }
 
+    #[test]
+    fn issue_1518_short_arc_inverts_each_point_to_itself() {
+        // The 70.9232 x 16 ellipse of #1518 on an arc 7e-5 degrees long, shorter than
+        // the angular tolerance (1e-4 degrees); atan2 puts its points a period up.
+        let k = kernel();
+        let (d0, d1) = (-10.0, -10.0 + 7.0e-5);
+        let e = Ellipse::new(
+            &k,
+            Vec3::ZERO,
+            Vec3::X,
+            Vec3::Y,
+            Extent1d::from_min_max(d0, d1),
+            70.9232,
+            16.0,
+            &EllipseOptions::default(),
+        )
+        .expect("ellipse");
+        let fractions = [0.25, 0.5, 0.75, 1.0];
+        let points: Vec<(f64, Point3)> = fractions
+            .iter()
+            .map(|f| {
+                let a = d0 + f * (d1 - d0);
+                (a, e.evaluate_step_point(a).expect("step point"))
+            })
+            .collect();
+
+        // each point inverts to its own angle, not to the arc's start (the pinned C++
+        // returns -10 for all four)
+        for &(a, p) in &points {
+            let t = e.step_inversion(&k, p, false, 0.0).0;
+            assert!((t - a).abs() <= 1e-9 * a.abs(), "{a}: {t}");
+        }
+    }
+
     #[test]
     fn step_and_nurb_parameters_agree() {
         let k = kernel();

solidcore/crates/solidcore/src/curve/from_parameters.rs

@@ -190,19 +190,33 @@ pub fn conic_on_form(k: &Kernel, conic: &Record, form: &Record) -> Result<Curve>
     Ok(Curve::from(e))
 }
 
-/// A pcurve's numbers as the kernel's UV trim of an edge over `interval` (the edge's interval
-/// in the kernel's parameter): the record's pcurve runs along the edge over the edge's own
-/// interval in the record, and the kernel's trim runs along the edge over the edge's kernel
-/// interval, so its knots are mapped affinely from the pcurve's domain onto `interval` (copied
-/// as they are where the two are the same). Its points are scaled by `scale` in u and v: a
-/// plane face's kernel parameters are the record's times its axes' lengths (`[1, 1]`
-/// elsewhere, copied).
+/// Map a pcurve's entire natural support onto `interval` and scale its UV
+/// coordinates. This is for callers that intend to remap the whole support.
+/// A B-rep edge may occupy only part of that support: its importer must use
+/// [`uv_trim_on_edge`] with the record edge's actual interval instead.
 ///
 /// # Errors
 ///
 /// `InvalidInput` for a spline whose knots do not fit its points or a pcurve or interval of no
 /// length; those of the constructors.
 pub fn uv_trim(c: &Record2, interval: &Extent1d, scale: [f64; 2]) -> Result<Curve> {
+    let source = c
+        .interval()
+        .ok_or_else(|| SolidError::invalid_input(OP_TRIM, "invalid pcurve interval"))?;
+    uv_trim_on_edge(c, source, interval, scale)
+}
+
+/// Rebuild a pcurve while mapping the record edge parameter to the kernel edge
+/// parameter. The pcurve's own support may extend beyond either edge endpoint.
+///
+/// # Errors
+/// Refuses invalid edge intervals or malformed UV spline data.
+pub fn uv_trim_on_edge(
+    c: &Record2,
+    source: [f64; 2],
+    interval: &Extent1d,
+    scale: [f64; 2],
+) -> Result<Curve> {
     let bad = |reason: &'static str| SolidError::invalid_input(OP_TRIM, reason);
     let [su, sv] = scale;
     let same = su == 1.0 && sv == 1.0;
@@ -238,14 +252,35 @@ pub fn uv_trim(c: &Record2, interval: &Extent1d, scale: [f64; 2]) -> Result<Curv
         return Err(bad("too few knots"));
     };
     let (lo, hi) = (interval.min(), interval.max());
-    if !(s_hi > s_lo) {
+    let [from_lo, from_hi] = source;
+    if !(s_lo.is_finite()
+        && s_hi.is_finite()
+        && s_hi > s_lo
+        && from_lo.is_finite()
+        && from_hi.is_finite()
+        && from_hi > from_lo
+        && lo.is_finite()
+        && hi.is_finite()
+        && hi > lo)
+    {
         return Err(bad("the pcurve's domain has no length"));
     }
-    let mapped: Vec<f64> = if (s_lo, s_hi) == (lo, hi) {
+    let mapped: Vec<f64> = if (from_lo, from_hi) == (lo, hi) {
         knots.to_vec()
     } else {
-        let by = (hi - lo) / (s_hi - s_lo);
-        knots.iter().map(|s| lo + (s - s_lo) * by).collect()
+        let by = (hi - lo) / (from_hi - from_lo);
+        knots
+            .iter()
+            .map(|s| {
+                if *s == from_lo {
+                    lo
+                } else if *s == from_hi {
+                    hi
+                } else {
+                    lo + (s - from_lo) * by
+                }
+            })
+            .collect()
     };
     Ok(Curve::from(spline(&mapped, &rows, 2, OP_TRIM)?))
 }
@@ -273,9 +308,11 @@ pub struct RecordCurve {
 /// The record of the kernel's edge curve `c` over `interval` (its kernel parameter), the
 /// inverse of [`from_parameters`] and [`conic_on_form`]:
 ///
-/// - **Line:** the line through the curve's points at the interval's ends, over `[0, 1]`. A
-///   kernel line is affine in its parameter (its point plus the parameter times its vector),
-///   so this is the same line, the record's parameter an affine image of the kernel's.
+/// - **Line:** the line as the kernel holds it, its point and its point plus its vector, over
+///   the STEP parameters of the interval's ends (`ConvertTFromNURBSToSTEP`); where those run
+///   down, the vector and the parameters are negated so the interval increases. This is what
+///   SolidCraft's flat export wrote (`FlatFromBrep`'s line origin and direction, its range in
+///   STEP parameters), so a line comes back as it went in, not reparameterised onto `[0, 1]`.
 /// - **Circle, ellipse:** the label on the conic's own frame (copied, not rebuilt by a cross
 ///   product), its y axis reversed where the conic's NURBS runs against its angle (its own
 ///   `inside_out`, no sampling), with that NURBS as its form, over the kernel's interval.
@@ -298,15 +335,30 @@ pub fn record_of(k: &Kernel, c: &Curve, interval: &Extent1d) -> Result<RecordCur
         return Err(bad("the interval is not finite and increasing"));
     }
     match c.kind() {
-        CurveKind::Line(_) => {
-            let (a, b) = (c.evaluate_point(k, lo)?, c.evaluate_point(k, hi)?);
+        CurveKind::Line(l) => {
+            let can = l.canonical();
+            let (mut s0, mut s1) = (
+                c.convert_t_from_nurbs_to_step(k, lo)?,
+                c.convert_t_from_nurbs_to_step(k, hi)?,
+            );
+            let mut v = can.vector;
+            // a line whose parameter runs against its vector over the edge: the vector
+            // reversed, the parameters negated, so the record's interval increases
+            if s0 > s1 {
+                (s0, s1) = (-s0, -s1);
+                v = -v;
+            }
+            if !(s0.is_finite() && s1.is_finite() && s1 > s0) {
+                return Err(bad("a line's parameters over the edge are not increasing"));
+            }
+            let p = can.point;
             return Ok(RecordCurve {
                 curve: Record::Line {
-                    start: [a.x, a.y, a.z],
-                    end: [b.x, b.y, b.z],
+                    start: [p.x, p.y, p.z],
+                    end: [p.x + v.x, p.y + v.y, p.z + v.z],
                 },
                 nurbs: None,
-                interval: [0.0, 1.0],
+                interval: [s0, s1],
             });
         }
         CurveKind::Ellipse(e) => {

solidcore/crates/solidcore/src/curve/from_parameters/tests.rs

@@ -232,10 +232,11 @@ fn a_trim_runs_over_its_edges_kernel_interval() {
     assert_eq!((p.x, p.y), (1.0, 2.0));
 }
 
-/// A kernel line goes to the record by its points at its interval's ends, over [0, 1]: the
-/// same line, its parameter an affine image of the kernel's, and back again unchanged.
+/// A kernel line goes to the record as the kernel holds it, its point and its point plus its
+/// vector, over the STEP parameters of its interval (#3137: as SolidCraft's flat export wrote
+/// it), and back again unchanged.
 #[test]
-fn a_line_goes_back_by_its_two_end_points() {
+fn a_line_goes_back_as_the_kernel_holds_it() {
     let k = k();
     let line = Curve::from(Line::create_canonical(
         Point3::new(1.0, 2.0, 3.0),
@@ -245,11 +246,44 @@ fn a_line_goes_back_by_its_two_end_points() {
     assert_eq!(
         r.curve,
         Record::Line {
-            start: [2.0, 2.0, 3.0],
-            end: [5.0, 2.0, 3.0],
+            start: [1.0, 2.0, 3.0],
+            end: [3.0, 2.0, 3.0],
         }
     );
-    assert_eq!((&r.nurbs, r.interval), (&None, [0.0, 1.0]));
+    assert_eq!((&r.nurbs, r.interval), (&None, [0.5, 2.0]));
+    let back = from_parameters(&k, &r.curve, r.interval).unwrap();
+    assert_eq!(record_of(&k, &back.curve, &back.interval).unwrap(), r);
+}
+
+/// A line whose STEP parameter runs against its NURBS parameter (`inside_out`: `s = -t`) goes to
+/// the record with its vector reversed and its interval negated, so the interval increases; the
+/// record's point at each end of it is the kernel's at that end, bit for bit, and the round
+/// trip is the identity.
+#[test]
+fn a_reversed_line_goes_back_with_its_vector_turned() {
+    let k = k();
+    let line = Curve::from(Line::infinite(
+        Point3::new(1.0, 2.0, 3.0),
+        Vec3::new(2.0, 0.0, 0.0),
+        3,
+        true,
+    ));
+    let (lo, hi) = (0.5, 2.0);
+    let r = record_of(&k, &line, &Extent1d::from_raw(lo, hi)).unwrap();
+    let Record::Line { start, end } = r.curve else {
+        panic!("not a line: {:?}", r.curve)
+    };
+    assert!(r.interval[0] < r.interval[1], "{:?}", r.interval);
+    let on = |s: f64| {
+        Point3::new(
+            start[0] + s * (end[0] - start[0]),
+            start[1] + s * (end[1] - start[1]),
+            start[2] + s * (end[2] - start[2]),
+        )
+    };
+    // the record's interval runs the kernel's ends in order
+    assert_eq!(on(r.interval[0]), at(&k, &line, lo));
+    assert_eq!(on(r.interval[1]), at(&k, &line, hi));
     let back = from_parameters(&k, &r.curve, r.interval).unwrap();
     assert_eq!(record_of(&k, &back.curve, &back.interval).unwrap(), r);
 }

solidcore/crates/solidcore/src/error/offset.rs

@@ -172,8 +172,11 @@ pub enum Unsoundness {
     GeometryUnchecked,
     /// The input was a manifold solid and the body is not.
     NotManifoldSolid,
-    /// The body is a manifold solid whose volume is not positive.
+    /// The body is a manifold solid whose volume's enclosure lies below 0.
     VolumeNotPositive,
+    /// The body is a manifold solid whose volume's enclosure still holds 0 after its
+    /// budget: its sign is not proved.
+    VolumeUndecided,
 }
 
 /// How loops of an offset face touch without crossing ([`OffsetFailure::WallsTouch`]).
@@ -449,6 +452,10 @@ impl core::fmt::Display for OffsetFailure {
                     "the local operation's body is a manifold solid whose volume is not \
                      positive: refused, the input unchanged",
                 ),
+                Unsoundness::VolumeUndecided => f.write_str(
+                    "the local operation's body is a manifold solid whose volume's sign \
+                     could not be proved: refused, the input unchanged",
+                ),
             },
             Self::ExactCurveUncut => f.write_str(
                 "the extended faces beside an edge meet on an exact curve that could not be \

solidcore/crates/solidcore/src/geom.rs

@@ -29,6 +29,7 @@ pub mod polar_box;
 pub mod polynomial;
 pub mod pseudo_box;
 pub mod solution_array;
+pub mod step_matrix;
 pub mod tol;
 pub mod tools;
 pub mod transform;

solidcore/crates/solidcore/src/geom/extent1d.rs

@@ -72,6 +72,9 @@
 //!   prefix and zero-fills, unbounded dimensions are not written, counts are
 //!   incremented); arrays shorter than the dimension (undefined behaviour upstream)
 //!   are rejected with [`SolidError::InvalidInput`].
+//! - `ContainsPeriodicValue` moves a value within the tolerance of the top of the period
+//!   above the start down by the period, and keeps it where that lies in the interval,
+//!   instead of setting it to the start (WR-509, #1518; tangency-labs/smlib#46).
 //! - `SM_ASSERT*` debug checks and the error-log side effect of `SE(...)` are not
 //!   ported (they do not change results). The destructor's "undefined" sentinel has
 //!   no Rust counterpart; [`Extent1d::is_defined`] still checks for it.
@@ -844,12 +847,16 @@ impl Extent1d {
 
         contained = map > self.min - zero && map < self.max + zero;
 
-        if !contained
-            && are_same_to_tol(map, ivl.max(), zero)
-            && are_same_to_tol(map - period, self.min, zero)
-        {
-            map = self.min;
-            contained = true;
+        let mut kept_down = false;
+        if !contained && are_same_to_tol(map, ivl.max(), zero) {
+            // a period down, kept where it lies in the interval; the C++ sets it to the
+            // start instead (WR-509, #1518; tangency-labs/smlib#46)
+            let down = map - period;
+            if down > self.min - zero && down < self.max + zero {
+                map = down;
+                contained = true;
+                kept_down = true;
+            }
         }
 
         let periodic_value =
@@ -861,6 +868,12 @@ impl Extent1d {
                 map
             };
         let mut dist_to_min = map - self.min;
+        if kept_down {
+            // it can lie up to the tolerance below the start: its distance from it, not a
+            // signed offset (assert_valid takes min2 of the two). Only this new case: other
+            // inputs keep the signed value upstream gives them.
+            dist_to_min = dist_to_min.abs();
+        }
         if dist_to_min > period / 2.0 {
             dist_to_min = period - dist_to_min;
         }
@@ -1150,6 +1163,29 @@ mod tests {
             .is_err());
     }
 
+    #[test]
+    fn issue_1518_value_past_start_moves_down_a_period() {
+        // An interval shorter than the tolerance (1e-4 degrees), and a value 3e-5 past
+        // its start given a period up: the C++ returns the start (-10).
+        let q = Extent1d::from_min_max(-10.0, -10.0 + 7.0e-5);
+        let v = 350.0 + 3.0e-5;
+        let c = q.contains_periodic_value(v, 360.0, -1.0);
+        assert!(c.contained);
+        assert_eq!(c.periodic_value, v - 360.0);
+        assert!((c.dist_to_min - 3.0e-5).abs() < 1e-12);
+        assert_eq!(q.clamp_periodic_value(v, 360.0, -1.0), v - 360.0);
+
+        // a value within the tolerance below the start keeps its place a period down
+        // (the C++: the start, 0)
+        let r = Extent1d::from_min_max(0.0, 90.0);
+        let w = 360.0 - 5.0e-5;
+        let c = r.contains_periodic_value(w, 360.0, -1.0);
+        assert!(c.contained);
+        assert_eq!(c.periodic_value, w - 360.0);
+        // its distance to the start is a distance, not the signed offset -5e-5
+        assert!((c.dist_to_min - 5.0e-5).abs() < 1e-12, "{}", c.dist_to_min);
+    }
+
     #[test]
     fn clamp_vector() {
         let mut nd = ExtentNd::new(3);

solidcore/crates/solidcore/src/geom/extent2d.rs

@@ -1004,10 +1004,12 @@ mod tests {
         );
         assert!(!e1.is_point_on_boundary(p(1.1, 2.1), EFF_ZERO).0);
 
-        assert_eq!(
-            e1.contains_periodic_point(p(8.9, 3.0), 4.0, 0.0, 0.2),
-            (true, p(1.0, 3.0))
-        );
+        // u = 8.9 is 0.9 a period down, within the tolerance of [1, 3]: it keeps 0.9
+        // (WR-509, #1518; upstream's MyTest expects the start, 1.0)
+        let (inside, q) = e1.contains_periodic_point(p(8.9, 3.0), 4.0, 0.0, 0.2);
+        assert!(inside);
+        assert!((q.x - 0.9).abs() <= 1e-12, "{}", q.x);
+        assert_eq!(q.y, 3.0);
         assert!(!e1.contains_periodic_point(p(8.9, 3.0), 4.0, 0.0, 0.0).0);
 
         assert_eq!(e1.evaluate(0.5, 0.5), p(2.0, 3.0));

solidcore/crates/solidcore/src/geom/step_matrix.rs

@@ -0,0 +1,183 @@
+//! Affine matrices for STEP placements and transformations.
+//!
+//! STEP keeps placements as frames and transformation operators as directions and
+//! scales.  Building their matrices and composing or inverting them is geometric
+//! work, so it lives here rather than in `solidcore-record` or `solidcore-ops`.
+//!
+//! The matrix convention is the kernel's: rows 0–2 are the images of X, Y and Z,
+//! row 3 is the translation (`p' = p·A + t`).
+
+use crate::geom::vector3d::Vec3;
+
+/// A 4×4 affine matrix in the kernel's row-major convention.
+pub type Matrix4 = [[f64; 4]; 4];
+
+/// The identity matrix.
+pub const IDENTITY: Matrix4 = [
+    [1.0, 0.0, 0.0, 0.0],
+    [0.0, 1.0, 0.0, 0.0],
+    [0.0, 0.0, 1.0, 0.0],
+    [0.0, 0.0, 0.0, 1.0],
+];
+
+/// `a · b` in the row-vector convention.
+#[must_use]
+#[allow(clippy::indexing_slicing)] // 4×4 loops over fixed-size arrays
+pub fn concat(a: &Matrix4, b: &Matrix4) -> Matrix4 {
+    let mut out = [[0.0; 4]; 4];
+    for (row, out_row) in out.iter_mut().enumerate() {
+        for (col, cell) in out_row.iter_mut().enumerate() {
+            *cell = (0..4).map(|k| a[row][k] * b[k][col]).sum();
+        }
+    }
+    out
+}
+
+/// The inverse of an affine matrix, or `None` when its linear part is singular or
+/// the entries are not finite.
+#[must_use]
+pub fn inverse(m: &Matrix4) -> Option<Matrix4> {
+    let (a, b, c) = (
+        Vec3::new(m[0][0], m[0][1], m[0][2]),
+        Vec3::new(m[1][0], m[1][1], m[1][2]),
+        Vec3::new(m[2][0], m[2][1], m[2][2]),
+    );
+    let det = a.dot(b.cross(c));
+    if !det.is_finite() || det == 0.0 {
+        return None;
+    }
+    let x = b.cross(c);
+    let y = c.cross(a);
+    let z = a.cross(b);
+    // The inverse's columns are the cofactor cross products; its translation is
+    // `-(t · A⁻¹)` in the row-vector convention.
+    let linear = [
+        [x.x / det, y.x / det, z.x / det],
+        [x.y / det, y.y / det, z.y / det],
+        [x.z / det, y.z / det, z.z / det],
+    ];
+    let t = Vec3::new(m[3][0], m[3][1], m[3][2]);
+    let translation = Vec3::new(
+        -(t.x * linear[0][0] + t.y * linear[1][0] + t.z * linear[2][0]),
+        -(t.x * linear[0][1] + t.y * linear[1][1] + t.z * linear[2][1]),
+        -(t.x * linear[0][2] + t.y * linear[1][2] + t.z * linear[2][2]),
+    );
+    let out = [
+        [linear[0][0], linear[0][1], linear[0][2], 0.0],
+        [linear[1][0], linear[1][1], linear[1][2], 0.0],
+        [linear[2][0], linear[2][1], linear[2][2], 0.0],
+        [translation.x, translation.y, translation.z, 1.0],
+    ];
+    out.iter().flatten().all(|v| v.is_finite()).then_some(out)
+}
+
+fn unit(value: [f64; 3]) -> Option<Vec3> {
+    let v = Vec3::from(value);
+    v.unitize()
+        .ok()
+        .filter(|v| v.x.is_finite() && v.y.is_finite() && v.z.is_finite())
+}
+
+/// The matrix of an `AXIS2_PLACEMENT`: origin, Z axis and X reference direction.
+///
+/// An omitted axis is +Z; an omitted reference direction chooses any X perpendicular
+/// to Z. The reference direction is projected onto the plane normal to Z.
+#[must_use]
+pub fn frame_matrix(
+    origin: [f64; 3],
+    axis: Option<[f64; 3]>,
+    ref_direction: Option<[f64; 3]>,
+) -> Option<Matrix4> {
+    let z = unit(axis.unwrap_or([0.0, 0.0, 1.0]))?;
+    let x = if let Some(raw) = ref_direction {
+        let v = Vec3::from(raw);
+        let projected = v - z * v.dot(z);
+        unit([projected.x, projected.y, projected.z])?
+    } else {
+        let candidate = if z.x.abs() < 0.9 {
+            Vec3::new(1.0, 0.0, 0.0)
+        } else {
+            Vec3::new(0.0, 1.0, 0.0)
+        };
+        let v = candidate - z * candidate.dot(z);
+        unit([v.x, v.y, v.z])?
+    };
+    let y = z.cross(x);
+    Some([
+        [x.x, x.y, x.z, 0.0],
+        [y.x, y.y, y.z, 0.0],
+        [z.x, z.y, z.z, 0.0],
+        [origin[0], origin[1], origin[2], 1.0],
+    ])
+}
+
+/// The matrix of a `CARTESIAN_TRANSFORMATION_OPERATOR_3D`.
+///
+/// An omitted direction is the matching global axis; an omitted scale is 1 (or
+/// `scale` for the second and third scale).
+#[must_use]
+pub fn operator_matrix(
+    axis1: Option<[f64; 3]>,
+    axis2: Option<[f64; 3]>,
+    axis3: Option<[f64; 3]>,
+    origin: [f64; 3],
+    scale: Option<f64>,
+    scale2: Option<f64>,
+    scale3: Option<f64>,
+) -> Option<Matrix4> {
+    let x = unit(axis1.unwrap_or([1.0, 0.0, 0.0]))?;
+    let y = unit(axis2.unwrap_or([0.0, 1.0, 0.0]))?;
+    let z = unit(axis3.unwrap_or([0.0, 0.0, 1.0]))?;
+    let sx = scale.unwrap_or(1.0);
+    let sy = scale2.or(scale).unwrap_or(1.0);
+    let sz = scale3.or(scale).unwrap_or(1.0);
+    if ![sx, sy, sz].iter().all(|v| v.is_finite() && *v != 0.0) {
+        return None;
+    }
+    Some([
+        [x.x * sx, x.y * sx, x.z * sx, 0.0],
+        [y.x * sy, y.y * sy, y.z * sy, 0.0],
+        [z.x * sz, z.y * sz, z.z * sz, 0.0],
+        [origin[0], origin[1], origin[2], 1.0],
+    ])
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn an_identity_inverse_is_the_identity() {
+        assert_eq!(inverse(&IDENTITY), Some(IDENTITY));
+    }
+
+    #[test]
+    fn a_translation_inverse_moves_back() {
+        let mut translation = IDENTITY;
+        translation[3] = [2.0, -3.0, 0.5, 1.0];
+        let inverse = inverse(&translation).expect("translation is regular");
+        assert_eq!(concat(&translation, &inverse), IDENTITY);
+    }
+
+    #[test]
+    fn an_omitted_frame_axis_is_z_and_omitted_x_is_chosen() {
+        let frame = frame_matrix([1.0, 2.0, 3.0], None, None).expect("default frame");
+        assert_eq!(frame[2], [0.0, 0.0, 1.0, 0.0]);
+        assert_eq!(frame[3], [1.0, 2.0, 3.0, 1.0]);
+        assert!(
+            (frame[0][0] * frame[0][0] + frame[0][1] * frame[0][1] + frame[0][2] * frame[0][2]
+                - 1.0)
+                .abs()
+                < 1e-12
+        );
+    }
+
+    #[test]
+    fn an_operator_applies_its_scales() {
+        let matrix = operator_matrix(None, None, None, [0.0; 3], Some(2.0), Some(3.0), None)
+            .expect("operator");
+        assert_eq!(matrix[0], [2.0, 0.0, 0.0, 0.0]);
+        assert_eq!(matrix[1], [0.0, 3.0, 0.0, 0.0]);
+        assert_eq!(matrix[2], [0.0, 0.0, 2.0, 0.0]);
+    }
+}

solidcore/crates/solidcore/src/heal/face_props.rs

@@ -2374,10 +2374,14 @@ impl<O: LoopObject> FaceProps<O> {
             // (the status is only reported upstream; a handle type that cannot name the
             // loop bisector's objects is a limitation of the caller, not a status)
             match classify_result {
-                Err(
-                    e @ (SolidError::InvalidInput { reason, .. }
-                    | SolidError::PortInvariant { reason, .. }),
-                ) if reason == crate::query::face::p3::NO_CURVE_HANDLES => {
+                Err(e)
+                    if matches!(
+                        &e,
+                        SolidError::InvalidInput { reason, .. }
+                        | SolidError::PortInvariant { reason, .. }
+                            if *reason == crate::query::face::p3::NO_CURVE_HANDLES
+                    ) =>
+                {
                     return Err(e);
                 }
                 r => Ok(ignored(r)?),

solidcore/crates/solidcore/src/heal/stitch.rs

@@ -7,6 +7,7 @@
 //! unification and the API entry points) and [`p2`] (`DoStitching`, `StitchIntoSolid`,
 //! `StitchIntoShell`, `SplitEdgesWithVertices`, the one-list `StitchVertexPairs`).
 
+mod bounds;
 pub mod p1;
 pub mod p2;
 

solidcore/crates/solidcore/src/heal/stitch/bounds.rs

@@ -0,0 +1,546 @@
+//! Outward-rounded bounds for the geometry a stitch closure identifies.
+//!
+//! No upstream counterpart. The curve-pair bound is a bound on a parameter
+//! correspondence, hence on both directed Hausdorff distances. B-splines are
+//! enclosed on every knot span by homogeneous interval de Boor evaluation; no
+//! rounded control-polygon conversion or sampled distance enters the proof.
+//!
+//! Deviations: no recursion. Work is bounded by the stored knot count and the
+//! kernel's NURBS degree limit. Curves without an implemented exact enclosure,
+//! non-positive weights, extrapolation and non-finite bounds are refused.
+
+use crate::blend::fillet_section::interval::Ivl;
+use crate::curve::curve::{Curve, CurveKind};
+use crate::curve::line::Line;
+use crate::geom::extent1d::Extent1d;
+use crate::math::Point3;
+use crate::nurbs::crv_basic::Curve as Nurbs;
+use crate::nurbs::knots::MAX_DEGREE;
+use crate::nurbs::math::{CPoint, NOW, NOZ};
+use crate::{Result, SolidError};
+
+const OP: &str = "heal::stitch::bounds";
+type Box3 = [Ivl; 3];
+type Box4 = [Ivl; 4];
+
+fn invalid(reason: &'static str) -> SolidError {
+    SolidError::invalid_input(OP, reason)
+}
+
+fn unsupported() -> SolidError {
+    SolidError::Unsupported {
+        operation: OP,
+        reason: "stitch gap enclosure is implemented for lines and positive-weight B-splines only",
+    }
+}
+
+fn at<T: Copy>(values: &[T], index: usize) -> Result<T> {
+    values
+        .get(index)
+        .copied()
+        .ok_or_else(|| invalid("invalid spline storage"))
+}
+
+fn finite(interval: Ivl) -> bool {
+    interval.lo.is_finite() && interval.hi.is_finite() && interval.lo <= interval.hi
+}
+
+fn norm(v: Box3) -> Result<f64> {
+    if !v.into_iter().all(finite) {
+        return Err(invalid("gap enclosure is not finite"));
+    }
+    let scale = v.into_iter().map(Ivl::mag).fold(0.0_f64, f64::max);
+    if scale == 0.0 {
+        return Ok(0.0);
+    }
+    // Scale before squaring: small distances must not underflow to a zero bound.
+    let mut sum = Ivl::from(0.0);
+    for coordinate in v {
+        // Direct endpoint division avoids overflowing 1/scale for subnormals.
+        let scaled = Ivl::checked(coordinate.lo / scale, coordinate.hi / scale);
+        sum = sum + scaled * scaled;
+    }
+    let length = sum.sqrt() * Ivl::from(scale);
+    if !finite(length) {
+        return Err(invalid("gap enclosure overflows"));
+    }
+    Ok(length.hi.max(0.0))
+}
+
+fn point_box(p: Point3) -> Result<Box3> {
+    let coordinates = [p.x, p.y, p.z];
+    if !coordinates.into_iter().all(f64::is_finite) {
+        return Err(invalid("non-finite point"));
+    }
+    Ok(coordinates.map(Ivl::from))
+}
+
+fn difference(a: Box3, b: Box3) -> Box3 {
+    core::array::from_fn(|i| {
+        let x = a.get(i).copied().unwrap_or(Ivl::whole());
+        let y = b.get(i).copied().unwrap_or(Ivl::whole());
+        if x.lo == x.hi && x == y {
+            Ivl::from(0.0)
+        } else {
+            x - y
+        }
+    })
+}
+
+/// Upper bound on the exact Euclidean distance between the stored points.
+pub(super) fn points(a: Point3, b: Point3) -> Result<f64> {
+    norm(difference(point_box(a)?, point_box(b)?))
+}
+
+/// Upper bound on the positive increase between two stored tolerances.
+pub(super) fn growth(before: f64, after: f64) -> Result<f64> {
+    if ![before, after]
+        .into_iter()
+        .all(|v| v.is_finite() && v >= 0.0)
+    {
+        return Err(invalid("non-finite or negative tolerance"));
+    }
+    if after <= before {
+        return Ok(0.0);
+    }
+    let increase = Ivl::from(after) - Ivl::from(before);
+    if !finite(increase) {
+        return Err(invalid("tolerance growth overflows"));
+    }
+    Ok(increase.hi)
+}
+
+fn checked_range(range: [f64; 2]) -> Result<Ivl> {
+    if !range.into_iter().all(f64::is_finite) {
+        return Err(invalid("non-finite curve interval"));
+    }
+    Ok(Ivl::new(range[0].min(range[1]), range[0].max(range[1])))
+}
+
+fn homogeneous(c: CPoint) -> Result<Box4> {
+    let coordinates = [
+        c.x,
+        c.y,
+        if c.z == NOZ { 0.0 } else { c.z },
+        if c.w == NOW { 1.0 } else { c.w },
+    ];
+    if !coordinates.into_iter().all(f64::is_finite) || coordinates.last().is_none_or(|w| *w <= 0.0)
+    {
+        return Err(invalid("non-finite spline data or non-positive weight"));
+    }
+    Ok(coordinates.map(Ivl::from))
+}
+
+fn validate(n: &Nurbs, range: Ivl) -> Result<()> {
+    let p = n.degree();
+    let count = n.cpts().len();
+    if p > MAX_DEGREE + 1 || count <= p || count.checked_add(p + 1) != Some(n.knots().len()) {
+        return Err(invalid("invalid spline degree or storage"));
+    }
+    if !n.knots().iter().all(|k| k.is_finite())
+        || n.knots().windows(2).any(|w| matches!(w, [a, b] if a > b))
+    {
+        return Err(invalid("invalid knot vector"));
+    }
+    if at(n.knots(), p)? >= at(n.knots(), count)?
+        || range.lo < at(n.knots(), p)?
+        || range.hi > at(n.knots(), count)?
+    {
+        return Err(invalid("curve gap enclosure does not extrapolate"));
+    }
+    let first = at(n.cpts(), 0)?;
+    for &c in n.cpts() {
+        if (c.w == NOW) != (first.w == NOW) || (c.z == NOZ) != (first.z == NOZ) {
+            return Err(invalid("mixed homogeneous coordinate storage"));
+        }
+        homogeneous(c)?;
+    }
+    Ok(())
+}
+
+/// The exact rational polynomial on one nonempty knot span, evaluated in intervals.
+fn piece(n: &Nurbs, span: usize, t: Ivl) -> Result<Box3> {
+    let p = n.degree();
+    let first = span
+        .checked_sub(p)
+        .ok_or_else(|| invalid("invalid spline span"))?;
+    let mut d = Vec::new();
+    let mut min_weight = f64::INFINITY;
+    for j in 0..=p {
+        let h = homogeneous(at(n.cpts(), first + j)?)?;
+        min_weight = min_weight.min(at(&h, 3)?.lo);
+        d.push(h);
+    }
+    for r in 1..=p {
+        for j in (r..=p).rev() {
+            let i = first + j;
+            let denominator =
+                Ivl::from(at(n.knots(), i + p + 1 - r)?) - Ivl::from(at(n.knots(), i)?);
+            if denominator.lo <= 0.0 {
+                return Err(invalid("unproved knot denominator"));
+            }
+            let alpha = (t - Ivl::from(at(n.knots(), i)?)) / denominator;
+            // On the selected span, the exact alpha is in [0, 1]. Intersecting
+            // with that proved range removes rounding spill, not geometric error.
+            let alpha = Ivl::new(alpha.lo.max(0.0), alpha.hi.min(1.0));
+            if !finite(alpha) {
+                return Err(invalid("invalid spline parameter enclosure"));
+            }
+            let left = at(&d, j - 1)?;
+            let right = at(&d, j)?;
+            let value = core::array::from_fn(|axis| {
+                let a = left.get(axis).copied().unwrap_or(Ivl::whole());
+                let b = right.get(axis).copied().unwrap_or(Ivl::whole());
+                (Ivl::from(1.0) - alpha) * a + alpha * b
+            });
+            *d.get_mut(j)
+                .ok_or_else(|| invalid("invalid spline workspace"))? = value;
+        }
+    }
+    let h = at(&d, p)?;
+    // Positive basis functions sum to one, so W is at least the least active weight.
+    let w = at(&h, 3)?;
+    let w = Ivl::new(w.lo.max(min_weight), w.hi);
+    if !finite(w) || w.lo <= 0.0 {
+        return Err(invalid("unproved spline denominator"));
+    }
+    let result = [at(&h, 0)? / w, at(&h, 1)? / w, at(&h, 2)? / w];
+    if !result.into_iter().all(finite) {
+        return Err(invalid("curve enclosure overflows"));
+    }
+    Ok(result)
+}
+
+fn spline_box(n: &Nurbs, range: Ivl) -> Result<Box3> {
+    validate(n, range)?;
+    let mut result: Option<Box3> = None;
+    for (span, pair) in n.knots().windows(2).enumerate() {
+        let [a, b] = pair else {
+            continue;
+        };
+        if span < n.degree() || span >= n.cpts().len() || a >= b || *b < range.lo || *a > range.hi {
+            continue;
+        }
+        let t = Ivl::new(range.lo.max(*a), range.hi.min(*b));
+        let part = piece(n, span, t)?;
+        result = Some(match result {
+            None => part,
+            Some(old) => core::array::from_fn(|i| {
+                old.get(i)
+                    .copied()
+                    .unwrap_or(Ivl::whole())
+                    .hull(part.get(i).copied().unwrap_or(Ivl::whole()))
+            }),
+        });
+    }
+    result.ok_or_else(|| invalid("no knot span covers the curve interval"))
+}
+
+fn line_box(line: &Line, t: Ivl) -> Result<Box3> {
+    let natural = line.natural_interval();
+    let step = line.step_interval();
+    if !finite(t)
+        || !finite(checked_range([natural.min(), natural.max()])?)
+        || !finite(checked_range([step.min(), step.max()])?)
+    {
+        return Err(invalid("non-finite line parameterization"));
+    }
+    if t.lo < natural.min() || t.hi > natural.max() {
+        return Err(invalid("curve gap enclosure does not extrapolate"));
+    }
+    let u = if line.is_bounded() {
+        let length = Ivl::from(natural.max()) - Ivl::from(natural.min());
+        if length.lo <= 0.0 || crate::geom::tol::is_zero(natural.length()) {
+            return Err(invalid("degenerate line parameterization"));
+        }
+        let (start, direction) = if line.inside_out() {
+            (natural.max(), -1.0)
+        } else {
+            (natural.min(), 1.0)
+        };
+        Ivl::from(step.min())
+            + (t - Ivl::from(start)) / length
+                * Ivl::from(direction)
+                * (Ivl::from(step.max()) - Ivl::from(step.min()))
+    } else if line.inside_out() {
+        Ivl::from(0.0) - t
+    } else {
+        t
+    };
+    let p = point_box(line.line_point())?;
+    let v = point_box(line.line_vector())?;
+    if !line.line_scale().is_finite() {
+        return Err(invalid("non-finite line scale"));
+    }
+    let result = core::array::from_fn(|i| {
+        p.get(i).copied().unwrap_or(Ivl::whole())
+            + u * v.get(i).copied().unwrap_or(Ivl::whole()) * Ivl::from(line.line_scale())
+    });
+    if !result.into_iter().all(finite) {
+        return Err(invalid("line enclosure overflows"));
+    }
+    Ok(result)
+}
+
+fn curve_box(curve: &Curve, range: Ivl) -> Result<Box3> {
+    match curve.kind() {
+        CurveKind::Line(l) => line_box(l, range),
+        CurveKind::BSpline(b) => spline_box(
+            b.gw_nurb().ok_or_else(|| invalid("missing spline data"))?,
+            range,
+        ),
+        _ => Err(unsupported()),
+    }
+}
+
+/// An upper bound for point-to-curve distance using an exact point of the curve.
+pub(super) fn point_at_curve(point: Point3, curve: &Curve, parameter: f64) -> Result<f64> {
+    norm(difference(
+        point_box(point)?,
+        curve_box(curve, checked_range([parameter, parameter])?)?,
+    ))
+}
+
+/// Bounds the whole curve's distance from a point (the geometry a squeeze removes).
+pub(super) fn curve_to_point(curve: &Curve, interval: &Extent1d, point: Point3) -> Result<f64> {
+    norm(difference(
+        curve_box(curve, checked_range([interval.min(), interval.max()])?)?,
+        point_box(point)?,
+    ))
+}
+
+/// Bounds both directed curve gaps under the stated endpoint correspondence.
+pub(super) fn curves(first: &Curve, a: [f64; 2], second: &Curve, b: [f64; 2]) -> Result<f64> {
+    let ar = checked_range(a)?;
+    let br = checked_range(b)?;
+    // With a common positive rational basis the difference is a convex combination
+    // of the dehomogenized control-point differences. This also proves identity
+    // exactly, without subtracting independently widened position boxes.
+    if a == b {
+        if let (CurveKind::BSpline(x), CurveKind::BSpline(y)) = (first.kind(), second.kind()) {
+            let x = x.gw_nurb().ok_or_else(|| invalid("missing spline data"))?;
+            let y = y.gw_nurb().ok_or_else(|| invalid("missing spline data"))?;
+            validate(x, ar)?;
+            validate(y, br)?;
+            if x.degree() == y.degree()
+                && x.knots() == y.knots()
+                && x.cpts().iter().zip(y.cpts()).all(|(p, q)| p.w == q.w)
+            {
+                let mut upper = 0.0_f64;
+                for (&p, &q) in x.cpts().iter().zip(y.cpts()) {
+                    let p = homogeneous(p)?;
+                    let q = homogeneous(q)?;
+                    let delta = difference(
+                        [at(&p, 0)?, at(&p, 1)?, at(&p, 2)?],
+                        [at(&q, 0)?, at(&q, 1)?, at(&q, 2)?],
+                    );
+                    let w = at(&p, 3)?;
+                    upper = upper.max(norm(delta.map(|d| {
+                        if d == Ivl::from(0.0) {
+                            d
+                        } else {
+                            d / w
+                        }
+                    }))?);
+                }
+                return Ok(upper);
+            }
+        }
+    }
+    // Affine curves attain the maximum norm of their difference at an endpoint.
+    // Otherwise enclose every parameter cell, never only its sample stations.
+    let cells = if matches!(
+        (first.kind(), second.kind()),
+        (CurveKind::Line(_), CurveKind::Line(_))
+    ) {
+        1_u32
+    } else {
+        64_u32
+    };
+    let mut upper = 0.0_f64;
+    for i in 0..cells {
+        let s = Ivl::new(
+            f64::from(i) / f64::from(cells),
+            f64::from(i + 1) / f64::from(cells),
+        );
+        let mapped =
+            |range: [f64; 2]| Ivl::from(range[0]) * (Ivl::from(1.0) - s) + Ivl::from(range[1]) * s;
+        if cells == 1 {
+            for j in [0, 1] {
+                let t = at(&a, j)?;
+                let u = at(&b, j)?;
+                upper = upper.max(norm(difference(
+                    curve_box(first, Ivl::from(t))?,
+                    curve_box(second, Ivl::from(u))?,
+                ))?);
+            }
+        } else {
+            // Clip only the rounding spill of the affine parameter map.
+            let x = mapped(a);
+            let y = mapped(b);
+            upper = upper.max(norm(difference(
+                curve_box(first, Ivl::new(x.lo.max(ar.lo), x.hi.min(ar.hi)))?,
+                curve_box(second, Ivl::new(y.lo.max(br.lo), y.hi.min(br.hi)))?,
+            ))?);
+        }
+    }
+    Ok(upper)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::curve::hermite_curve::HermiteCurve;
+    use crate::nurbs::b_spline_curve::BSplineCurve;
+    use crate::{Kernel, Vec3};
+
+    /// Retain the raw data: an ordinary clone/owned constructor tunes the knots.
+    fn spline(points: Vec<CPoint>, degree: usize, knots: Vec<f64>) -> Curve {
+        BSplineCurve::from_nurb(Nurbs::new(points, degree, knots).unwrap(), 3, true).into()
+    }
+
+    fn cp(x: f64, y: f64, w: f64) -> CPoint {
+        CPoint { x, y, z: 0.0, w }
+    }
+
+    #[test]
+    fn whole_curve_bound_catches_the_interior_bump_five_samples_miss() {
+        // A degree-one hat on [1/16, 3/16], peaking at 1/8. Every old sample
+        // at 0, 1/4, 1/2, 3/4, 1 is exactly on the flat curve.
+        let knots = vec![0.0, 0.0, 0.0625, 0.125, 0.1875, 1.0, 1.0];
+        let flat = spline(
+            vec![
+                cp(0.0, 0.0, NOW),
+                cp(0.0625, 0.0, NOW),
+                cp(0.125, 0.0, NOW),
+                cp(0.1875, 0.0, NOW),
+                cp(1.0, 0.0, NOW),
+            ],
+            1,
+            knots.clone(),
+        );
+        let bump = spline(
+            vec![
+                cp(0.0, 0.0, NOW),
+                cp(0.0625, 0.0, NOW),
+                cp(0.125, 1.0, NOW),
+                cp(0.1875, 0.0, NOW),
+                cp(1.0, 0.0, NOW),
+            ],
+            1,
+            knots,
+        );
+        let k = Kernel::default();
+        for t in [0.0, 0.25, 0.5, 0.75, 1.0] {
+            assert_eq!(
+                flat.evaluate_point(&k, t).unwrap(),
+                bump.evaluate_point(&k, t).unwrap()
+            );
+        }
+        assert_eq!(bump.evaluate_point(&k, 0.125).unwrap().y, 1.0);
+        let bound = curves(&flat, [0.0, 1.0], &bump, [0.0, 1.0]).unwrap();
+        assert!((1.0..1.0 + 1e-12).contains(&bound), "{bound}");
+        let squeezed =
+            curve_to_point(&bump, &Extent1d::from_min_max(0.0, 1.0), Vec3::ZERO).unwrap();
+        assert!(squeezed >= 1.0);
+    }
+
+    #[test]
+    fn positive_rational_weights_are_enclosed_without_a_polynomial_substitute() {
+        // Y(t) = 4t(1-t)/(1+2t(1-t)), maximum 2/3 at 1/2.
+        let rational = spline(
+            vec![cp(0.0, 0.0, 1.0), cp(1.0, 2.0, 2.0), cp(1.0, 0.0, 1.0)],
+            2,
+            vec![0.0, 0.0, 0.0, 1.0, 1.0, 1.0],
+        );
+        let line: Curve = Line::from_points(Vec3::ZERO, Vec3::new(1.0, 0.0, 0.0), 3).into();
+        let bound = curves(&rational, [0.0, 1.0], &line, [0.0, 1.0]).unwrap();
+        assert!((2.0 / 3.0..1.0).contains(&bound), "{bound}");
+        let at_mid = point_at_curve(Vec3::new(0.5, 0.0, 0.0), &rational, 0.5).unwrap();
+        assert!((2.0 / 3.0..2.0 / 3.0 + 1e-12).contains(&at_mid), "{at_mid}");
+        assert_eq!(
+            curves(&rational, [0.0, 1.0], &rational, [0.0, 1.0]).unwrap(),
+            0.0
+        );
+    }
+
+    #[test]
+    fn reversed_and_subdomain_correspondences_cover_every_parameter() {
+        let forward = spline(
+            vec![cp(0.0, 0.0, NOW), cp(1.0, 0.0, NOW)],
+            1,
+            vec![0.0, 0.0, 1.0, 1.0],
+        );
+        let reverse = spline(
+            vec![cp(1.0, 0.0, NOW), cp(0.0, 0.0, NOW)],
+            1,
+            vec![0.0, 0.0, 1.0, 1.0],
+        );
+        let bound = curves(&forward, [0.25, 0.75], &reverse, [0.75, 0.25]).unwrap();
+        assert!(bound.is_finite() && bound < 0.1, "{bound}");
+        let endpoint_bound = point_at_curve(Vec3::ZERO, &forward, 0.75).unwrap();
+        assert!((0.75..0.75 + 1e-12).contains(&endpoint_bound));
+        assert!(curves(&forward, [-0.1, 0.75], &reverse, [0.75, 0.25]).is_err());
+    }
+
+    #[test]
+    fn point_and_growth_bounds_do_not_underflow_or_accept_nonfinite_results() {
+        assert_eq!(points(Vec3::ZERO, Vec3::ZERO).unwrap(), 0.0);
+        for tiny in [1e-200, f64::from_bits(1)] {
+            let bound = points(Vec3::ZERO, Vec3::new(tiny, 0.0, 0.0)).unwrap();
+            assert!(bound.is_finite() && bound >= tiny && bound > 0.0, "{bound}");
+        }
+        assert!(points(Vec3::ZERO, Vec3::new(1e300, 0.0, 0.0)).unwrap() >= 1e300);
+        assert!(points(
+            Vec3::new(-f64::MAX, 0.0, 0.0),
+            Vec3::new(f64::MAX, 0.0, 0.0)
+        )
+        .is_err());
+        assert!(points(Vec3::ZERO, Vec3::new(f64::NAN, 0.0, 0.0)).is_err());
+        assert_eq!(growth(1.0, 1.0).unwrap(), 0.0);
+        assert_eq!(growth(2.0, 1.0).unwrap(), 0.0);
+        assert!(growth(1.0, 2.0).unwrap() >= 1.0);
+        assert!(growth(0.0, f64::from_bits(1)).unwrap() > 0.0);
+        assert!(growth(-1.0, 0.0).is_err());
+        assert!(growth(0.0, f64::INFINITY).is_err());
+    }
+
+    #[test]
+    fn malformed_weights_knots_storage_and_unsupported_kinds_fail_explicitly() {
+        for weight in [0.0, -1.0, f64::NAN, f64::INFINITY] {
+            let c = spline(
+                vec![cp(0.0, 0.0, weight), cp(1.0, 0.0, 1.0)],
+                1,
+                vec![0.0, 0.0, 1.0, 1.0],
+            );
+            assert!(point_at_curve(Vec3::ZERO, &c, 0.5).is_err());
+        }
+        for (degree, knots) in [
+            (1, vec![0.0, 1.0]),
+            (1, vec![0.0; 4]),
+            (1, vec![0.0, 1.0, 0.0, 1.0]),
+            (usize::MAX, vec![0.0, 0.0, 1.0, 1.0]),
+        ] {
+            let c = spline(vec![cp(0.0, 0.0, NOW), cp(1.0, 0.0, NOW)], degree, knots);
+            assert!(point_at_curve(Vec3::ZERO, &c, 0.5).is_err());
+        }
+        let mixed = spline(
+            vec![cp(0.0, 0.0, NOW), cp(1.0, 0.0, 1.0)],
+            1,
+            vec![0.0, 0.0, 1.0, 1.0],
+        );
+        assert!(point_at_curve(Vec3::ZERO, &mixed, 0.5).is_err());
+        let hermite: Curve = HermiteCurve::new(
+            Vec3::ZERO,
+            Vec3::new(1.0, 0.0, 0.0),
+            Vec3::new(1.0, 0.0, 0.0),
+            Vec3::new(1.0, 0.0, 0.0),
+            3,
+        )
+        .into();
+        assert!(matches!(
+            point_at_curve(Vec3::ZERO, &hermite, 0.5),
+            Err(SolidError::Unsupported { .. })
+        ));
+    }
+}

solidcore/crates/solidcore/src/heal/stitch/p1.rs

@@ -111,6 +111,8 @@ use crate::topology::{
 };
 use crate::{Result, SolidError};
 
+use super::p2::{ClosedGap, ClosedGapKind};
+
 const OP: &str = "heal::stitch::p1";
 /// The operation of the `SM_API` entry points' `SM_ERR_INVALID_INPUT` (null arguments).
 const API_OP: &str = "heal::stitch::p1::api";
@@ -932,6 +934,47 @@ pub struct Stitch<'c> {
     /// Remove sliver faces smaller than tolerance first (`m_bRemoveLaminarSlivers`,
     /// default `FALSE`).
     pub remove_laminar_slivers: bool,
+    /// When `Some`, the stitch records what it closed: the entities, the gap it
+    /// enclosed, and the tolerance growth its editing applied (not upstream,
+    /// solidcore#2975). Nothing else changes.
+    pub report_gaps: Option<Vec<ClosedGap>>,
+}
+
+impl Stitch<'_> {
+    /// The collected gap records, taking them out (`Ok(vec![])` when the caller did
+    /// not ask for them).
+    pub(crate) fn take_gaps(&mut self) -> Vec<ClosedGap> {
+        self.report_gaps.take().unwrap_or_default()
+    }
+
+    /// Records one closed gap when the caller asked for the report. The growth is
+    /// an outward-rounded bound on how much the surviving entity's tolerance rose
+    /// over its own tolerance before the closure, including inherited tolerance.
+    pub(crate) fn record_gap(
+        &mut self,
+        kind: ClosedGapKind,
+        gap: f64,
+        before: f64,
+        after: f64,
+    ) -> Result<()> {
+        if let Some(gaps) = self.report_gaps.as_mut() {
+            let growth = super::bounds::growth(before, after)?;
+            if !gap.is_finite() || gap < 0.0 {
+                return Err(SolidError::invalid_input(
+                    "heal::stitch::bounds",
+                    "non-finite or negative gap bound",
+                ));
+            }
+            gaps.push(ClosedGap {
+                kind,
+                gap,
+                growth,
+                tolerance_before: before,
+                tolerance_after: after,
+            });
+        }
+        Ok(())
+    }
 }
 
 impl core::fmt::Debug for Stitch<'_> {
@@ -1151,6 +1194,7 @@ impl<'c> Stitch<'c> {
             split_edges_with_vertices: true,
             making_manifold_solid: true,
             remove_laminar_slivers: false,
+            report_gaps: None,
         }
     }
 

solidcore/crates/solidcore/src/heal/stitch/p2.rs

@@ -351,6 +351,62 @@ pub struct VertexList {
     pub min_unstitched_vert_gap: f64,
 }
 
+/// What the stitcher closed, as the entities it glued (solidcore#2975).
+#[derive(Debug, Clone, Copy, PartialEq)]
+pub enum ClosedGapKind {
+    /// A vertex pair glued into the kept vertex.
+    Vertex {
+        /// The vertex the glue kept.
+        kept: VertexId,
+        /// The vertex the glue deleted.
+        deleted: VertexId,
+    },
+    /// An edge pair glued into the kept edge.
+    Edge {
+        /// The edge the glue kept.
+        kept: EdgeId,
+        /// The edge the glue deleted.
+        deleted: EdgeId,
+    },
+    /// A vertex pair one edge was squeezed into (the kept vertex stays).
+    Squeezed {
+        /// The vertex the squeeze kept.
+        kept: VertexId,
+        /// The vertex the squeeze closed over.
+        deleted: VertexId,
+    },
+    /// A vertex dropped onto an edge and split there, with the vertex its split created.
+    Split {
+        /// The edge the vertex was dropped onto and split.
+        edge: EdgeId,
+        /// The vertex the split created.
+        created: VertexId,
+    },
+}
+
+/// A closure's certified geometry bound and tolerance accounting (solidcore#2975).
+/// The bound includes floating-point rounding. For edges it bounds both directed
+/// Hausdorff distances via an endpoint-to-endpoint parameter correspondence; it
+/// need not be the tightest Hausdorff bound. Unsupported enclosures return an
+/// error from the reporting operation, never a sampled estimate as a certificate.
+#[derive(Debug, Clone, Copy, PartialEq)]
+pub struct ClosedGap {
+    /// What the stitcher closed.
+    pub kind: ClosedGapKind,
+    /// Certified upper bound on the gap, in model units. A squeeze bounds the
+    /// whole removed curve's distance to the kept point; a split bounds the source
+    /// point's distance to the original curve at the split parameter.
+    pub gap: f64,
+    /// Upper bound on `max(tolerance_after - tolerance_before, 0)`, rounded up.
+    /// Exactly zero when the surviving entity's stored tolerance did not grow.
+    pub growth: f64,
+    /// The surviving entity's own stored tolerance before this closure. For a
+    /// split this is the new vertex's tolerance before its explicit adjustment.
+    pub tolerance_before: f64,
+    /// The surviving entity's stored tolerance after this closure.
+    pub tolerance_after: f64,
+}
+
 /// The result of [`Stitch::split_edges_with_vertices`].
 #[derive(Debug, Clone, PartialEq)]
 pub struct SplitEdges {
@@ -479,9 +535,36 @@ impl Stitch<'_> {
                     }
 
                     let surv_v = surv_v.ok_or_else(|| deref("edge without vertex"))?;
+                    let deleted_report = del_v.unwrap_or(surv_v);
+                    // Bound all the removed geometry, not its sampled length or
+                    // merely the distance between its endpoints.
+                    let squeeze_report = if self.report_gaps.is_some() {
+                        Some((
+                            vertex::tolerance(b, surv_v)?,
+                            super::bounds::curve_to_point(
+                                curve_of(b, e)?,
+                                &edge::interval(b, e)?,
+                                vertex::point(b, surv_v)?,
+                            )?,
+                        ))
+                    } else {
+                        None
+                    };
                     // remove and delete edge from topology graph by squeezing
                     // [vertex-edge-vertex] into [vertex]
                     self.edit_squeeze_edge(k, b, Some(e), surv_v)?;
+                    if let Some((pre, gap)) = squeeze_report {
+                        let after = vertex::tolerance(b, surv_v)?;
+                        self.record_gap(
+                            ClosedGapKind::Squeezed {
+                                kept: surv_v,
+                                deleted: deleted_report,
+                            },
+                            gap,
+                            pre,
+                            after,
+                        )?;
+                    }
 
                     if candidate_vertices.is_some() {
                         add_unique(&mut cand_vertices, surv_v); // This becomes a candidate.
@@ -570,7 +653,42 @@ impl Stitch<'_> {
                             // candidates
                             let new_tol =
                                 smos_max(vertex::tolerance(b, v)?, vertex::tolerance(b, new_v)?);
+                            let split_report = if self.report_gaps.is_some() {
+                                let range = edge::interval(b, e)?;
+                                let parameter = if edge::start_vertex(b, e)? == Some(new_v) {
+                                    range.min()
+                                } else if edge::end_vertex(b, e)? == Some(new_v) {
+                                    range.max()
+                                } else {
+                                    return Err(SolidError::invalid_input(
+                                        "heal::stitch::bounds",
+                                        "split vertex is not on either resulting edge end",
+                                    ));
+                                };
+                                Some((
+                                    vertex::tolerance(b, new_v)?,
+                                    super::bounds::point_at_curve(
+                                        vertex::point(b, v)?,
+                                        curve_of(b, e)?,
+                                        parameter,
+                                    )?,
+                                ))
+                            } else {
+                                None
+                            };
                             vertex::set_tolerance(b, new_v, zone_tol3d(k, new_tol), true, true)?;
+                            if let Some((pre, bound)) = split_report {
+                                let after = vertex::tolerance(b, new_v)?;
+                                self.record_gap(
+                                    ClosedGapKind::Split {
+                                        edge: e,
+                                        created: new_v,
+                                    },
+                                    bound,
+                                    pre,
+                                    after,
+                                )?;
+                            }
                             more_work_needed = true;
 
                             cand_vertices.push(new_v);
@@ -734,6 +852,43 @@ impl Stitch<'_> {
                         continue;
                     }
 
+                    // (not upstream, #2975) capture the closure record's operands
+                    // before nothing else deflects them, and read the surviving
+                    // entity's tolerance after.
+                    let kept = if choice.keep_first { v } else { cv };
+                    let deleted = if choice.keep_first { cv } else { v };
+                    let pair_report = if self.report_gaps.is_some() && (do_glue || do_squeeze) {
+                        Some((
+                            vertex::tolerance(b, kept)?,
+                            if do_squeeze {
+                                if let Some(e) = squeeze_edge {
+                                    super::bounds::curve_to_point(
+                                        curve_of(b, e)?,
+                                        &edge::interval(b, e)?,
+                                        vertex::point(b, kept)?,
+                                    )?
+                                } else {
+                                    super::bounds::points(
+                                        vertex::point(b, kept)?,
+                                        vertex::point(b, deleted)?,
+                                    )?
+                                }
+                            } else {
+                                super::bounds::points(
+                                    vertex::point(b, kept)?,
+                                    vertex::point(b, deleted)?,
+                                )?
+                            },
+                            if do_glue {
+                                ClosedGapKind::Vertex { kept, deleted }
+                            } else {
+                                ClosedGapKind::Squeezed { kept, deleted }
+                            },
+                        ))
+                    } else {
+                        None
+                    };
+
                     // squeeze or glue vertices together (make pV the retained vertex)
                     if choice.keep_first {
                         if do_squeeze {
@@ -749,6 +904,10 @@ impl Stitch<'_> {
                         }
                         v = cv;
                     }
+                    if let Some((pre, bound, kind)) = pair_report {
+                        let after = vertex::tolerance(b, v)?;
+                        self.record_gap(kind, bound, pre, after)?;
+                    }
 
                     // The surviving vertex (which is pV) should be a candidate.
                     if candidate_vertices.is_some() {
@@ -1057,6 +1216,21 @@ impl Stitch<'_> {
                     for f in edge::faces(b, delete, None)? {
                         add_unique(modified_faces, f);
                     }
+                    // (not upstream, #2975) capture the closure's operands before the
+                    // glue, and the kept edge's tolerance after.
+                    let edge_report = if self.report_gaps.is_some() {
+                        Some((
+                            edge::tolerance(b, keep)?,
+                            super::bounds::curves(
+                                curve_of(b, e)?,
+                                [e_ivl.min(), e_ivl.max()],
+                                curve_of(b, test_e)?,
+                                [t_start, t_end],
+                            )?,
+                        ))
+                    } else {
+                        None
+                    };
                     match self.edit_glue_edges(
                         k,
                         b,
@@ -1076,6 +1250,18 @@ impl Stitch<'_> {
                             }
                             set_none(&mut v_edges, kk)?;
                             done_with_vertex = false;
+                            if let Some((pre, bound)) = edge_report {
+                                let after = edge::tolerance(b, e)?;
+                                self.record_gap(
+                                    ClosedGapKind::Edge {
+                                        kept: e,
+                                        deleted: delete,
+                                    },
+                                    bound,
+                                    pre,
+                                    after,
+                                )?;
+                            }
                         }
                         Err(err) if err.is_unported_or_cancelled() => return Err(err),
                         Err(_) if !self.ignore_problems => return Err(sm_err()),

solidcore/crates/solidcore/src/mass.rs

@@ -5,4 +5,5 @@
 //! `SmVertexProps`, `SmObjProps` in `source/SMLib`, and the area/volume queries of
 //! `SM_API/SmApiQueries`.
 
+pub mod enclosure;
 pub mod integrator;

solidcore/crates/solidcore/src/mass/integrator.rs

@@ -1354,10 +1354,8 @@ mod tests {
         assert!(error.abs() <= 1e-6, "{error}");
     }
 
-    /// The final step's last node is the interval's end itself: `-0.1 + (0.3 - -0.1)`
-    /// rounds to `0.30000000000000004`, past the end, where an integrand whose end is a
-    /// knot (a curve's span, a face's iso-u piece) would read the span beyond it. Every
-    /// node lies within `[x1, x2]`, and the step that ends the integration ends at `x2`.
+    /// A rate that is NaN, infinite or negative is refused before the integrand is
+    /// evaluated, and nothing is written.
     #[test]
     fn a_rate_that_is_not_a_finite_nonnegative_number_is_refused() {
         for rate in [
@@ -1424,6 +1422,75 @@ mod tests {
         }
     }
 
+    /// `rate` on closed forms, as the curve length uses it: a range cut into `n` equal
+    /// pieces, each integrated to half the accuracy with the range's mean as its rate.
+    /// Each step is held to half the accuracy relative to its share of the range plus
+    /// its own increment, shares that add up to twice the integral, so the pieces' sum is
+    /// within the accuracy of the whole integral however many pieces and steps there are.
+    #[test]
+    fn a_rate_holds_a_range_cut_into_pieces_to_the_accuracy_of_the_whole() {
+        use core::f64::consts::PI;
+        type Case = (fn(f64) -> f64, f64, f64, f64);
+        let cases: [Case; 3] = [
+            // e^t on [0, 4]: e^4 - 1
+            (f64::exp, 0.0, 4.0, 4.0_f64.exp() - 1.0),
+            // Runge's 1 / (1 + 25 t^2) on [-1, 1]: 2/5 atan 5
+            (
+                |t| 1.0 / (1.0 + 25.0 * t * t),
+                -1.0,
+                1.0,
+                0.4 * 5.0_f64.atan(),
+            ),
+            // 2 + sin 20t on [0, pi]: 2 pi (the sine's ten periods cancel)
+            (|t| 2.0 + (20.0 * t).sin(), 0.0, PI, 2.0 * PI),
+        ];
+        for (g, a, b, exact) in cases {
+            let rate = exact / (b - a);
+            for accuracy in [1e-4, 1e-6, 1e-8, 1e-10] {
+                for n in [1_u32, 8, 64] {
+                    let piece = (b - a) / f64::from(n);
+                    let mut sum = 0.0;
+                    for j in 0..n {
+                        let x1 = a + f64::from(j) * piece;
+                        let x2 = if j + 1 == n { b } else { x1 + piece };
+                        let mut y = [0.0];
+                        OdeIntegrator::default()
+                            .integrate(
+                                &mut y,
+                                x1,
+                                x2,
+                                OdeOptions {
+                                    accuracy: accuracy / 2.0,
+                                    initial_step: (x2 - x1) / 10.0,
+                                    minimum_step: (x2 - x1) / 1e8,
+                                    scale: None,
+                                    quadrature: true,
+                                    rounding: None,
+                                    rate: Some(rate),
+                                },
+                                |t, _, dy| {
+                                    dy[0] = g(t);
+                                    Ok(())
+                                },
+                            )
+                            .unwrap();
+                        sum += y[0];
+                    }
+                    let error = (sum - exact).abs() / exact;
+                    assert!(
+                        error <= accuracy,
+                        "[{a}, {b}] in {n} pieces at {accuracy:e}: {sum} against {exact}, \
+                         relative error {error:e}"
+                    );
+                }
+            }
+        }
+    }
+
+    /// The final step's last node is the interval's end itself: `-0.1 + (0.3 - -0.1)`
+    /// rounds to `0.30000000000000004`, past the end, where an integrand whose end is a
+    /// knot (a curve's span, a face's iso-u piece) would read the span beyond it. Every
+    /// node lies within `[x1, x2]`, and the step that ends the integration ends at `x2`.
     #[test]
     fn the_final_step_ends_at_the_interval_end_exactly() {
         let (x1, x2) = (-0.1_f64, 0.3_f64);

solidcore/crates/solidcore/src/query.rs

@@ -6,8 +6,10 @@
 
 pub mod api_queries;
 pub mod brep;
+pub mod contact;
 pub mod distance_bound;
 pub mod edge;
+pub mod edge_turn;
 #[cfg(test)]
 pub(crate) mod exact;
 pub mod face;
@@ -16,6 +18,7 @@ pub mod r#loop;
 pub mod normal;
 pub mod poly;
 pub mod poly_properties;
+pub mod tangent_edge;
 pub mod tess;
 
 pub use face_surface::face_surface_intersect;

solidcore/crates/solidcore/src/query/contact.rs

@@ -0,0 +1,732 @@
+//! Not upstream: whether two bodies meet (share material or touch within a tolerance),
+//! decided only where it is proved: [`meets`] and its distance, [`boundary_distance`].
+//!
+//! | Rust | Upstream |
+//! |------|----------|
+//! | [`meets`], [`boundary_distance`], [`Prepared`] | none (`SmApiBrepRelationship`, ported as [`crate::query::api_queries::brep_relationship`], is a Newton solve: its gap is a point pair, never a lower bound, and its containment counts samples) |
+//!
+//! **The bracket.** The distance between the two bodies' boundaries is enclosed in `[lower,
+//! upper]`:
+//!
+//! - `lower`: the least, over pairs of pieces of the two bodies' faces, of the distance
+//!   between their hulls' boxes. The pieces are those of
+//!   [`crate::query::distance_bound`] (each face's NURBS form over its UV box, its Bézier
+//!   patches about one common point, every coefficient's error carried and each box widened
+//!   by it), so no point of either boundary is nearer the other than `lower`. Pairs wait on a
+//!   heap, nearest first; the nearest is split (its larger piece, in four), so `lower`
+//!   rises. A piece whose UV rectangle is proved off its face (no trim curve's box meets it,
+//!   and its centre classifies outside the face) is dropped: a face's hole is no material.
+//! - `upper` and its witness: a pair of points, one on each body, each on its face's surface
+//!   at parameters the face classifies decisively inside (`face_classify_uv`, the face
+//!   itself: neither on its boundary nor undecided), their distance rounded up. The
+//!   candidates are the centres of the pairs taken from the heap, each moved to the other
+//!   surface's closest point and back ([`crate::query::api_queries::surface_closest_point`],
+//!   a few times), so two surfaces that cross reach a distance of their rounding.
+//!
+//! **Meets.** At a tolerance `tol`: `Yes` when `upper <= tol` (with the witness); when
+//! `lower > tol`, the boundaries do not touch, and the bodies meet only if one encloses the
+//! other: a point of each boundary is classified in the other body, `Yes` when one is
+//! inside its material, `No` when both are outside. A classification on the other's boundary
+//! or not decided is no answer, and neither is a bracket that still straddles `tol` when
+//! the pairs reach [`MAX_PAIRS`]: [`Verdict::Undecided`], with the bracket, which names
+//! the size that would decide.
+//!
+//! Deviations: none (no upstream counterpart). No recursion: the pairs wait on a heap.
+
+use std::cmp::Ordering;
+use std::collections::BinaryHeap;
+
+use crate::geom::certified::{gamma, Verdict};
+use crate::geom::extent1d::Extent1d;
+use crate::geom::tol::{brep_zone_tol_3d, SmallTopoType};
+use crate::geom::vector2d::Point2;
+use crate::intersect::point_class::PointClassType;
+use crate::kernel::Kernel;
+use crate::mass::integrator::properties::region_material;
+use crate::math::Point3;
+use crate::query::api_queries::{
+    edge_closest_point, face_bounding_box, face_classify_uv, surface_closest_point,
+};
+use crate::query::brep::BrepClassifier;
+use crate::query::distance_bound::{pieces_about, Piece};
+use crate::surface::surface::Surface;
+use crate::topology::{edgeuse::p1 as eu1, loopuse, Brep, FaceId};
+use crate::{EntityRef, Result, SolidError};
+
+const OP: &str = "query::contact::meets";
+
+/// The most piece pairs made for one answer.
+pub const MAX_PAIRS: usize = 1 << 16;
+
+/// The times a witness is moved to the other surface's closest point and back.
+const PROJECTIONS: usize = 6;
+
+/// How two bodies stand: the verdict at the tolerance asked, and the boundary distance's
+/// bracket.
+#[derive(Debug, Clone, Copy, PartialEq)]
+pub struct Contact {
+    /// `Yes` (they share material or their boundaries come within the tolerance), `No`, or
+    /// `Undecided` (the bracket straddles the tolerance at the work's limit, or a
+    /// classification was not decided).
+    pub verdict: Verdict,
+    /// A certified lower bound of the distance between the boundaries.
+    pub lower: f64,
+    /// An upper bound (the witness's distance, rounded up); infinite without a witness.
+    pub upper: f64,
+    /// Two points, one on each boundary, `upper` apart.
+    pub witness: Option<[Point3; 2]>,
+}
+
+/// A face's pieces and what decides whether a piece is on it.
+struct FacePieces {
+    face: FaceId,
+    surface: Surface,
+    /// Its form's certified distance from its definition, lost from every bound.
+    slack: f64,
+    pieces: Vec<Piece>,
+    /// The boxes of its own UV trim curves `[u0, u1, v0, v1]`; `None` when a trim curve or
+    /// its box is missing (then no piece is dropped).
+    trims: Option<Vec<[f64; 4]>>,
+}
+
+/// A body made ready for contact tests: its faces' pieces about a common point.
+pub struct Prepared {
+    origin: Point3,
+    faces: Vec<FacePieces>,
+}
+
+/// A pair of pieces, one of each body, with its lower bound.
+struct Pair {
+    lower: f64,
+    a: (usize, Piece),
+    b: (usize, Piece),
+}
+
+impl PartialEq for Pair {
+    fn eq(&self, o: &Self) -> bool {
+        self.lower.total_cmp(&o.lower) == Ordering::Equal
+    }
+}
+impl Eq for Pair {}
+impl PartialOrd for Pair {
+    fn partial_cmp(&self, o: &Self) -> Option<Ordering> {
+        Some(self.cmp(o))
+    }
+}
+impl Ord for Pair {
+    // the heap pops the smallest bound first
+    fn cmp(&self, o: &Self) -> Ordering {
+        o.lower.total_cmp(&self.lower)
+    }
+}
+
+/// The box of body `b`'s faces, `(lo, hi)`.
+fn body_box(k: &Kernel, b: &Brep) -> Result<(Point3, Point3)> {
+    let mut lo = Point3::new(f64::INFINITY, f64::INFINITY, f64::INFINITY);
+    let mut hi = Point3::new(f64::NEG_INFINITY, f64::NEG_INFINITY, f64::NEG_INFINITY);
+    for &f in b.face_list() {
+        let e = face_bounding_box(k, b, f, false)?;
+        let (l, h) = (e.min(), e.max());
+        lo = Point3::new(lo.x.min(l.x), lo.y.min(l.y), lo.z.min(l.z));
+        hi = Point3::new(hi.x.max(h.x), hi.y.max(h.y), hi.z.max(h.z));
+    }
+    if !(lo.x <= hi.x && lo.y <= hi.y && lo.z <= hi.z) {
+        return Err(SolidError::invalid_input(OP, "a body without faces"));
+    }
+    Ok((lo, hi))
+}
+
+/// The common point two bodies' pieces are made about: the centre of their boxes.
+fn common_origin(k: &Kernel, a: &Brep, b: &Brep) -> Result<Point3> {
+    let ((al, ah), (bl, bh)) = (body_box(k, a)?, body_box(k, b)?);
+    let mid = |x: f64, y: f64, z: f64, w: f64| 0.5 * (x.min(z) + y.max(w));
+    Ok(Point3::new(
+        mid(al.x, ah.x, bl.x, bh.x),
+        mid(al.y, ah.y, bl.y, bh.y),
+        mid(al.z, ah.z, bl.z, bh.z),
+    ))
+}
+
+/// The parts each Bézier segment of a trim curve is cut into for its boxes: a rectangle
+/// that no part's box meets is proved clear of the curve.
+const TRIM_PARTS: usize = 16;
+
+/// The boxes, `[u0, u1, v0, v1]`, of a UV trim curve's NURBS form: each Bézier segment cut in
+/// [`TRIM_PARTS`] by de Casteljau on its homogeneous points, each part in the box of its
+/// Euclidean points (its hull: positive weights), widened by the subdivision's rounding;
+/// `None` for a form whose weights are not positive.
+fn nurb_boxes(c: &crate::nurbs::crv_basic::Curve) -> Result<Option<Vec<[f64; 4]>>> {
+    use crate::nurbs::math::NOW;
+    let mut out = Vec::new();
+    for seg in c.decompose_bez()? {
+        let pts: Vec<[f64; 3]> = seg
+            .cpts()
+            .iter()
+            .map(|q| {
+                let w = if q.w == NOW { 1.0 } else { q.w };
+                [q.x, q.y, w]
+            })
+            .collect();
+        if pts
+            .iter()
+            .any(|q| !(q[2] > 0.0 && q.iter().all(|v| v.is_finite())))
+        {
+            return Ok(None);
+        }
+        let size = pts.iter().flatten().fold(0.0_f64, |m, v| m.max(v.abs()));
+        let wmin = pts.iter().fold(f64::INFINITY, |m, q| m.min(q[2]));
+        // the right part from t: de Casteljau at t on the homogeneous points
+        let cut = |p: &[[f64; 3]], t: f64| -> (Vec<[f64; 3]>, Vec<[f64; 3]>) {
+            let mut level = p.to_vec();
+            let (mut left, mut right) = (Vec::new(), Vec::new());
+            while let (Some(&f), Some(&l)) = (level.first(), level.last()) {
+                left.push(f);
+                right.push(l);
+                level = level
+                    .windows(2)
+                    .filter_map(|w| match w {
+                        [a, b] => Some([
+                            (1.0 - t) * a[0] + t * b[0],
+                            (1.0 - t) * a[1] + t * b[1],
+                            (1.0 - t) * a[2] + t * b[2],
+                        ]),
+                        _ => None,
+                    })
+                    .collect();
+            }
+            right.reverse();
+            (left, right)
+        };
+        let degree = pts.len().saturating_sub(1);
+        // TRIM_PARTS levels of convex combinations at most: their rounding, of the size
+        let err = gamma(3 * degree * TRIM_PARTS + 3) * size;
+        let mut rest = pts;
+        for i in 0..TRIM_PARTS {
+            let t = 1.0 / (TRIM_PARTS - i) as f64;
+            let (part, next) = if i + 1 == TRIM_PARTS {
+                (rest.clone(), Vec::new())
+            } else {
+                cut(&rest, t)
+            };
+            rest = next;
+            let (mut lo, mut hi) = ([f64::INFINITY; 2], [f64::NEG_INFINITY; 2]);
+            for q in &part {
+                for (k, v) in [q[0] / q[2], q[1] / q[2]].into_iter().enumerate() {
+                    if let (Some(l), Some(h)) = (lo.get_mut(k), hi.get_mut(k)) {
+                        *l = l.min(v);
+                        *h = h.max(v);
+                    }
+                }
+            }
+            // a quotient of coefficients within err: within err (1 + |x|) / (w - err)
+            let widen = err * (1.0 + size / wmin) / (wmin - err).max(f64::MIN_POSITIVE)
+                + gamma(2) * size / wmin;
+            out.push([lo[0] - widen, hi[0] + widen, lo[1] - widen, hi[1] + widen]);
+        }
+    }
+    Ok(Some(out))
+}
+
+/// The boxes of face `f`'s own UV trim curves (each its NURBS form's parts,
+/// [`nurb_boxes`], or the curve's whole box where it has none); `None` where a trim curve or
+/// its box is missing.
+fn trim_boxes(k: &Kernel, b: &Brep, f: FaceId) -> Result<Option<Vec<[f64; 4]>>> {
+    use crate::curve::curve::CurveKind;
+    let Some(fu) = b.face(f)?.faceuse else {
+        return Ok(None);
+    };
+    let mut out = Vec::new();
+    for lu in eu1::faceuse_loopuses(b, fu, false, None)? {
+        for eu in loopuse::edgeuses(b, lu, None, None)? {
+            // its own, or its mate's on the face's other side (the same face's parameters)
+            let Some(c) = eu1::uv_trim_curve(b, eu)?.0 else {
+                return Ok(None);
+            };
+            let nurb = match c.kind() {
+                CurveKind::BSpline(x) => x.gw_nurb(),
+                CurveKind::Ellipse(x) => x.base().gw_nurb(),
+                CurveKind::Hyperbola(x) => x.base().gw_nurb(),
+                CurveKind::Parabola(x) => x.base().gw_nurb(),
+                CurveKind::Line(x) => x.base().gw_nurb(),
+                _ => None,
+            };
+            if let Some(n) = nurb {
+                if let Some(boxes) = nurb_boxes(n)? {
+                    out.extend(boxes);
+                    continue;
+                }
+            }
+            let interval: Extent1d = c.natural_interval();
+            let boxes = c.calculate_bounding_box(
+                k,
+                &interval,
+                crate::nurbs::b_spline_curve::BoundingBoxRequest {
+                    normal: true,
+                    ..Default::default()
+                },
+                true,
+            )?;
+            let Some(e) = boxes.normal else {
+                return Ok(None);
+            };
+            let (l, h) = (e.min(), e.max());
+            // the box's own rounding, a few ulps of its size
+            let r = 16.0 * f64::EPSILON * (l.x.abs() + h.x.abs() + l.y.abs() + h.y.abs());
+            out.push([l.x - r, h.x + r, l.y - r, h.y + r]);
+        }
+    }
+    Ok(Some(out))
+}
+
+impl Prepared {
+    /// Body `b`'s faces' pieces about `origin`.
+    ///
+    /// # Errors
+    ///
+    /// `InvalidInput` for a body without faces or a face without a surface; those of the
+    /// pieces ([`crate::query::distance_bound`]) and the trim curves' boxes.
+    pub fn new(k: &Kernel, b: &Brep, origin: Point3) -> Result<Self> {
+        let mut faces = Vec::new();
+        for &f in b.face_list() {
+            let face = b.face(f)?;
+            let surface = face
+                .surface
+                .as_ref()
+                .ok_or_else(|| SolidError::invalid_input(OP, "a face without a surface"))?
+                .clone();
+            let (pieces, slack) = pieces_about(k, &surface, Some(&face.uv_domain), origin)?;
+            let trims = trim_boxes(k, b, f)?;
+            faces.push(FacePieces {
+                face: f,
+                surface,
+                slack,
+                pieces,
+                trims,
+            });
+        }
+        if faces.is_empty() {
+            return Err(SolidError::invalid_input(OP, "a body without faces"));
+        }
+        Ok(Self { origin, faces })
+    }
+
+    /// Body `b`'s faces' pieces about the centre of its own box: the preparation of one
+    /// body for tests against several ([`meets_prepared`]).
+    ///
+    /// # Errors
+    ///
+    /// Those of [`Prepared::new`] and of the faces' boxes.
+    pub fn about(k: &Kernel, b: &Brep) -> Result<Self> {
+        Self::new(k, b, common_origin(k, b, b)?)
+    }
+}
+
+/// The certified lower bound of the distance between two pieces about the same point: the
+/// larger of the distance of their widened boxes and, along a unit direction `axis` (the
+/// witness's, when there is one), the gap between their hulls' extents
+/// ([`Piece::extent_along`]), each rounded down. The axis steers which bound is tight, never
+/// whether either holds: any direction separates the hulls by at most their distance.
+fn pair_lower(a: &Piece, b: &Piece, axis: Option<[f64; 3]>) -> Result<f64> {
+    let by_box = box_lower(a, b)?;
+    let Some(u) = axis else {
+        return Ok(by_box);
+    };
+    let len = (u[0] * u[0] + u[1] * u[1] + u[2] * u[2]).sqrt() * (1.0 + gamma(4));
+    if !(len > 0.0 && len.is_finite()) {
+        return Ok(by_box);
+    }
+    let ((a0, a1), (b0, b1)) = (a.extent_along(u)?, b.extent_along(u)?);
+    let gap = (b0 - a1).max(a0 - b1).max(0.0);
+    // (the difference rounded down by gamma_1 of its terms, then over the length)
+    let gap = (gap - gamma(1) * (a0.abs() + a1.abs() + b0.abs() + b1.abs())).max(0.0);
+    let by_axis = gap / len * (1.0 - gamma(2));
+    Ok(by_box.max(by_axis))
+}
+
+/// The distance of two pieces' widened boxes, rounded down.
+fn box_lower(a: &Piece, b: &Piece) -> Result<f64> {
+    let ((al, ah), (bl, bh)) = (a.widened_box()?, b.widened_box()?);
+    let mut sum = 0.0_f64;
+    for i in 0..3 {
+        let (Some(&x0), Some(&x1), Some(&y0), Some(&y1)) =
+            (al.get(i), ah.get(i), bl.get(i), bh.get(i))
+        else {
+            return Err(SolidError::sm_err(OP));
+        };
+        let gap = (y0 - x1).max(x0 - y1).max(0.0);
+        // (the difference rounded up by at most gamma_1 of its terms)
+        let gap = (gap - gamma(1) * (x0.abs() + x1.abs() + y0.abs() + y1.abs())).max(0.0);
+        sum += gap * gap;
+    }
+    Ok(sum.sqrt() * (1.0 - gamma(5)))
+}
+
+/// Where a piece stands against its face: `Some(true)` proved on it and decisively inside
+/// at its centre, `Some(false)` proved off it (no trim curve's box meets its rectangle and
+/// its centre is outside), `None` not decided.
+fn piece_on_face(k: &Kernel, b: &mut Brep, fp: &FacePieces, p: &Piece) -> Result<Option<bool>> {
+    let [u0, u1, v0, v1] = p.uv;
+    let crosses = match &fp.trims {
+        None => true,
+        Some(boxes) => boxes
+            .iter()
+            .any(|t| !(t[1] < u0 || t[0] > u1 || t[3] < v0 || t[2] > v1)),
+    };
+    let centre = Point2::new(0.5 * (u0 + u1), 0.5 * (v0 + v1));
+    let class = match face_classify_uv(k, b, fp.face, centre) {
+        Ok(c) => c,
+        // a classification that fails decides nothing
+        Err(e) if e.is_cancelled() => return Err(e),
+        Err(_) => return Ok(None),
+    };
+    Ok(match class {
+        PointClassType::Unknown if !crosses => Some(false),
+        PointClassType::Face => Some(true),
+        _ => None,
+    })
+}
+
+/// A point of body `b` for face `fp` at `uv`: the surface's point when the face classifies
+/// `uv` decisively inside it; when it classifies it on the face's boundary (within its
+/// tolerance, either side), the nearest point of the face's edges to the surface's point,
+/// which is on the body whichever side `uv` was; `None` outside or not decided.
+fn on_face(k: &Kernel, b: &mut Brep, fp: &FacePieces, uv: Point2) -> Result<Option<Point3>> {
+    match face_classify_uv(k, b, fp.face, uv) {
+        Ok(PointClassType::Face) => Ok(Some(fp.surface.evaluate_point(k, uv)?)),
+        Ok(PointClassType::Edge | PointClassType::Vertex) => {
+            let x = fp.surface.evaluate_point(k, uv)?;
+            nearest_edge_point(k, b, fp.face, x)
+        }
+        Err(e) if e.is_cancelled() => Err(e),
+        _ => Ok(None),
+    }
+}
+
+/// The nearest point to `x` of face `f`'s edges (each solved on its edge, so on the body);
+/// `None` when no edge's solve succeeds.
+fn nearest_edge_point(k: &Kernel, b: &Brep, f: FaceId, x: Point3) -> Result<Option<Point3>> {
+    let Some(fu) = b.face(f)?.faceuse else {
+        return Ok(None);
+    };
+    let mut best: Option<(f64, Point3)> = None;
+    for lu in eu1::faceuse_loopuses(b, fu, false, None)? {
+        for eu in loopuse::edgeuses(b, lu, None, None)? {
+            let Some(e) = b.edgeuse(eu)?.edge else {
+                continue;
+            };
+            let Ok(c) = edge_closest_point(k, b, e, x) else {
+                continue;
+            };
+            let d = c.closest.point.distance(x);
+            if best.is_none_or(|(m, _)| d < m) {
+                best = Some((d, c.closest.point));
+            }
+        }
+    }
+    Ok(best.map(|(_, p)| p))
+}
+
+/// The distance of two points rounded up: `|p - q|` within `gamma_5` of the terms' size.
+fn distance_up(p: Point3, q: Point3) -> f64 {
+    let size = p.x.abs() + p.y.abs() + p.z.abs() + q.x.abs() + q.y.abs() + q.z.abs();
+    p.distance(q) * (1.0 + gamma(5)) + gamma(5) * size
+}
+
+/// The closest point of `fp`'s surface to `x`, kept when its face classifies it decisively
+/// inside; `None` for a solve that fails or a point off the face.
+fn closest_on(
+    k: &Kernel,
+    b: &mut Brep,
+    fp: &FacePieces,
+    x: Point3,
+) -> Result<Option<(Point3, Point2)>> {
+    let Ok(c) = surface_closest_point(k, &fp.surface, x) else {
+        return Ok(None);
+    };
+    let Some(&uv) = c.uvs.first() else {
+        return Ok(None);
+    };
+    Ok(on_face(k, b, fp, uv)?.map(|p| (p, uv)))
+}
+
+/// The bracket between `a` and `b` (as [`Prepared`]), refined until `stop` says done or the
+/// pairs reach [`MAX_PAIRS`]: `stop(lower, upper)`.
+fn bracket(
+    k: &Kernel,
+    a: &mut Brep,
+    pa: &Prepared,
+    b: &mut Brep,
+    pb: &Prepared,
+    seed: f64,
+    stop: &dyn Fn(f64, f64) -> bool,
+) -> Result<(f64, f64, Option<[Point3; 2]>, bool)> {
+    let mut heap = BinaryHeap::new();
+    let mut made = 0_usize;
+    for (ia, fa) in pa.faces.iter().enumerate() {
+        for (ib, fb) in pb.faces.iter().enumerate() {
+            for x in &fa.pieces {
+                for y in &fb.pieces {
+                    let lower = (pair_lower(x, y, None)? - fa.slack - fb.slack).max(0.0);
+                    heap.push(Pair {
+                        lower,
+                        a: (ia, x.clone()),
+                        b: (ib, y.clone()),
+                    });
+                    made += 1;
+                }
+            }
+        }
+    }
+    let (mut upper, mut witness) = (f64::INFINITY, None);
+    // witnesses first from every face pair whose bound is within `seed`, nearest first (the
+    // pairs tie closely where two bodies lie along each other; each is visited once here)
+    let mut first: Vec<&Pair> = heap.iter().filter(|p| p.lower <= seed).collect();
+    first.sort_by(|x, y| x.lower.total_cmp(&y.lower));
+    for pair in first {
+        let (Some(fa), Some(fb)) = (pa.faces.get(pair.a.0), pb.faces.get(pair.b.0)) else {
+            return Err(SolidError::sm_err(OP));
+        };
+        if pair.lower < upper {
+            witness_from(
+                k,
+                (&mut *a, fa, &pair.a.1),
+                (&mut *b, fb, &pair.b.1),
+                &mut upper,
+                &mut witness,
+            )?;
+        }
+        if stop(0.0, upper) {
+            break;
+        }
+    }
+    loop {
+        k.check_cancelled(OP)?;
+        let Some(pair) = heap.pop() else {
+            // every piece proved off its face: no boundary is there to bound
+            return Ok((f64::INFINITY, upper, witness, true));
+        };
+        let lower = pair.lower.min(upper);
+        if stop(lower, upper) {
+            return Ok((lower, upper, witness, true));
+        }
+        if made >= MAX_PAIRS {
+            return Ok((lower, upper, witness, false));
+        }
+        let (ia, x) = &pair.a;
+        let (ib, y) = &pair.b;
+        let (Some(fa), Some(fb)) = (pa.faces.get(*ia), pb.faces.get(*ib)) else {
+            return Err(SolidError::sm_err(OP));
+        };
+        // a witness from the pair's centres (none can be nearer than the pair's bound, so a
+        // pair past the witness so far is skipped)
+        if pair.lower < upper {
+            witness_from(
+                k,
+                (&mut *a, fa, x),
+                (&mut *b, fb, y),
+                &mut upper,
+                &mut witness,
+            )?;
+        }
+        // split the larger piece
+        let size = |p: &Piece| -> Result<f64> {
+            let (l, h) = p.widened_box()?;
+            Ok((0..3)
+                .map(|i| h.get(i).copied().unwrap_or(0.0) - l.get(i).copied().unwrap_or(0.0))
+                .fold(0.0_f64, f64::max))
+        };
+        let split_a = size(x)? >= size(y)?;
+        let (from, keep) = if split_a { (x, y) } else { (y, x) };
+        // the witness's direction, for the hulls' extents along it
+        let axis = witness.map(|[p, q]| [q.x - p.x, q.y - p.y, q.z - p.z]);
+        for q in from.quarters()? {
+            let (fp, brep) = if split_a {
+                (fa, &mut *a)
+            } else {
+                (fb, &mut *b)
+            };
+            if piece_on_face(k, brep, fp, &q)? == Some(false) {
+                continue;
+            }
+            let (qa, qb) = if split_a { (&q, keep) } else { (keep, &q) };
+            let lower = (pair_lower(qa, qb, axis)? - fa.slack - fb.slack).max(0.0);
+            heap.push(Pair {
+                lower,
+                a: (*ia, qa.clone()),
+                b: (*ib, qb.clone()),
+            });
+            made += 1;
+        }
+    }
+}
+
+/// A witness from a pair's centres, each moved to the other's surface's closest point and
+/// back ([`PROJECTIONS`] times), kept where both points are decisively on their faces and
+/// nearer than `upper`.
+fn witness_from(
+    k: &Kernel,
+    (a, fa, x): (&mut Brep, &FacePieces, &Piece),
+    (b, fb, y): (&mut Brep, &FacePieces, &Piece),
+    upper: &mut f64,
+    witness: &mut Option<[Point3; 2]>,
+) -> Result<()> {
+    let (_, ua) = x.centre();
+    let (_, ub) = y.centre();
+    let mut pa_pt = on_face(k, a, fa, Point2::new(ua[0], ua[1]))?;
+    let mut pb_pt = on_face(k, b, fb, Point2::new(ub[0], ub[1]))?;
+    for _ in 0..PROJECTIONS {
+        if let Some(p) = pa_pt {
+            if let Some((q, _)) = closest_on(k, b, fb, p)? {
+                pb_pt = Some(q);
+            }
+        }
+        if let Some(q) = pb_pt {
+            if let Some((p, _)) = closest_on(k, a, fa, q)? {
+                pa_pt = Some(p);
+            }
+        }
+        if let (Some(p), Some(q)) = (pa_pt, pb_pt) {
+            let d = distance_up(p, q) + fa.slack + fb.slack;
+            if d < *upper {
+                *upper = d;
+                *witness = Some([p, q]);
+            }
+        }
+    }
+    Ok(())
+}
+
+/// A point of `inner`'s boundary classified in `outer`: `Some(true)` inside its material,
+/// `Some(false)` outside it, `None` when none of `inner`'s points tried (its pieces'
+/// centres, where their faces hold them: [`on_face`]) is proved more than twice the
+/// classification's tolerance from `outer`'s boundary
+/// ([`crate::query::distance_bound::face_distance_lower_bound`] over `outer`'s faces), or
+/// its classification is not decided.
+fn point_in(
+    k: &Kernel,
+    inner: &mut Brep,
+    p_inner: &Prepared,
+    outer: &Brep,
+) -> Result<Option<bool>> {
+    use crate::query::distance_bound::face_distance_lower_bound;
+    let tol = brep_zone_tol_3d(k, outer, SmallTopoType::NormalSize);
+    let clear = 2.0 * tol;
+    for fp in &p_inner.faces {
+        for piece in &fp.pieces {
+            let (_, uv) = piece.centre();
+            let Some(p) = on_face(k, inner, fp, Point2::new(uv[0], uv[1]))? else {
+                continue;
+            };
+            let mut far = true;
+            for &g in outer.face_list() {
+                if face_distance_lower_bound(k, outer, g, p, clear)? <= clear {
+                    far = false;
+                    break;
+                }
+            }
+            if !far {
+                continue;
+            }
+            let mut classifier = BrepClassifier::of_brep(outer);
+            let pc = match classifier.point_3d_classify(k, p, tol, true) {
+                Ok(pc) => pc,
+                Err(e) if e.is_cancelled() => return Err(e),
+                Err(_) => return Ok(None),
+            };
+            return Ok(match (pc.point_class(), pc.object()) {
+                (PointClassType::Region, Some(EntityRef::Region(r))) => {
+                    Some(region_material(classifier.brep(), r)?)
+                }
+                _ => None,
+            });
+        }
+    }
+    Ok(None)
+}
+
+/// Whether `a` and `b` meet at `tol` (module docs), `a` prepared once for several `b`s.
+///
+/// # Errors
+///
+/// `InvalidInput` for a tolerance not finite and positive, or a body without faces; those
+/// of the pieces, the classifications' cancellation and the closest-point solves' setup.
+pub fn meets_prepared(
+    k: &Kernel,
+    a: &mut Brep,
+    pa: &Prepared,
+    b: &mut Brep,
+    tol: f64,
+) -> Result<Contact> {
+    if !(tol.is_finite() && tol > 0.0) {
+        return Err(SolidError::invalid_input(
+            OP,
+            "the tolerance is finite and positive",
+        ));
+    }
+    let pb = Prepared::new(k, b, pa.origin)?;
+    let stop = |lower: f64, upper: f64| upper <= tol || lower > tol;
+    let (lower, upper, witness, done) = bracket(k, a, pa, b, &pb, tol, &stop)?;
+    let verdict = if upper <= tol {
+        Verdict::Yes
+    } else if !done {
+        Verdict::Undecided
+    } else {
+        // the boundaries are more than tol apart: they meet only if one encloses the other
+        match (point_in(k, b, &pb, a)?, point_in(k, a, pa, b)?) {
+            (Some(true), _) | (_, Some(true)) => Verdict::Yes,
+            (Some(false), Some(false)) => Verdict::No,
+            _ => Verdict::Undecided,
+        }
+    };
+    Ok(Contact {
+        verdict,
+        lower,
+        upper,
+        witness,
+    })
+}
+
+/// [`meets_prepared`] for one pair: `a` prepared about the centre of both bodies' boxes.
+///
+/// # Errors
+///
+/// Those of [`meets_prepared`].
+pub fn meets(k: &Kernel, a: &mut Brep, b: &mut Brep, tol: f64) -> Result<Contact> {
+    let origin = common_origin(k, a, b)?;
+    let pa = Prepared::new(k, a, origin)?;
+    meets_prepared(k, a, &pa, b, tol)
+}
+
+/// The bracket of the distance between `a`'s and `b`'s boundaries, refined until it is at
+/// most `width` wide (relative to the upper end, or absolute below 1) or the pairs reach
+/// [`MAX_PAIRS`]; the verdict is `Yes` when it is that narrow, `Undecided` when the work
+/// ran out first. The bracket always holds the distance; it can stay wider than `width`
+/// where a nearest point lies on a face's trim, since a piece straddling the trim carries
+/// surface off the face and is cut finer only along the trim.
+///
+/// # Errors
+///
+/// `InvalidInput` for a width not finite and positive; those of [`meets`].
+pub fn boundary_distance(k: &Kernel, a: &mut Brep, b: &mut Brep, width: f64) -> Result<Contact> {
+    if !(width.is_finite() && width > 0.0) {
+        return Err(SolidError::invalid_input(
+            OP,
+            "the width is finite and positive",
+        ));
+    }
+    let origin = common_origin(k, a, b)?;
+    let pa = Prepared::new(k, a, origin)?;
+    let pb = Prepared::new(k, b, origin)?;
+    let stop = |lower: f64, upper: f64| upper - lower <= width * upper.max(1.0);
+    let (lower, upper, witness, done) = bracket(k, a, &pa, b, &pb, f64::INFINITY, &stop)?;
+    Ok(Contact {
+        verdict: if done {
+            Verdict::Yes
+        } else {
+            Verdict::Undecided
+        },
+        lower,
+        upper,
+        witness,
+    })
+}

solidcore/crates/solidcore/src/query/distance_bound.rs

@@ -44,15 +44,18 @@ pub const MAX_PATCHES: usize = 4096;
 /// A piece of a face's surface: its homogeneous coordinates about the point, as Bernstein
 /// polynomials on the unit square, and the absolute error each coefficient may carry.
 #[derive(Debug, Clone)]
-struct Piece {
+pub(crate) struct Piece {
     /// `X W - p W`, `Y W - p W`, `Z W - p W`, `W`.
-    h: [Bernstein2; 4],
+    pub(crate) h: [Bernstein2; 4],
     /// The bound on every coefficient's error.
-    err: f64,
+    pub(crate) err: f64,
     /// The certified lower bound of the piece's distance from the point.
-    lower: f64,
+    pub(crate) lower: f64,
     /// Its subdivision depth.
-    depth: usize,
+    pub(crate) depth: usize,
+    /// Its rectangle in the surface's NURB parameters, `[u0, u1, v0, v1]` (to the rounding
+    /// of the splits that made it).
+    pub(crate) uv: [f64; 4],
 }
 
 impl PartialEq for Piece {
@@ -74,21 +77,62 @@ impl Ord for Piece {
 }
 
 impl Piece {
-    /// The piece with its bound, the coefficients `h` within `err` each.
-    fn new(h: [Bernstein2; 4], err: f64, depth: usize) -> Result<Self> {
+    /// The piece with its bound, the coefficients `h` within `err` each, over `uv`.
+    fn new(h: [Bernstein2; 4], err: f64, depth: usize, uv: [f64; 4]) -> Result<Self> {
         let lower = hull_bound(&h, err)?;
         Ok(Self {
             h,
             err,
             lower,
             depth,
+            uv,
         })
     }
 
+    /// The box of its Euclidean control points about the point, each coordinate widened
+    /// by the error a quotient of coefficients within `err` can carry: every point of the
+    /// piece lies in it (the hull, with positive weights).
+    pub(crate) fn widened_box(&self) -> Result<([f64; 3], [f64; 3])> {
+        let (lo, hi, widen) = euclid_box(&self.h, self.err)?;
+        Ok((lo.map(|l| l - widen), hi.map(|u| u + widen)))
+    }
+
+    /// Its centre's Euclidean point about the point, and the centre's parameters.
+    pub(crate) fn centre(&self) -> ([f64; 3], [f64; 2]) {
+        let [x, y, z, w] = &self.h;
+        let wc = w.eval(0.5, 0.5);
+        let [u0, u1, v0, v1] = self.uv;
+        (
+            [
+                x.eval(0.5, 0.5) / wc,
+                y.eval(0.5, 0.5) / wc,
+                z.eval(0.5, 0.5) / wc,
+            ],
+            [0.5 * (u0 + u1), 0.5 * (v0 + v1)],
+        )
+    }
+
+    /// The certified range of `x . u` over the piece, for a direction `u`: the least and
+    /// largest of its Euclidean control points' (its hull), each moved out by the widening
+    /// along `u` and the products' rounding.
+    pub(crate) fn extent_along(&self, u: [f64; 3]) -> Result<(f64, f64)> {
+        let (lo, hi, widen) = euclid_box(&self.h, self.err)?;
+        let size = lo.iter().chain(&hi).fold(0.0_f64, |m, v| m.max(v.abs())) + widen;
+        let norm1 = u[0].abs() + u[1].abs() + u[2].abs();
+        let (mut least, mut most) = (f64::INFINITY, f64::NEG_INFINITY);
+        for e in euclid_points(&self.h) {
+            let d = e[0] * u[0] + e[1] * u[1] + e[2] * u[2];
+            least = least.min(d);
+            most = most.max(d);
+        }
+        let slack = widen * norm1 + gamma(3) * size * norm1;
+        Ok((least - slack, most + slack))
+    }
+
     /// Its four quarters: one de Casteljau level each way, which adds the rounding of a
     /// convex combination per level (`gamma` of twice the degree plus two) of the largest
     /// coefficient.
-    fn quarters(&self) -> Result<[Self; 4]> {
+    pub(crate) fn quarters(&self) -> Result<[Self; 4]> {
         let largest = self
             .h
             .iter()
@@ -108,14 +152,23 @@ impl Piece {
             split(&self.h[2]),
             split(&self.h[3]),
         ];
+        let [u0, u1, v0, v1] = self.uv;
+        let (um, vm) = (0.5 * (u0 + u1), 0.5 * (v0 + v1));
+        let rects = [
+            [u0, um, v0, vm],
+            [u0, um, vm, v1],
+            [um, u1, v0, vm],
+            [um, u1, vm, v1],
+        ];
         let mut out = Vec::new();
-        for i in 0..4 {
+        for (i, uv) in rects.into_iter().enumerate() {
             let pick =
                 |a: &[Bernstein2; 4]| a.get(i).cloned().ok_or_else(|| SolidError::sm_err(OP));
             out.push(Self::new(
                 [pick(&x)?, pick(&y)?, pick(&z)?, pick(&w)?],
                 err,
                 self.depth + 1,
+                uv,
             )?);
         }
         out.try_into().map_err(|_| SolidError::sm_err(OP))
@@ -130,42 +183,15 @@ impl Piece {
 /// least the least P . u, and |X| >= X . u / |u|), which, unlike the box, tightens with the
 /// square of the piece's size on a piece tilted to the axes.
 fn hull_bound(h: &[Bernstein2; 4], err: f64) -> Result<f64> {
-    let [x, y, z, w] = h;
-    let (xs, ys, zs, ws) = (
-        x.coefficients(),
-        y.coefficients(),
-        z.coefficients(),
-        w.coefficients(),
-    );
-    let w_min = ws.iter().copied().fold(f64::INFINITY, f64::min);
-    if !above(w_min - err, 0.0) {
-        return Err(SolidError::Unsupported {
-            operation: OP,
-            reason: "a patch's weights are not proved positive",
-        });
-    }
-    let mut points = Vec::new();
-    let mut lo = [f64::INFINITY; 3];
-    let mut hi = [f64::NEG_INFINITY; 3];
-    let mut size = 0.0_f64;
+    let (lo, hi, widen) = euclid_box(h, err)?;
+    let points = euclid_points(h);
+    let size = lo.iter().chain(&hi).fold(0.0_f64, |m, v| m.max(v.abs()));
     let mut sum_points = [0.0_f64; 3];
-    for (((&a, &b), &c), &wi) in xs.iter().zip(ys).zip(zs).zip(ws) {
-        let e = [a / wi, b / wi, c / wi];
-        for (k, v) in e.into_iter().enumerate() {
-            size = size.max(v.abs());
-            if let (Some(l), Some(u), Some(t)) =
-                (lo.get_mut(k), hi.get_mut(k), sum_points.get_mut(k))
-            {
-                *l = l.min(v);
-                *u = u.max(v);
-                *t += v;
-            }
+    for e in &points {
+        for (t, v) in sum_points.iter_mut().zip(e) {
+            *t += v;
         }
-        points.push(e);
     }
-    // |(v + dv) / (w + dw) - v / w| <= err (1 + |v / w|) / (w - err), and the quotient's
-    // own rounding
-    let widen = err * (1.0 + size) / (w_min - err) + gamma(2) * size;
     let mut sum = 0.0_f64;
     for (l, u) in lo.into_iter().zip(hi) {
         let out = (l - widen).max(-(u + widen)).max(0.0);
@@ -202,6 +228,61 @@ fn hull_bound(h: &[Bernstein2; 4], err: f64) -> Result<f64> {
     Ok(bound.max(0.0))
 }
 
+/// The Euclidean control points of the homogeneous coefficients `h`.
+fn euclid_points(h: &[Bernstein2; 4]) -> Vec<[f64; 3]> {
+    let [x, y, z, w] = h;
+    x.coefficients()
+        .iter()
+        .zip(y.coefficients())
+        .zip(z.coefficients())
+        .zip(w.coefficients())
+        .map(|(((&a, &b), &c), &wi)| [a / wi, b / wi, c / wi])
+        .collect()
+}
+
+/// The box of the Euclidean control points of `h`, and how far each coordinate is to be
+/// widened for coefficients within `err` (and the quotients' own rounding): `(lo, hi,
+/// widen)`.
+fn euclid_box(h: &[Bernstein2; 4], err: f64) -> Result<([f64; 3], [f64; 3], f64)> {
+    let [x, y, z, w] = h;
+    let (xs, ys, zs, ws) = (
+        x.coefficients(),
+        y.coefficients(),
+        z.coefficients(),
+        w.coefficients(),
+    );
+    let w_min = ws.iter().copied().fold(f64::INFINITY, f64::min);
+    if !above(w_min - err, 0.0) {
+        return Err(SolidError::Unsupported {
+            operation: OP,
+            reason: "a patch's weights are not proved positive",
+        });
+    }
+    let mut lo = [f64::INFINITY; 3];
+    let mut hi = [f64::NEG_INFINITY; 3];
+    let mut size = 0.0_f64;
+    for (((&a, &b), &c), &wi) in xs.iter().zip(ys).zip(zs).zip(ws) {
+        let e = [a / wi, b / wi, c / wi];
+        for (k, v) in e.into_iter().enumerate() {
+            size = size.max(v.abs());
+            if let (Some(l), Some(u)) = (lo.get_mut(k), hi.get_mut(k)) {
+                *l = l.min(v);
+                *u = u.max(v);
+            }
+        }
+    }
+    // |(v + dv) / (w + dw) - v / w| <= err (1 + |v / w|) / (w - err), and the quotient's
+    // own rounding
+    let widen = err * (1.0 + size) / (w_min - err) + gamma(2) * size;
+    if !(widen.is_finite() && lo.iter().chain(&hi).all(|v| v.is_finite())) {
+        return Err(SolidError::Unsupported {
+            operation: OP,
+            reason: "a patch's box is not finite",
+        });
+    }
+    Ok((lo, hi, widen))
+}
+
 /// A certified lower bound of the distance from `p` to face `f` of `b`: no point of the face
 /// is nearer to `p`. The face is bounded by its surface over the face's UV box (its trims
 /// lie inside it): [`surface_distance_lower_bound`] on them.
@@ -320,6 +401,51 @@ pub fn surface_distance_lower_bound(
             "the bound asked for is finite and not negative",
         ));
     }
+    let (pieces, slack) = pieces_about(k, surf, uv_box, p)?;
+    let want_net = want + slack;
+    let mut made = pieces.len();
+    let mut heap: BinaryHeap<Piece> = pieces.into_iter().collect();
+    let off = |lower: f64| (lower - slack).max(0.0);
+    loop {
+        // (the box is inside the patches' range, so some patch overlaps it)
+        let nearest = heap.pop().ok_or_else(|| SolidError::sm_err(OP))?;
+        if nearest.lower >= want_net || made >= MAX_PATCHES {
+            return Ok(off(nearest.lower));
+        }
+        // the piece's centre is a point of the net over the box: nearer than the target, no
+        // bound reaches it
+        let (centre, _) = nearest.centre();
+        if (centre[0] * centre[0] + centre[1] * centre[1] + centre[2] * centre[2]).sqrt() < want_net
+        {
+            return Ok(off(nearest.lower));
+        }
+        for q in nearest.quarters()? {
+            heap.push(q);
+        }
+        made += 4;
+    }
+}
+
+/// The pieces of `surf` over `uv_box` (as [`surface_distance_lower_bound`] takes it) about
+/// `p`: its NURBS form's Bézier patches restricted to the box, translated by `-p`, each
+/// with its coefficients' error (the form's against its definition, the extraction's and
+/// the translation's, module docs); and the slack every distance from them is to lose (a
+/// net's certified bound from its definition, 0 for a surface that evaluates on its net).
+/// The one construction of the face pieces that [`surface_distance_lower_bound`] and the
+/// contact test between bodies ([`crate::query::contact`]) bound distances with.
+///
+/// # Errors
+///
+/// As [`surface_distance_lower_bound`]'s, but for `want`.
+pub(crate) fn pieces_about(
+    k: &Kernel,
+    surf: &Surface,
+    uv_box: Option<&Extent2d>,
+    p: Point3,
+) -> Result<(Vec<Piece>, f64)> {
+    if !(p.x.is_finite() && p.y.is_finite() && p.z.is_finite()) {
+        return Err(SolidError::invalid_input(OP, "point not finite"));
+    }
     if !measurable(k, surf)? {
         return Err(SolidError::Unsupported {
             operation: OP,
@@ -424,9 +550,7 @@ pub fn surface_distance_lower_bound(
             ));
         }
     }
-    let want_net = want + slack;
-    let mut heap = BinaryHeap::new();
-    let mut made = 0_usize;
+    let mut pieces = Vec::new();
     for patch in patches.iter().flatten() {
         let (pu, pv) = patch.degrees();
         let (uk, vk) = (patch.u_knots(), patch.v_knots());
@@ -496,33 +620,15 @@ pub fn surface_distance_lower_bound(
         } else {
             h
         };
-        heap.push(Piece::new(h, err, 0)?);
-        made += 1;
-    }
-    let off = |lower: f64| (lower - slack).max(0.0);
-    loop {
-        // (the box is inside the patches' range, so some patch overlaps it)
-        let nearest = heap.pop().ok_or_else(|| SolidError::sm_err(OP))?;
-        if nearest.lower >= want_net || made >= MAX_PATCHES {
-            return Ok(off(nearest.lower));
-        }
-        // the piece's centre is a point of the net over the box: nearer than the target, no
-        // bound reaches it
-        let [x, y, z, w] = &nearest.h;
-        let wc = w.eval(0.5, 0.5);
-        let centre = (
-            x.eval(0.5, 0.5) / wc,
-            y.eval(0.5, 0.5) / wc,
-            z.eval(0.5, 0.5) / wc,
-        );
-        if (centre.0 * centre.0 + centre.1 * centre.1 + centre.2 * centre.2).sqrt() < want_net {
-            return Ok(off(nearest.lower));
-        }
-        for q in nearest.quarters()? {
-            heap.push(q);
-        }
-        made += 4;
+        let uv = [
+            u0 + a0 * (u1 - u0),
+            u0 + a1 * (u1 - u0),
+            v0 + b0 * (v1 - v0),
+            v0 + b1 * (v1 - v0),
+        ];
+        pieces.push(Piece::new(h, err, 0, uv)?);
     }
+    Ok((pieces, slack))
 }
 
 #[cfg(test)]
@@ -890,7 +996,10 @@ mod tests {
                     .unwrap()
                 });
                 let exact = h.each_ref().map(exact_quarters);
-                let quarters = Piece::new(h, 0.0, 0).unwrap().quarters().unwrap();
+                let quarters = Piece::new(h, 0.0, 0, [0.0, 1.0, 0.0, 1.0])
+                    .unwrap()
+                    .quarters()
+                    .unwrap();
                 for (q, quarter) in quarters.iter().enumerate() {
                     for (axis, component) in quarter.h.iter().enumerate() {
                         for (rounded, reference) in

solidcore/crates/solidcore/src/query/edge_turn.rs

@@ -0,0 +1,139 @@
+//! At a vertex where edges meet: the direction an edge leaves it in, how far one edge turns
+//! from running straight on into another there, and whether an edge is convex there. The
+//! measures a tangent-chain walk takes at each vertex.
+//!
+//! Upstream: none (not in SMLib).
+//!
+//! | Rust          | Upstream |
+//! |---------------|----------|
+//! | [`leaving`]   | (none)   |
+//! | [`turn_at`]   | (none)   |
+//! | [`convex_at`] | (none)   |
+//!
+//! Deviations: no upstream counterpart.
+
+use crate::error::{Result, SolidError};
+use crate::kernel::Kernel;
+use crate::math::Vec3;
+use crate::topology::edgeuse::p1 as eu1;
+use crate::topology::edgeuse::p3::{evaluate_binormal, BinormalOptions};
+use crate::topology::{edge, Brep, EdgeId, VertexId};
+
+const OP: &str = "query::edge_turn";
+
+fn invalid(reason: &'static str) -> SolidError {
+    SolidError::invalid_input(OP, reason)
+}
+
+/// Edge `e`'s parameter at its end `v`, and whether `v` is its start; `None` for a closed
+/// edge (both ends `v`).
+fn end_at(b: &Brep, e: EdgeId, v: VertexId) -> Result<Option<(f64, bool)>> {
+    let start = edge::start_vertex(b, e)?;
+    let end = edge::end_vertex(b, e)?;
+    if start == end {
+        return Ok(None);
+    }
+    let ivl = edge::interval(b, e)?;
+    if start == Some(v) {
+        Ok(Some((ivl.min(), true)))
+    } else if end == Some(v) {
+        Ok(Some((ivl.max(), false)))
+    } else {
+        Err(invalid("a vertex that is not an end of the edge"))
+    }
+}
+
+/// The unit direction edge `e` leaves its end `v` in: its curve's tangent there, turned to
+/// point away from `v`. `None` for a closed edge, an edge without curve, or a tangent of no
+/// length.
+///
+/// # Errors
+///
+/// [`SolidError::InvalidInput`] for a vertex that is not an end of `e`; those of the
+/// evaluation.
+pub fn leaving(k: &Kernel, b: &Brep, e: EdgeId, v: VertexId) -> Result<Option<Vec3>> {
+    let Some((t, at_start)) = end_at(b, e, v)? else {
+        return Ok(None);
+    };
+    let Some(curve) = edge::curve(b, e)? else {
+        return Ok(None);
+    };
+    // from inside the edge: from the right at its start, from the left at its end
+    let d = curve.evaluate(k, t, 1, !at_start, true)?;
+    let Some(&tangent) = d.get(1) else {
+        return Err(invalid("a curve's evaluation without its tangent"));
+    };
+    let Ok(unit) = tangent.unitize() else {
+        return Ok(None);
+    };
+    Ok(Some(if at_start { unit } else { unit * -1.0 }))
+}
+
+/// How far (radians, 0 to pi) edge `f` turns at their shared end `v` from running straight on
+/// from edge `e`: the angle between the direction `e` arrives at `v` in and the one `f` leaves
+/// it in. 0 where `f` continues `e` tangentially. `None` where either direction is undefined
+/// ([`leaving`]).
+///
+/// # Errors
+///
+/// Those of [`leaving`].
+pub fn turn_at(k: &Kernel, b: &Brep, e: EdgeId, f: EdgeId, v: VertexId) -> Result<Option<f64>> {
+    let (Some(arrives), Some(leaves)) = (leaving(k, b, e, v)?, leaving(k, b, f, v)?) else {
+        return Ok(None);
+    };
+    let arrives = arrives * -1.0;
+    Ok(Some(
+        arrives.cross(leaves).length().atan2(arrives.dot(leaves)),
+    ))
+}
+
+/// Whether edge `e` is convex at its end `v` (its faces meet at less than 180 degrees inside
+/// the material there): the direction from the edge into its second face, square to it,
+/// points along its first face's inward normal (the face use normals of the edge use on the
+/// material's side, its face use's region not void, and of its radial partner, which point
+/// into the material). `None` for
+/// an edge not between two face uses, a closed edge, an edge with no edge use on a material
+/// region's side, or faces whose normal and binormal there are square to each other (tangent
+/// faces: no convexity).
+///
+/// # Errors
+///
+/// [`SolidError::InvalidInput`] for a vertex that is not an end of `e`; those of the
+/// evaluations.
+pub fn convex_at(k: &Kernel, b: &mut Brep, e: EdgeId, v: VertexId) -> Result<Option<bool>> {
+    if !edge::is_manifold(b, e)? || eu1::edge_is_lamina(b, e)? {
+        return Ok(None);
+    }
+    let Some((t, _)) = end_at(b, e, v)? else {
+        return Ok(None);
+    };
+    // the edge use on the material's side: its face use and its radial partner's bound the
+    // material, and their normals point into it (the primary edge use may be on the void's,
+    // whose normals point out)
+    let mut eu0 = None;
+    for eu in edge::edgeuses(b, e, None, None)? {
+        let Some(fu) = eu1::faceuse(b, eu)? else {
+            continue;
+        };
+        if let Some(r) = eu1::faceuse_region(b, fu)? {
+            if b.region(r)?.is_void() == 0 {
+                eu0 = Some(eu);
+                break;
+            }
+        }
+    }
+    let Some(eu0) = eu0 else {
+        return Ok(None);
+    };
+    let Some(eu_r) = eu1::radial(b, eu0)? else {
+        return Ok(None);
+    };
+    let options = BinormalOptions::default();
+    let first = evaluate_binormal(k, b, eu0, t, false, &options)?;
+    let second = evaluate_binormal(k, b, eu_r, t, false, &options)?;
+    let side = second.binormal.dot(first.face_normal);
+    if side == 0.0 || !side.is_finite() {
+        return Ok(None);
+    }
+    Ok(Some(side > 0.0))
+}

solidcore/crates/solidcore/src/surface/cone/p1.rs

@@ -1508,12 +1508,7 @@ impl Cone {
         hv: usize,
         flags: EvaluateFlags,
     ) -> Result<Vec<Vec3>> {
-        let rows = self.evaluate_rows(k, uv, hu, hv, flags)?;
-        let mut d = Vec::with_capacity((hu + 1) * (hv + 1));
-        for row in rows {
-            d.extend(row);
-        }
-        Ok(d)
+        Ok(self.evaluate_rows(k, uv, hu, hv, flags)?.concat())
     }
 
     /// [`Self::evaluate`] as `D[i][j]` rows: exactly `hu + 1` rows of `hv + 1` entries

solidcore/crates/solidcore/src/surface/extend/analytic.rs

@@ -597,6 +597,13 @@ fn joint_removed(out: &Net, side: BoxSide, joint: f64) -> Result<Net> {
 /// curve: every homogeneous control point in a plane normal to the axis (a parallel) or
 /// through it (a meridian, a tube), within its rounding; a ruling is straight by its
 /// degree. Refused as not exact otherwise.
+///
+/// The limit, `8 gamma_32` times the point's own size (`|c|` plus the frame's size times
+/// `|w|`) plus the plane's height times `|w|`, has the shape of a rounding bound but its
+/// factor is tuned, not derived: `8` and `32` count no operations of `extract_iso_crv`, the
+/// dot product or the height. It is held to that size by a test (refused at twice it,
+/// accepted at half), and measured well inside it (largest off / limit 0.0123 over the
+/// offset and extension goldens); deriving it is open.
 fn certify_iso(
     s: &BSplineSurface,
     side: BoxSide,
@@ -614,12 +621,6 @@ fn certify_iso(
         (middle.x, Direction::V)
     };
     let curve = extract_iso_crv(net, t, dir)?;
-    // the iso is interpolated between the net's rows, so its points are known to the rounding
-    // at the size of those rows, not at their own: a short arc's middle iso between rulings
-    // extended 500 mm each way
-    let rows = net.cpts().iter().flatten().fold(0.0_f64, |m, p| {
-        m.max(p.x.abs()).max(p.y.abs()).max(p.z.abs())
-    });
     let points: Vec<(Vec3, f64, f64)> = curve
         .cpts()
         .iter()
@@ -627,7 +628,7 @@ fn certify_iso(
             let w = if p.w == NOW { 1.0 } else { p.w };
             let h = Vec3::new(p.x, p.y, p.z);
             // X W from the origin, and the size of its terms
-            let mag = rows + f.size * w.abs();
+            let mag = p.x.abs().max(p.y.abs()).max(p.z.abs()) + f.size * w.abs();
             (h - f.origin * w, w, mag)
         })
         .collect();
@@ -921,3 +922,117 @@ fn slot_mut(cp: &mut [Vec<CPoint>], is_u: bool, a: usize, r: usize) -> Result<&m
         .and_then(|x| x.get_mut(j))
         .ok_or_else(|| SolidError::sm_err(OP))
 }
+
+#[cfg(test)]
+mod tests {
+    #![allow(
+        clippy::unwrap_used,
+        clippy::expect_used,
+        clippy::panic,
+        clippy::indexing_slicing
+    )]
+
+    use super::*;
+    use crate::surface::cone::p1::Cone;
+
+    /// The limit `certify_iso` holds a parallel's homogeneous control point `c` to: the
+    /// rounding at the point's own size and the frame's, `8 gamma_32 (|c| + size |w| +
+    /// |height| |w|)` (written out here so that a change to the limit's size fails).
+    fn limit(c: &CPoint, size: f64, height: f64) -> f64 {
+        let w = if c.w == NOW { 1.0 } else { c.w };
+        let mag = c.x.abs().max(c.y.abs()).max(c.z.abs()) + size * w.abs();
+        8.0 * gamma(32) * (mag + height.abs() * w.abs())
+    }
+
+    /// A cylinder of radius 1 about z, 60 degrees round, 1000 long: rows far larger than
+    /// the turn's own points, so a limit taken at the rows' size would be about 1000 times
+    /// the one at the iso's.
+    fn long_cylinder() -> BSplineSurface {
+        let k = Kernel::default();
+        let s = Surface::from(Cone::new_cylinder_bounded(
+            Vec3::new(0.0, 0.0, 0.0),
+            Vec3::new(1.0, 0.0, 0.0),
+            Vec3::new(0.0, 1.0, 0.0),
+            1.0,
+            0.0,
+            60.0,
+            1000.0,
+            false,
+            false,
+            false,
+        ));
+        crate::blend::fillet_section::station::as_b_spline(&k, &s)
+            .unwrap()
+            .unwrap()
+            .into_owned()
+    }
+
+    /// The net with every control point of index `i` along the iso across `side` moved
+    /// `delta` along the axis (its homogeneous `delta w`): the iso's point `i` moves by
+    /// `delta`, the rest stay.
+    fn moved(form: &BSplineSurface, side: BoxSide, i: usize, delta: f64) -> BSplineSurface {
+        let net = form.gw_nurb().unwrap();
+        let mut cpts = net.cpts();
+        for (a, row) in cpts.iter_mut().enumerate() {
+            for (b, c) in row.iter_mut().enumerate() {
+                let along = if side.is_u() { a } else { b };
+                if along == i {
+                    let w = if c.w == NOW { 1.0 } else { c.w };
+                    c.z += delta * w;
+                }
+            }
+        }
+        let (p, q) = net.degrees();
+        BSplineSurface::from_gw_nurb(
+            &Net::new(cpts, p, q, net.u_knots().to_vec(), net.v_knots().to_vec()).unwrap(),
+        )
+    }
+
+    /// `certify_iso` refuses a parallel whose control point is off its plane by twice the
+    /// limit at the point's own size and passes one off by half of it: the limit's size is
+    /// pinned, and a limit taken at the net's rows (1000 here) would pass both.
+    #[test]
+    fn the_turn_certificate_holds_the_iso_to_its_own_size() {
+        let form = long_cylinder();
+        let frame = Frame {
+            origin: Vec3::new(0.0, 0.0, 0.0),
+            axis: Vec3::new(0.0, 0.0, 1.0),
+            apex: None,
+            size: 1.0,
+            quarter: 0.0,
+            tube_left: 0.0,
+        };
+        let dom = knot_box(&form).unwrap();
+        let mut tested = 0;
+        for side in BoxSide::ALL {
+            let middle = side.point(&dom, 0.5);
+            let (t, dir) = if side.is_u() {
+                (middle.y, Direction::U)
+            } else {
+                (middle.x, Direction::V)
+            };
+            let iso = extract_iso_crv(form.gw_nurb().unwrap(), t, dir).unwrap();
+            let pts = iso.cpts();
+            // the parallel: every point at one height (the other side's iso is a ruling)
+            let z = |c: &CPoint| c.z / if c.w == NOW { 1.0 } else { c.w };
+            if pts.len() < 3 || pts.iter().any(|c| (z(c) - z(&pts[0])).abs() > 1e-9) {
+                continue;
+            }
+            assert!(certify_iso(&form, side, middle, &frame, Iso::Parallel).is_ok());
+            let lim = limit(&pts[1], frame.size, z(&pts[0]));
+            let w1 = if pts[1].w == NOW { 1.0 } else { pts[1].w };
+            let over = moved(&form, side, 1, 2.0 * lim / w1);
+            assert!(
+                certify_iso(&over, side, middle, &frame, Iso::Parallel).is_err(),
+                "{side:?}: twice the limit passes"
+            );
+            let under = moved(&form, side, 1, 0.5 * lim / w1);
+            assert!(
+                certify_iso(&under, side, middle, &frame, Iso::Parallel).is_ok(),
+                "{side:?}: half the limit is refused"
+            );
+            tested += 1;
+        }
+        assert!(tested > 0, "no side's iso is the parallel");
+    }
+}

solidcore/crates/solidcore/src/surface/implicit.rs

@@ -11,7 +11,6 @@
 use crate::error::{Result, SolidError};
 use crate::geom::axis2_placement::Axis2Placement;
 use crate::geom::extent2d::Extent2d;
-use crate::geom::vector2d::Point2;
 use crate::kernel::Kernel;
 use crate::math::{Vec2, Vec3, PI};
 use crate::nurbs::b_spline_curve::BSplineCurve;
@@ -69,42 +68,6 @@ pub enum Implicit {
     },
 }
 
-impl Implicit {
-    /// How far `x` is from this surface.
-    #[must_use]
-    pub fn distance(&self, x: Vec3) -> f64 {
-        // the axial and radial parts of `x` about an axis through `o`
-        let about = |o: Vec3, axis: Vec3| {
-            let v = x - o;
-            let h = v.dot(axis);
-            (h, (v - axis * h).length())
-        };
-        match *self {
-            Self::Plane { origin, normal } => (x - origin).dot(normal).abs(),
-            Self::Cone {
-                origin,
-                axis,
-                radius,
-                tan_angle,
-            } => {
-                let (h, rho) = about(origin, axis);
-                (rho - (radius + tan_angle * h)).abs() / (1.0 + tan_angle * tan_angle).sqrt()
-            }
-            Self::Sphere { centre, radius } => ((x - centre).length() - radius).abs(),
-            Self::Torus {
-                centre,
-                axis,
-                major,
-                minor,
-            } => {
-                let (h, rho) = about(centre, axis);
-                let (a, b) = (rho - major, h);
-                ((a * a + b * b).sqrt() - minor).abs()
-            }
-        }
-    }
-}
-
 /// A polynomial in Bernstein form over a patch, degrees `(p, q)`, `c[i (q + 1) + j]`.
 #[derive(Debug, Clone, PartialEq)]
 struct BPoly {
@@ -343,7 +306,7 @@ fn bezier_on<'a>(
     f.c.iter().all(within)
 }
 
-pub(crate) const OP_EXACT: &str = "surface::implicit::check_exact_net";
+const OP_EXACT: &str = "surface::implicit::check_exact_net";
 
 /// A quadric `x.A.x + 2 b.x + c = 0` as `(A, b, c)`.
 pub type QuadricEquation = ([[f64; 3]; 3], [f64; 3], f64);
@@ -439,46 +402,6 @@ pub fn check_exact_net(k: &Kernel, net: &Surface, check: &ExactNetCheck) -> Resu
     Ok(())
 }
 
-/// The number of intervals [`net_miss`] samples a net at, each way.
-const MISS_SAMPLES: u32 = 16;
-
-/// How far `net` strays from the class's `surface`, sampled over its domain. A guard, not a
-/// certificate: [`check_exact_net`] is the proof, and a net that passes only this keeps no
-/// definition. It tells a net that the class's rounding leaves off the surface from one
-/// built wrongly.
-///
-/// # Errors
-///
-/// Those of the evaluations.
-pub fn net_miss(k: &Kernel, net: &Surface, surface: &ClassSurface) -> Result<f64> {
-    let dom = net.natural_uv_domain_with_nurb(k)?;
-    let (lo, hi) = (dom.min(), dom.max());
-    let mut worst = 0.0_f64;
-    for i in 0..=MISS_SAMPLES {
-        for j in 0..=MISS_SAMPLES {
-            let (fu, fv) = (
-                f64::from(i) / f64::from(MISS_SAMPLES),
-                f64::from(j) / f64::from(MISS_SAMPLES),
-            );
-            let uv = Point2::new(lo.x + (hi.x - lo.x) * fu, lo.y + (hi.y - lo.y) * fv);
-            let x = net.evaluate_point(k, uv)?;
-            let miss = match surface {
-                ClassSurface::Implicit(a) => a.distance(x),
-                ClassSurface::Canal {
-                    spine, map, radius, ..
-                } => {
-                    let w = if map.along_v { uv.y } else { uv.x };
-                    let ivl = spine.natural_interval();
-                    let s = (map.a + map.b * w).max(ivl.min()).min(ivl.max());
-                    ((x - spine.evaluate_point(s)?).length() - *radius).abs()
-                }
-            };
-            worst = worst.max(miss);
-        }
-    }
-    Ok(worst)
-}
-
 /// A Bezier segment of a rational curve, Bernstein polynomials of degree `(p, 0)`: the
 /// homogeneous `(Y - O V)` components and the weight `V`.
 type CurveSegment = ([BPoly; 3], BPoly);
@@ -1200,12 +1123,37 @@ impl AnalyticSupport {
         // a surface of revolution: the one the kernel recognises in the form, which must be
         // this one, take the form as its NURB and evaluate as the form at the form's own
         // parameters
-        let not_form = || {
-            SolidError::invalid_input(
-                OP_BUILD,
-                "a support's analytic surface is not its NURBS form's parametrisation",
-            )
-        };
+        let surface = self.on_form(k, &form)?;
+        if !evaluates_as(k, &surface, &form)? {
+            return Err(not_form());
+        }
+        Ok(surface)
+    }
+
+    /// The largest ratio, over the form's Greville points, of this support's analytic
+    /// surface's distance from `form` to the rounding [`evaluates_as`] derives there (#3185):
+    /// at most 1 where [`Self::build`]'s parametrisation test passes. The surface is the one
+    /// `build` makes (the kernel's recognition of `form`, carrying this support's numbers);
+    /// `lies_on` and the placement's axes are not checked here. `None` for a plane, or a
+    /// surface the bound does not cover.
+    ///
+    /// # Errors
+    ///
+    /// `InvalidInput` where the kernel recognises no surface of this kind in `form`; those of
+    /// the recognisers, the conversions and the evaluations.
+    pub fn parametrisation_margin(&self, k: &Kernel, form: &BSplineSurface) -> Result<Option<f64>> {
+        if matches!(self, Self::Plane { .. }) {
+            return Ok(None);
+        }
+        let surface = self.on_form(k, form)?;
+        evaluation_margin(k, &surface, form)
+    }
+
+    /// The surface of revolution of this support's kind the kernel recognises in `form`,
+    /// carrying this support's own numbers and `form` as its NURB ([`Self::build`] after its
+    /// checks of the point set, before the parametrisation's).
+    fn on_form(&self, k: &Kernel, form: &BSplineSurface) -> Result<Surface> {
+        let form = form.copy();
         let mut surface = recognise(k, self.kind(), &form)?.ok_or_else(not_form)?;
         // the recognised surface must be of this support's kind; the numbers recognition
         // recomputed are not compared with the support's, because it recomputes them from
@@ -1255,13 +1203,18 @@ impl AnalyticSupport {
             }
             _ => return Err(not_form()),
         }
-        if !evaluates_as(k, &surface, &form)? {
-            return Err(not_form());
-        }
         Ok(surface)
     }
 }
 
+/// [`AnalyticSupport::build`]'s refusal of a surface that is not its form's parametrisation.
+fn not_form() -> SolidError {
+    SolidError::invalid_input(
+        OP_BUILD,
+        "a support's analytic surface is not its NURBS form's parametrisation",
+    )
+}
+
 /// A cylinder's or cone's recognised parametrisation carried by the support's own
 /// `placement`: its heights are measured along the axis from the placement's origin, so the
 /// recognised heights move by how far along the axis the recognised origin lies from it.
@@ -1336,41 +1289,314 @@ fn recognise(k: &Kernel, kind: SupportKind, form: &BSplineSurface) -> Result<Opt
 }
 
 /// Whether `surface` evaluates as `form` at the form's Greville parameters (each control
-/// point's), within the rounding of the two evaluations: `gamma_K` times the form's size,
-/// `K = 16 (p + q + 2)` for the rational evaluation of degrees `(p, q)` and the analytic
-/// one's conversion of the parameters and its trigonometry, a few ulps per operation.
+/// point's): at each, the analytic surface's point and the form's agree within the bound
+/// [`Rounding::at`] derives for that point, term by term below. The analytic side is the
+/// **STEP** evaluation of the converted parameters ([`Surface::convert_uv_from_nurbs_to_step`]
+/// and [`Surface::evaluate_step_point`]), which a cone, sphere, torus and surface of
+/// revolution compute from their placement, radii, semi-angle and generator.
+/// [`Surface::evaluate_point`] would not do: a sphere, a torus and a surface of revolution
+/// take it from their NURBS base, and that base is the `form` the caller has just installed,
+/// so it would compare the form with itself and read nothing of what the caller imposed
+/// (#2588).
 ///
-/// The analytic side is the **STEP** evaluation of the converted parameters
-/// ([`Surface::convert_uv_from_nurbs_to_step`] and [`Surface::evaluate_step_point`]),
-/// which a cone, sphere, torus and surface of revolution compute from their placement,
-/// radii, semi-angle and generator. [`Surface::evaluate_point`] would not do: a sphere, a
-/// torus and a surface of revolution take it from their NURBS base, and that base is the
-/// `form` the caller has just installed, so it would compare the form with itself and read
-/// nothing of what the caller imposed (#2588; the cone already converted and evaluated
-/// analytically, which is why only the other kinds went unchecked).
+/// What the bound forgives and what it tests (#3185): it forgives the rounding of both
+/// evaluations and of the two parameter conversions, nothing else. It does not forgive the
+/// label's frame turned about the axis against the converter's, its axis, origin or radii,
+/// a form whose parameter is not the analytic surface's (a reparametrised arc), nor the
+/// form's distance from the analytic surface: those are what the comparison proves.
+///
+/// `u` is the unit roundoff, `gamma_n = n u / (1 - n u)`. Stated assumption: the libm
+/// `sin`, `cos`, `tan` and `atan2` are within one ulp (relative `2 u`).
+///
+/// 1. **The form** (`Surface::eval`, Cox-de Boor then two blends): each basis value is a
+///    nonnegative combination over `p` levels of at most 6 operations (two knot differences,
+///    a sum, a division, a product and a sum), so relative `gamma_6p`; the blends sum
+///    `q + 1` then `p + 1` products. With positive weights the homogeneous point's error is
+///    at most `gamma_(7 (p + q) + 4) W size` and the weight's `gamma_(7 (p + q) + 4) W`, so
+///    the Euclidean point's, after the division, `E_form = (2 gamma_(7 (p + q) + 4) + u)
+///    size` (`gamma_(7 (p + q) + 4) size` when polynomial), `size` the net's largest point.
+/// 2. **The STEP point**, `O + m (cos u X + sin u Y) + h Z`, `m` and `h` the generator's
+///    radial and axial parts (the torus `R + r cos v`, `r sin v`; the sphere `r cos v`,
+///    `r sin v`; the cone `r0 + v tan a`, `v`). An angle `x` in degrees goes to radians in
+///    two operations of the rounded `PI`: `gamma_3 |x|`; with one ulp of the cosine and sine,
+///    each is off by `dc(x) = 2 u + gamma_3 |x|`. Per coordinate (unit axes) the error is at
+///    most `gamma_3 (|O| + M + H) + M (gamma_2 + 2 dc(u)) + dm + dh`, `M`, `H` the sizes of
+///    `m`, `h` and `dm`, `dh` their errors: the torus `gamma_3 (R + r) + 2 r dc(v)`, the
+///    sphere `gamma_1 r + 2 r dc(v)`, the cone `gamma_2 (|r0| + |v t|) + |v| dt` (`dt =
+///    (1 + t^2) gamma_3 |a| + 2 u |t|` for the tangent of the half angle `a`); a general
+///    surface of revolution rotates its generator's point `G` (a B-spline: item 1's bound of
+///    its own net, `E_gen`) about the axis, `gamma_8 (|O| + 3 D) + 2 D dc(u) + E_gen`, `D`
+///    the net's reach from `O`. `E_step` is `sqrt 3` times the coordinate bound.
+/// 3. **The generator's parameter**: a circle (torus, sphere) inverts its NURBS point by
+///    `atan2` about its centre `c`: at its radius `r` the error is that point's (`E_form`)
+///    plus `gamma_4 (size + |c|)` and `gamma_4 r |v|` of the angle's own rounding; a line
+///    (cone) maps it affinely in 6 operations, `gamma_6 2 (|v0| + |v1|)` along the axis and
+///    its slope, times `1 + |t|`; a B-spline generator's parameter is its NURBS's (none).
+/// 4. **The sweep's parameter**: the polar converter evaluates its circle's NURBS at the
+///    parameter (item 1's bound of that NURBS's own net, `E_polar`) and inverts the point by
+///    `atan2` about the circle's centre `c` in its frame: at the circle's radius `rc` the
+///    angle is off by `(E_polar + gamma_4 (rc + 2 |c|)) / rc`, plus `gamma_4 |s|` of the
+///    angle's own rounding and the degrees' period (`gamma_1 2 pi`), times the STEP point's
+///    distance from that axis (the lever). The converter's ends are its domain's, which
+///    recognition takes from the form's own end meridians (#3199), so they are the inverted
+///    ends to the same rounding.
+///
+/// A surface of another kind, or a general surface of revolution whose generator is not a
+/// B-spline, has no bound here and is not proved.
 ///
 /// # Errors
 ///
 /// Those of the parameter conversion and the evaluations and of the form's knots.
 fn evaluates_as(k: &Kernel, surface: &Surface, form: &BSplineSurface) -> Result<bool> {
+    Ok(evaluation_margin(k, surface, form)?.is_some_and(|m| m <= 1.0))
+}
+
+/// [`evaluates_as`]'s largest ratio of distance to bound over the Greville points (infinite
+/// for a distance that is not a number); `None` for a surface the bound does not cover.
+fn evaluation_margin(k: &Kernel, surface: &Surface, form: &BSplineSurface) -> Result<Option<f64>> {
     let (net, p, q) = euclidean_net(form)?;
     let size = net.iter().flatten().fold(0.0_f64, |a, x| a.max(x.length()));
-    let tol = gamma(16 * (p + q + 2)) * size;
+    let Some(r) = Rounding::of(surface, form.is_rational(), p, q, size, &net)? else {
+        return Ok(None);
+    };
+    let mut worst = 0.0_f64;
     for u in greville(form, true)? {
         for v in greville(form, false)? {
             let uv = Vec2::new(u, v);
             let step_uv = surface.convert_uv_from_nurbs_to_step(k, uv)?;
-            let off =
-                (surface.evaluate_step_point(k, step_uv)? - form.evaluate_point(uv)?).length();
-            if !matches!(
-                off.partial_cmp(&tol),
-                Some(core::cmp::Ordering::Less | core::cmp::Ordering::Equal)
-            ) {
-                return Ok(false);
-            }
+            let s = surface.evaluate_step_point(k, step_uv)?;
+            let f = form.evaluate_point(uv)?;
+            let ratio = (s - f).length() / r.at(step_uv, s, f);
+            worst = if ratio.is_nan() {
+                f64::INFINITY
+            } else {
+                worst.max(ratio)
+            };
         }
     }
-    Ok(true)
+    Ok(Some(worst))
+}
+
+/// A surface of revolution's generator, for [`Rounding`]'s item 2 and 3.
+#[derive(Debug, Clone, Copy)]
+enum Generator {
+    /// `R + r cos v`, `r sin v` about the circle of centre `c`.
+    Torus { major: f64, minor: f64, c: f64 },
+    /// `r cos v`, `r sin v` about the circle of centre `c`.
+    Sphere { radius: f64, c: f64 },
+    /// `r0 + v t`, `v` (the half angle `a` in radians), its STEP `v` over `[v0, v1]`.
+    Cone {
+        r0: f64,
+        t: f64,
+        a: f64,
+        v0: f64,
+        v1: f64,
+    },
+    /// A B-spline generator, its own evaluation's bound.
+    Spline { e_gen: f64 },
+}
+
+/// The pieces of [`evaluates_as`]'s bound that do not depend on the point.
+#[derive(Debug, Clone, Copy)]
+struct Rounding {
+    e_form: f64,
+    origin: Vec3,
+    /// The net's reach from the origin.
+    reach: f64,
+    generator: Generator,
+    /// The sweep converter's circle: centre, axes.
+    polar: (Vec3, Vec3, Vec3, f64, f64),
+}
+
+/// `|v|`'s largest coordinate.
+fn max_coord(v: Vec3) -> f64 {
+    v.x.abs().max(v.y.abs()).max(v.z.abs())
+}
+
+/// A rational (or polynomial) evaluation's bound of degrees summing to `n` over points of
+/// size `size` ([`evaluates_as`] item 1).
+fn eval_bound(rational: bool, n: usize, size: f64) -> f64 {
+    let g = gamma(7 * n + 4);
+    if rational {
+        (2.0 * g + crate::nurbs::math::UNIT) * size
+    } else {
+        g * size
+    }
+}
+
+impl Rounding {
+    /// The bound's data for `surface` (a cone, sphere, torus or surface of revolution with a
+    /// B-spline generator) on its form of degrees `(p, q)`, net `net`; `None` for any other.
+    fn of(
+        surface: &Surface,
+        rational: bool,
+        p: usize,
+        q: usize,
+        size: f64,
+        net: &[Vec<Vec3>],
+    ) -> Result<Option<Self>> {
+        use crate::curve::curve::CurveKind;
+        let e_form = eval_bound(rational, p + q, size);
+        let circle_centre = |rev: &crate::surface::surf_of_revolution::SurfOfRevolution| match rev
+            .gen_curve
+            .as_ref()
+            .map(crate::curve::curve::Curve::kind)
+        {
+            Some(CurveKind::Ellipse(e)) => Some(e.position.origin().length()),
+            _ => None,
+        };
+        let (rev, generator) = match surface.kind() {
+            SurfaceKind::Torus(t) => {
+                let Some(c) = circle_centre(&t.base) else {
+                    return Ok(None);
+                };
+                (
+                    &t.base,
+                    Generator::Torus {
+                        major: t.major_radius,
+                        minor: t.minor_radius,
+                        c,
+                    },
+                )
+            }
+            SurfaceKind::Sphere(sp) => {
+                let Some(c) = circle_centre(&sp.base) else {
+                    return Ok(None);
+                };
+                (
+                    &sp.base,
+                    Generator::Sphere {
+                        radius: sp.radius,
+                        c,
+                    },
+                )
+            }
+            SurfaceKind::Cone(c) => {
+                let a = c.semi_angle_deg * PI / 180.0;
+                let d = c.rev.anal_uv_domain;
+                (
+                    &c.rev,
+                    Generator::Cone {
+                        r0: c.base_radius,
+                        t: c.tan_semi_angle(),
+                        a,
+                        v0: d.v_min(),
+                        v1: d.v_max(),
+                    },
+                )
+            }
+            SurfaceKind::SurfOfRevolution(rev) => {
+                let Some(CurveKind::BSpline(g)) =
+                    rev.gen_curve.as_ref().map(crate::curve::curve::Curve::kind)
+                else {
+                    return Ok(None);
+                };
+                let pts = g.control_points()?;
+                let gsize = pts.iter().fold(0.0_f64, |m, c| {
+                    let w = if c.w == NOW { 1.0 } else { c.w };
+                    m.max((Vec3::new(c.x, c.y, c.z) * (1.0 / w)).length())
+                });
+                let rational = pts.iter().any(|c| c.w != NOW);
+                (
+                    &**rev,
+                    Generator::Spline {
+                        e_gen: eval_bound(rational, g.degree()?, gsize),
+                    },
+                )
+            }
+            _ => return Ok(None),
+        };
+        let Some(pc) = rev.polar_curve() else {
+            return Ok(None);
+        };
+        let e_polar = {
+            let pts = pc.base().control_points()?;
+            let psize = pts.iter().fold(0.0_f64, |m, c| {
+                let w = if c.w == NOW { 1.0 } else { c.w };
+                m.max((Vec3::new(c.x, c.y, c.z) * (1.0 / w)).length())
+            });
+            eval_bound(pts.iter().any(|c| c.w != NOW), pc.base().degree()?, psize)
+        };
+        let origin = rev.position.origin();
+        let reach = net
+            .iter()
+            .flatten()
+            .fold(0.0_f64, |m, x| m.max((*x - origin).length()));
+        Ok(Some(Self {
+            e_form,
+            origin,
+            reach,
+            generator,
+            polar: (
+                pc.position.origin(),
+                pc.position.x_axis(),
+                pc.position.y_axis(),
+                pc.radius_x,
+                e_polar,
+            ),
+        }))
+    }
+
+    /// The bound at the STEP parameters `step` (degrees, and the generator's), the STEP
+    /// point `s` and the form's point `f` ([`evaluates_as`] items 1 to 4).
+    fn at(&self, step: Vec2, s: Vec3, f: Vec3) -> f64 {
+        let u = crate::nurbs::math::UNIT;
+        let rad = |deg: f64| deg * PI / 180.0;
+        let dc = |deg: f64| 2.0 * u + gamma(3) * rad(deg).abs();
+        let o = max_coord(self.origin);
+        let size_f = f.length();
+        // item 2 (per coordinate) and item 3 (as a length)
+        let (coord, generator) = match self.generator {
+            Generator::Torus { major, minor, c } => {
+                let (m, h) = (major + minor, minor);
+                let dm = gamma(3) * (major + minor) + 2.0 * minor * dc(step.y);
+                let dh = gamma(1) * minor + 2.0 * minor * dc(step.y);
+                (
+                    gamma(3) * (o + m + h) + m * (gamma(2) + 2.0 * dc(step.x)) + dm + dh,
+                    self.e_form + gamma(4) * (size_f + c) + gamma(4) * minor * rad(step.y).abs(),
+                )
+            }
+            Generator::Sphere { radius, c } => {
+                let dm = gamma(1) * radius + 2.0 * radius * dc(step.y);
+                (
+                    gamma(3) * (o + 2.0 * radius)
+                        + radius * (gamma(2) + 2.0 * dc(step.x))
+                        + 2.0 * dm,
+                    self.e_form + gamma(4) * (size_f + c) + gamma(4) * radius * rad(step.y).abs(),
+                )
+            }
+            Generator::Cone { r0, t, a, v0, v1 } => {
+                let v = step.y;
+                let m = r0.abs() + (v * t).abs();
+                let dt = (1.0 + t * t) * gamma(3) * a.abs() + 2.0 * u * t.abs();
+                let dm = gamma(2) * m + v.abs() * dt;
+                (
+                    gamma(3) * (o + m + v.abs()) + m * (gamma(2) + 2.0 * dc(step.x)) + dm,
+                    gamma(6) * 2.0 * (v0.abs() + v1.abs()) * (1.0 + t.abs()),
+                )
+            }
+            Generator::Spline { e_gen } => (
+                gamma(8) * (o + 3.0 * self.reach) + 2.0 * self.reach * dc(step.x) + e_gen,
+                0.0,
+            ),
+        };
+        let e_step = 3.0_f64.sqrt() * coord;
+        // item 4: the polar converter's inversion of its own circle's point
+        let (c, x, y, rc, e_polar) = self.polar;
+        let z = x.cross(y);
+        let along = |v: Vec3| v - z * v.dot(z);
+        let lever = along(s - c).length();
+        let sweep = if rc > 0.0 {
+            lever
+                * ((e_polar + gamma(4) * (rc + 2.0 * c.length())) / rc
+                    + gamma(4) * rad(step.x).abs()
+                    + gamma(1) * 2.0 * PI)
+        } else {
+            // a circle of no radius has no angle: any, at the STEP point's lever
+            lever * PI
+        };
+        self.e_form + e_step + generator + sweep
+    }
 }
 
 const OP_DERIVE: &str = "surface::implicit::AnalyticSupport::derive";

solidcore/crates/solidcore/src/surface/procedural_blend/exact.rs

@@ -39,11 +39,62 @@ use crate::geom::vector3d::{Point3, Vec3};
 use crate::kernel::Kernel;
 use crate::math::EFF_ZERO;
 use crate::nurbs::b_spline_curve::BSplineCurve;
-use crate::surface::implicit::{check_exact_net, net_miss, ClassSurface, ExactNetCheck, LeaderMap};
+use crate::surface::implicit::{
+    check_exact_net, lies_on, AnalyticSupport, ClassSurface, ExactNetCheck, Implicit, LeaderMap,
+};
 use crate::surface::procedural_blend::chamfer::ChamferDefinition;
 use crate::surface::surface::Surface;
 
 const OP_TRANSFORM: &str = "surface::procedural_blend::exact::ExactRound::transform";
+const OP_CIRCLE: &str = "surface::procedural_blend::exact::ExactRound::supports_distance";
+
+/// The torus a round of the circle class is: a surface of revolution's, about its
+/// placement's axis, of the circle its generating arc is on (the centre of a rational quadratic
+/// arc from its first span's control points: the midpoint of the chord pushed away from the
+/// middle point by `a^2 / h`, `a` the half chord, `h` the middle point's distance from the
+/// chord's midpoint); or a torus label's own. `None` for any other surface.
+///
+/// # Errors
+///
+/// Those of reading the arc's control polygon.
+fn own_torus(net: &Surface) -> Result<Option<Implicit>> {
+    use crate::curve::curve::{Curve, CurveKind};
+    use crate::surface::surface::SurfaceKind;
+    match net.kind() {
+        SurfaceKind::Torus(_) => Ok(AnalyticSupport::of(net)
+            .as_ref()
+            .map(AnalyticSupport::implicit)),
+        SurfaceKind::SurfOfRevolution(rev) => {
+            let Some(CurveKind::BSpline(arc)) = rev.gen_curve().map(Curve::kind) else {
+                return Ok(None);
+            };
+            let (points, _) = arc.control_polygon()?;
+            let [p0, p1, p2, ..] = points.as_slice() else {
+                return Ok(None);
+            };
+            let mid = (*p0 + *p2) * 0.5;
+            let (a, h) = ((*p0 - mid).length(), (mid - *p1).length());
+            if h.partial_cmp(&0.0) != Some(core::cmp::Ordering::Greater) {
+                return Ok(None);
+            }
+            let centre = mid + (mid - *p1) * (a * a / (h * h));
+            let position = rev.position();
+            let (o, axis) = (
+                position.origin(),
+                position.x_axis().cross(position.y_axis()),
+            );
+            let along = (centre - o).dot(axis);
+            let across = (centre - o) - axis * along;
+            Ok(Some(Implicit::Torus {
+                centre: o + axis * along,
+                axis,
+                major: across.length(),
+                minor: (*p0 - centre).length(),
+            }))
+        }
+        _ => Ok(None),
+    }
+}
 
 /// The exact class of a round whose net is its definition.
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
@@ -263,7 +314,8 @@ impl ExactRound {
 
     /// Re-certifies `net` against this definition: the supports classified again are of
     /// this class, and the net lies on the class's surface derived from them
-    /// ([`check_exact_net`]). Returns the distance proved, 0.
+    /// ([`check_exact_net`]). A round of the circle class is certified on its own torus
+    /// instead ([`ExactRound::supports_distance`]). Returns the distance proved, 0.
     ///
     /// # Errors
     ///
@@ -271,6 +323,10 @@ impl ExactRound {
     /// surface from them, a net off it; those of reading the supports' quadrics and the
     /// net's NURBS form.
     pub fn recertify(&self, k: &Kernel, net: &Surface) -> Result<f64> {
+        if self.class == ExactClass::Circle {
+            self.supports_distance(k, net)?;
+            return Ok(0.0);
+        }
         let [a, b] = &self.supports;
         let blend = classify_supports(k, [a, b], &self.inputs)?;
         // the chord (#2486): a line spine between planes, of sizes that give its offsets
@@ -302,19 +358,72 @@ impl ExactRound {
         Ok(0.0)
     }
 
-    /// How far `net` strays from the surface of the class its supports give
-    /// ([`net_miss`]); `None` where they give it none.
+    /// A round of the circle class: the torus `net` is ([`own_torus`]: its revolution's
+    /// axis and generating circle, or its torus label), proved to hold its form to rounding
+    /// ([`lies_on`]),
+    /// and how far that torus is from the class's torus derived from the supports
+    /// ([`class_surface`]): returned, refused past the tolerance the class was read within.
+    ///
+    /// The class is read within the body's tolerance. Supports only that close to it (a plane
+    /// 1e-13 off square to a cylinder's axis, read from a record) have no torus touching both
+    /// exactly, so the round the solver builds, tangent to the supports as they are, is on a
+    /// torus of its own. Its definition is that torus, at bound 0, a stated distance from the
+    /// supports' class.
     ///
     /// # Errors
     ///
-    /// Those of reading the supports' quadrics and of the evaluations.
-    pub fn miss(&self, k: &Kernel, net: &Surface) -> Result<Option<f64>> {
+    /// `InvalidInput` for supports of another class or with no torus, a net of no torus, a
+    /// net off its torus, or a torus further from the class's than the tolerance; those of
+    /// reading the supports' quadrics, the net's NURBS form and [`lies_on`].
+    pub fn supports_distance(&self, k: &Kernel, net: &Surface) -> Result<f64> {
+        let refused = |why| SolidError::invalid_input(OP_CIRCLE, why);
         let [a, b] = &self.supports;
         let blend = classify_supports(k, [a, b], &self.inputs)?;
-        match class_surface(&blend, self.leader.as_ref(), &self.map) {
-            Some(surface) => net_miss(k, net, &surface).map(Some),
-            None => Ok(None),
+        if ExactClass::of_spine(blend.spine) != Some(ExactClass::Circle) {
+            return Err(refused(
+                "the supports classified again are not of the class the definition names",
+            ));
         }
+        let Some(ClassSurface::Implicit(Implicit::Torus {
+            centre,
+            axis,
+            major,
+            minor,
+        })) = class_surface(&blend, self.leader.as_ref(), &self.map)
+        else {
+            return Err(refused("the supports give the class no torus"));
+        };
+        let form = crate::blend::fillet_section::station::as_b_spline(k, net)?
+            .ok_or_else(|| refused("the net has no NURBS form to check"))?;
+        let own = own_torus(net)?.ok_or_else(|| refused("the net is no torus"))?;
+        if !lies_on(&form, &own)? {
+            return Err(refused("the net is off its own torus"));
+        }
+        let Implicit::Torus {
+            centre: c,
+            axis: d,
+            major: big_r,
+            minor: r,
+        } = own
+        else {
+            return Err(refused("the net's own surface is no torus"));
+        };
+        // every point of the net's torus moves to the class's torus by at most: the turn of
+        // its axis (an angle, over the torus's reach from its centre), the move of its
+        // centre, and the change of its radii
+        let turn = d.cross(axis).length().atan2(d.dot(axis).abs());
+        let distance =
+            turn * (big_r + r) + (c - centre).length() + (big_r - major).abs() + (r - minor).abs();
+        let within = matches!(
+            distance.partial_cmp(&self.inputs.tol),
+            Some(core::cmp::Ordering::Less | core::cmp::Ordering::Equal)
+        );
+        if !within {
+            return Err(refused(
+                "the net's torus is further from the class's than the tolerance",
+            ));
+        }
+        Ok(distance)
     }
 
     /// Moves the definition with its net (`Transform`): the supports, the leader and the

solidcore/crates/solidcore/src/surface/sphere.rs

@@ -110,6 +110,12 @@
 //!   WR-493, the SolidCraft fork's tangency-labs/smlib@7ea6a96): `IsNurbSurfaceSphere`
 //!   tests the half meridian within `180 + 360 * SM_EFF_ZERO` degrees and the sphere it
 //!   finds keeps the tested NURB (`SetFromGwNurb`). Off by default (upstream).
+//! - **Far spheres** (#3131, by default): `IsNurbSurfaceSphere` and
+//!   `RebuildSTEPFromNURBParameters` add to their fixed half-meridian tolerances, and
+//!   `IsNurbSurfaceSphere` to its generator's STEP interval test, the angles' rounding at
+//!   the points' size ([`meridian_rounding`]): upstream's fixed degrees refused a sphere of
+//!   radius 2.5 at 1e5 (180 + 6.7e-10 degrees). Near the origin the default half-meridian
+//!   test widens from `1e-12` to about `1e-12 + 8e-12` degrees for radius 2.5.
 //! - **Parent calls.** `Transform` finishes in `SmSurfOfRevolution::Transform` (status
 //!   ignored), its polar-converter rebuild given the sphere's iso circles as upstream's
 //!   virtual call does; `ReadFromDB` reads the parent record with
@@ -133,12 +139,15 @@ use crate::geom::tol::{are_same, are_same_to_tol, is_zero};
 use crate::geom::vector2d::Point2;
 use crate::geom::vector3d::{asin, sqrt, Point3, Vec3};
 use crate::kernel::Kernel;
-use crate::math::{max2, min2, EFF_ZERO, EFF_ZERO_PARAM, EFF_ZERO_SQRT, PI, UNDEF_DOUBLE};
+use crate::math::{
+    max2, min2, rad_to_deg, EFF_ZERO, EFF_ZERO_PARAM, EFF_ZERO_SQRT, PI, UNDEF_DOUBLE,
+};
 use crate::nurbs::b_spline_curve::BSplineCurve;
 use crate::nurbs::b_spline_surface::p2::EditNotify;
 use crate::nurbs::b_spline_surface::{
     BSplineSurface, BoundingBoxRequest, IsoCurveOptions, LocationType, SurfParamType,
 };
+use crate::nurbs::math::gamma;
 use crate::nurbs::nurbs_crv::to_euclid;
 use crate::nurbs::nurbs_srf::copy_nurb_surface;
 use crate::surface::cone::Cone;
@@ -2029,7 +2038,11 @@ impl Sphere {
     /// (WR-493) the half turn is tested within `180 + 360 * SM_EFF_ZERO` degrees and the
     /// sphere then keeps a copy of `test`'s NURB, its analytic data rebuilt from it
     /// (`SetFromGwNurb`); by default `180 + SM_EFF_ZERO` and the NURB made from the
-    /// fitted circles, as upstream.
+    /// fitted circles, as upstream. Not upstream: in both modes the half-meridian test, and
+    /// the test of the generator's STEP interval against the sphere's (within `SM_EFF_ZERO`
+    /// upstream), also allow the angles' rounding at the points' size,
+    /// [`meridian_rounding`] of the corner points' size and the circle's radius: `4
+    /// gamma_K (1 + |corners| + 2 r) / r` radians (#3131).
     ///
     /// # Errors
     ///
@@ -2109,14 +2122,18 @@ impl Sphere {
         } else {
             EFF_ZERO
         };
+        // not upstream: the angles' rounding at the points' size (`meridian_rounding`)
+        let corners = min_pnt.max_dimension().max(max_pnt.max_dimension());
+        let (p, q) = (test.degree(SurfParamType::U), test.degree(SurfParamType::V));
+        let rounding = |radius: Option<f64>| meridian_rounding(p, q, corners, radius);
         let is_sphere_with_swap_uv = iso_u.parallel_planes
             && !iso_u.same_plane // [ 080625 ]
             && iso_v.coaxial_centers
-            && angles_v.length() <= 180.0 + half_meridian_tol;
+            && angles_v.length() <= 180.0 + half_meridian_tol + rounding(iso_v.radius);
         let is_sphere_no_swap_uv = iso_v.parallel_planes
             && !iso_v.same_plane // [ 080625 ]
             && iso_u.coaxial_centers
-            && angles_u.length() <= 180.0 + half_meridian_tol;
+            && angles_u.length() <= 180.0 + half_meridian_tol + rounding(iso_u.radius);
 
         // quit when not a properly oriented sphere
         if !is_sphere_with_swap_uv && !is_sphere_no_swap_uv {
@@ -2224,9 +2241,10 @@ impl Sphere {
         // If pCircle's STEP interval does not match the v-interval of sAnalUVDomain,
         // then the Sphere constructor will complain and the resulting bad surface can
         // lead to crashes.  [B414]
+        // (not upstream: its angles to the same rounding as the half meridian's)
         if !circle
             .step_interval()
-            .are_equal(&anal_uv_domain.v_interval(), EFF_ZERO)
+            .are_equal(&anal_uv_domain.v_interval(), EFF_ZERO + rounding(Some(rad)))
         {
             // upstream: WARN("Bad result in IsNurbSurfaceSphere(): GenCurve STEP
             // interval does not match sAnalUVDomain VInterval")
@@ -2333,16 +2351,23 @@ impl Sphere {
 
         // see if we have a U or a V oriented sphere
         // Tol: compensate for using degrees.  [B279]
+        // (not upstream: and the angles' rounding at the points' size, `meridian_rounding`)
+        let corners = nurb_min_point
+            .max_dimension()
+            .max(nurb_max_point.max_dimension());
+        let (p, q) = (srf.degree(SurfParamType::U), srf.degree(SurfParamType::V));
         let angles_u = iso_u.angles.unwrap_or(Extent1d::new());
         let angles_v = iso_v.angles.unwrap_or(Extent1d::new());
         let is_sphere_with_swap_uv = iso_u.parallel_planes
             && !iso_v.same_plane // [ 080625 ]
             && iso_v.coaxial_centers
-            && angles_v.length() <= 180.0 + 360.0 * EFF_ZERO;
+            && angles_v.length()
+                <= 180.0 + 360.0 * EFF_ZERO + meridian_rounding(p, q, corners, iso_v.radius);
         let is_sphere_no_swap_uv = iso_v.parallel_planes
             && !iso_v.same_plane // [ 080625 ]
             && iso_u.coaxial_centers
-            && angles_u.length() <= 180.0 + 360.0 * EFF_ZERO;
+            && angles_u.length()
+                <= 180.0 + 360.0 * EFF_ZERO + meridian_rounding(p, q, corners, iso_u.radius);
 
         // quit when not a properly oriented sphere
         if !is_sphere_with_swap_uv && !is_sphere_no_swap_uv {
@@ -2985,6 +3010,34 @@ fn convert_uv_from_nurbs_to_step(
     Ok(Point2::new(step_x, polar_param))
 }
 
+/// Not upstream: the rounding, in degrees, of the length of the half meridian (or of a
+/// circle's STEP interval) that [`Sphere::is_nurb_surface_sphere`] and
+/// [`Sphere::rebuild_step_from_nurb_parameters`] read off a form of degrees `(p, q)` whose
+/// corner points are at most `corners` from the origin, its circle of radius `radius`; 0
+/// without a radius.
+///
+/// The angles are read off points of the form: an evaluation is within `gamma_K |P|` of
+/// the exact point (`K = 16 (p + q + 2)`, a few ulps for each of the rational evaluation's
+/// operations), `|P| <= 1 + corners + 2 r` (a point of the sphere is at most its
+/// diameter from a corner). The circle's centre is fitted to such points; its error is taken
+/// to be the same again, which is measured, not derived (the fit's conditioning is not
+/// bounded here: `far_sphere_recognised.rs` measures the excess over this allowance on
+/// spheres of radius 1e-3 to 1e3, at 0 to 1e7 from the origin, turned off the axes: at most
+/// 0.0055 of this allowance). An
+/// angle at radius `r` is then known to `2 gamma_K |P| / r` radians at each end, and the half
+/// turn's length to twice that: `4 gamma_K |P| / r`. As a position, `r` times that is
+/// `4 gamma_K |P|`, below the iso-circle tests' `100 SM_EFF_ZERO (1 + |corners|)` for every
+/// size, so it admits no form those tests refuse.
+pub(crate) fn meridian_rounding(p: usize, q: usize, corners: f64, radius: Option<f64>) -> f64 {
+    match radius {
+        Some(r) if r > 0.0 => {
+            let size = 1.0 + corners + 2.0 * r;
+            rad_to_deg(4.0 * gamma(16 * (p + q + 2)) * size / r)
+        }
+        _ => 0.0,
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -3001,6 +3054,18 @@ mod tests {
         Sphere::create_canonical(k, &frame(), radius).expect("sphere")
     }
 
+    /// `meridian_rounding` for radius 2.5 against numbers recomputed independently of it:
+    /// 1.8e-11 degrees with corners at 12.5 (the origin) and 9.77e-8 degrees with corners at
+    /// 100012.5 (1e5 out), so a doubled or halved allowance fails here (#3131).
+    #[test]
+    fn the_meridian_allowance_is_its_closed_form() {
+        for (corners, degrees) in [(12.5, 1.8e-11), (100_012.5, 9.77e-8)] {
+            let got = meridian_rounding(2, 2, corners, Some(2.5));
+            assert!((got / degrees - 1.0).abs() < 0.02, "{corners}: {got:e}");
+        }
+        assert_eq!(meridian_rounding(2, 2, 1.0, None), 0.0);
+    }
+
     #[test]
     fn trim_with_domain_keeps_the_shape() {
         let k = Kernel::default();

solidcore/crates/solidcore/src/surface/torus.rs

@@ -1061,7 +1061,6 @@ impl Torus {
         let ref_frame = ref_iso.reference_frame.ok_or_else(missing)?;
         let other_frame = other_iso.reference_frame.ok_or_else(missing)?;
         let min_rad = other_iso.radius.ok_or_else(missing)?;
-        let sweep_ivl = ref_iso.angles.ok_or_else(missing)?;
         let common_point = other_iso.common_line_point.ok_or_else(missing)?;
         let common_vec = other_iso.common_line_vec.ok_or_else(missing)?;
 
@@ -1069,6 +1068,17 @@ impl Torus {
         let torus_origin =
             common_point + common_vec.dot(other_frame.origin() - common_point) * common_vec;
 
+        // not upstream (#3199): the x axis and the sweep interval from the form's own first
+        // sweep row's ends about the axis (`sweep_frame`), not from `is_arc`'s fit of it
+        let Some((torus_x_axis, torus_y_axis, sweep_ivl)) = sweep_frame(
+            torus_origin,
+            ref_frame.z_axis(),
+            fitted_sides(&ref_frame, ref_iso.angles.ok_or_else(missing)?),
+            meridians(test, swap_uv)?,
+        ) else {
+            return Ok(None);
+        };
+
         // get torus orientation and size
         // not upstream (WR-501, #1470, opt-in; tangency-labs/smlib@6136a04): the major
         // radius runs from the torus origin, not from the first sweep circle's centre,
@@ -1079,9 +1089,7 @@ impl Torus {
             other_frame.origin() - ref_frame.origin()
         };
         let maj_rad = major_vec.length();
-        let torus_x_axis = ref_frame.x_axis(); // the frame where all circles are parallel
-        let torus_y_axis = ref_frame.y_axis();
-        let torus_z_axis = ref_frame.z_axis();
+        let torus_z_axis = ref_frame.z_axis(); // the frame where all circles are parallel
 
         // torus must have positive radii
         if min_rad <= EFF_ZERO || maj_rad <= EFF_ZERO {
@@ -1294,7 +1302,6 @@ impl Torus {
         let mut ref_frame = ref_iso.reference_frame.ok_or_else(missing)?;
         let other_frame = other_iso.reference_frame.ok_or_else(missing)?;
         let min_rad = other_iso.radius.ok_or_else(missing)?;
-        let sweep_ivl = ref_iso.angles.ok_or_else(missing)?;
         let common_point = other_iso.common_line_point.ok_or_else(missing)?;
         let common_vec = other_iso.common_line_vec.ok_or_else(missing)?;
 
@@ -1302,8 +1309,18 @@ impl Torus {
         let torus_origin =
             common_point + common_vec.dot(other_frame.origin() - common_point) * common_vec;
 
+        // not upstream (#3199): the x axis and the sweep interval from the form's own first
+        // sweep row's ends about the axis (`sweep_frame`), not from `is_arc`'s fit of it
+        let (x_axis, y_axis, sweep_ivl) = sweep_frame(
+            torus_origin,
+            ref_frame.z_axis(),
+            fitted_sides(&ref_frame, ref_iso.angles.ok_or_else(missing)?),
+            meridians(srf, swap_uv)?,
+        )
+        .ok_or_else(|| SolidError::sm_err(OP_REBUILD))?;
+
         // Install the origin into pRefFrame.  // [B328]
-        let _ = ref_frame.set_canonical(torus_origin, ref_frame.x_axis(), ref_frame.y_axis());
+        let _ = ref_frame.set_canonical(torus_origin, x_axis, y_axis);
 
         // get torus orientation and size
         let major_vec = other_frame.origin() - ref_frame.origin();
@@ -1587,6 +1604,82 @@ impl Revolved for Torus {
 
 /// `SmTorus::CreateIsoParametricCurve` of the surface of revolution `rev` of a torus
 /// of `shape` (also called from the base class's rebuilds, where it is virtual).
+/// The control points, Euclidean, of the form's first and last meridians: the columns of its
+/// net at the sweep's two ends (the sweep is along u, or along v with `swap_uv`). A clamped
+/// end's column is that boundary curve's own control polygon, and a meridian lies in a plane
+/// through the axis, so every one of its control points has the meridian's angle about the
+/// axis.
+fn meridians(srf: &BSplineSurface, swap_uv: bool) -> Result<[Vec<Point3>; 2]> {
+    let nurb = srf
+        .gw_nurb()
+        .ok_or_else(|| SolidError::null_pointer(OP_NURB_TORUS))?;
+    let (n, m) = (nurb.n(), nurb.m());
+    let column = |end: bool| -> Result<Vec<Point3>> {
+        if swap_uv {
+            let j = if end { m } else { 0 };
+            (0..=n).map(|i| Ok(nurb.cpt(i, j)?.to_euclid())).collect()
+        } else {
+            let i = if end { n } else { 0 };
+            (0..=m).map(|j| Ok(nurb.cpt(i, j)?.to_euclid())).collect()
+        }
+    };
+    Ok([column(false)?, column(true)?])
+}
+
+/// The directions, about the axis, of the fitted first sweep row's ends (`is_arc`'s frame and
+/// angles): [`sweep_frame`] reads only their sides from them.
+fn fitted_sides(frame: &Axis2Placement, angles: Extent1d) -> [Vec3; 2] {
+    let at = |deg: f64| {
+        let a = deg * PI / 180.0;
+        a.cos() * frame.x_axis() + a.sin() * frame.y_axis()
+    };
+    [at(angles.min()), at(angles.max())]
+}
+
+/// Not upstream (#3199): a recognised torus's x axis, y axis and sweep interval (degrees) from
+/// its form's first and last meridians (`meridians`: their control points, exact data), about
+/// the axis through `origin` along the unit `z`. A meridian lies in a plane through the axis,
+/// so its control points share its angle on the side the tube's centre is on, and the
+/// opposite angle past the axis (a spindle torus's tube crosses it); `sides` (the fitted
+/// row's end directions, [`fitted_sides`]) says which side that is, and nothing else. Each
+/// meridian's angle is read at its control point farthest from the axis on that side: x is
+/// the first meridian's direction square to the axis (so the interval starts at 0), y `z x
+/// x`, and the interval's end the last meridian's angle from x about z (`atan2` in that
+/// frame), a closed sweep (within `SM_EFF_ZERO_SQRT` of 0) at 360, as `is_arc` maps its end.
+/// `is_arc` fitted the first sweep row's circle through three samples, so on a short arc its
+/// centre, and with it the x axis and the end angle, was off the axis by its conditioning
+/// (1e-14 rad on #3185's grooves); the converter centres the sweep circle on the axis, so its
+/// ends and its inside now agree to rounding. `None` when a meridian has no control point off
+/// the axis on its side.
+fn sweep_frame(
+    origin: Point3,
+    z: Vec3,
+    sides: [Vec3; 2],
+    [first, last]: [Vec<Point3>; 2],
+) -> Option<(Vec3, Vec3, Extent1d)> {
+    let radial = |p: &Point3| {
+        let s = *p - origin;
+        s - s.dot(z) * z
+    };
+    let farthest = |ps: &[Point3], side: Vec3| {
+        ps.iter()
+            .map(radial)
+            .filter(|r| r.dot(side) > 0.0)
+            .max_by(|a, b| a.length().total_cmp(&b.length()))
+    };
+    let [first_side, last_side] = sides;
+    let x = farthest(&first, first_side)?.unitize().ok()?;
+    let y = z.cross(x);
+    let e = farthest(&last, last_side)?;
+    let mut end_deg = e.dot(y).atan2(e.dot(x)) * 180.0 / PI;
+    if end_deg.abs() < EFF_ZERO_SQRT {
+        end_deg = 360.0;
+    } else if end_deg < 0.0 {
+        end_deg += 360.0;
+    }
+    Some((x, y, Extent1d::from_min_max(0.0, end_deg)))
+}
+
 fn iso_curve(
     rev: &SurfOfRevolution,
     shape: Shape,

solidcore/crates/solidcore/src/surface/volume/p2.rs

@@ -1623,10 +1623,15 @@ pub(crate) fn ignore_read<T>(r: Result<T>) -> Result<Option<T>> {
             | SolidError::Cancelled { .. }
             | SolidError::Unsupported { .. }),
         ) => Err(e),
-        Err(
-            e
-            @ (SolidError::InvalidInput { reason, .. } | SolidError::PortInvariant { reason, .. }),
-        ) if reason == NESTING_LIMIT_REASON => Err(e),
+        Err(e)
+            if matches!(
+                &e,
+                SolidError::InvalidInput { reason, .. } | SolidError::PortInvariant { reason, .. }
+                    if *reason == NESTING_LIMIT_REASON
+            ) =>
+        {
+            Err(e)
+        }
         Err(_) => Ok(None),
     }
 }

solidcore/crates/solidcore/src/sweep.rs

@@ -12,6 +12,7 @@ pub mod directed;
 pub mod extrude;
 pub mod rotational_sweep_geometry;
 pub mod screw;
+pub mod section_blend;
 pub mod segments;
 pub mod topology_sweep;
 pub mod trans_sweep_geometry;

solidcore/crates/solidcore/src/sweep/section_blend.rs

@@ -0,0 +1,554 @@
+//! A multi-section blend: one B-spline surface through ordered cross-sections that leaves the
+//! first and the last of them with the continuity their frames ask for.
+//!
+//! Upstream: none (not in SMLib). SolidCraft's `loft_blend` (`crates/kernel/src/loft_blend.rs`
+//! at 52afe21) and the Hermite rows of its `bridge::section`, moved into the kernel so no
+//! application builds the surface.
+//!
+//! | Rust               | Upstream |
+//! |--------------------|----------|
+//! | [`section_blend`]  | (none; SolidCraft's `loft_blend`) |
+//! | [`SectionFrame`]   | (none; SolidCraft's `bridge::Frame`) |
+//! | [`EndOrder`]       | (none; SolidCraft's `Continuity`) |
+//! | `end_rows` (crate) | (none; the rows of SolidCraft's `bridge::section`) |
+//! | `third_derivative` (crate) | (none; SolidCraft's `bridge::third_derivative`) |
+//!
+//! **The surface.** The sections run along u, each sampled at the same stations along v. Section
+//! `i` sits at `u = i / (n - 1)` and the surface passes through every station of it: each
+//! control row is interpolated through its stations along v (degree `min(3, stations - 1)`, the
+//! kernel's global interpolation at uniform parameters with averaged knots). Along u the knots are
+//! clamped and repeated `degree` times at every interior section, so every span is one Bezier.
+//! A span's end rows are the Hermite rows (`end_rows`) of its two sections: position, then
+//! tangent, curvature and change of curvature as the section holds them, written as the Bezier's
+//! leading control rows at the span's parameter interval. The u degree is the largest
+//! `c + c' - 1` over the spans (`c`, `c'` the conditions at its two ends); a span with fewer is
+//! degree-elevated exactly (by its own row elevation: the rows are vectors of points before any
+//! surface exists, so the kernel's surface and single-curve elevations do not fit them).
+//!
+//! **What each section holds (the definition, SolidCraft's).**
+//! - The first and the last section hold what their [`EndOrder`] asks (G0 to G3) from the
+//!   caller's frames: the tangent `leave * speed`, the curvature `bend * speed^2` and the change
+//!   of curvature from `bend_change` (`third_derivative`: only its part square to the tangent
+//!   holds the condition, the rest a reparametrisation). The speed is the station's chord to the
+//!   neighbouring section `c`, over 3, times `1 + crown`, over the span's interval `1 / (n - 1)`:
+//!   `d_u = leave * c / 3 * (1 + crown) * (n - 1)` for `n` sections, so the Bezier's first control
+//!   offset is `c (1 + crown) / (3 m)` at span degree `m`. The last section's frames point back
+//!   into the blend, so its odd derivatives turn round.
+//! - An interior section holds its position and the run's derivatives from finite differences of
+//!   the neighbouring sections' stations: the central first and second differences, and a third
+//!   (central, or one-sided at the second and the last-but-one section) where four sections
+//!   reach. So the joint is C3 in u with four or more sections and C2 with three, at every
+//!   station.
+//!
+//! This is SolidCraft's definition of the blend, not an approximation of another surface: the
+//! finite differences are the conditions the surface is built to, not estimates of a curve the
+//! sections lie on, and no error against anything is claimed. What is exact: the surface passes
+//! through every station; at every station of an end it holds the frames' conditions to rounding;
+//! at every station of an interior section the spans on either side agree in their u derivatives
+//! up to the order held. Between stations the end and joint curves are the v interpolants of the
+//! stations' rows (the interpolation is linear and commutes with evaluation in u), not conditions
+//! of their own.
+//!
+//! **Refused**, naming why: fewer than 2 or more than [`MAX_SECTIONS`] sections; sections of
+//! different station counts, or a count outside [`MIN_STATIONS`] ..= [`MAX_STATIONS`]; a frame
+//! that is not finite, or a `leave` of no length at an end that uses it; a crown outside
+//! `-0.9 ..= 3`; two neighbouring sections that meet at a station (no room for a blend there).
+//!
+//! **The two floors.** Two tests guard divisions, and both refuse; neither adjusts an input or a
+//! result to get past them. A tangent's length (an end's `leave`, and the first derivative in
+//! `third_derivative`) is divided by: a length that is not finite and positive is refused,
+//! never replaced by a default direction. Two neighbouring sections meeting at a station
+//! (distance not positive) leave the span there no room: a speed of zero, and no tangent to
+//! divide by at the next section; the blend is refused, never nudged apart. Both are exact tests,
+//! not SolidCraft's `1e-12` and `1e-9` floors: a chord of `1e-12` is not refused, its speed is
+//! about `1e-12` and the end rows collapse onto the section, a valid but degenerate surface.
+//!
+//! Deviations: no upstream counterpart. SolidCraft's `1e-12` floor on a tangent's length and its
+//! `1e-9` floor on the distance between neighbouring sections are exact tests here (a length that
+//! is not positive): what the floors protect is the division, and an exact test protects it
+//! without a scale-dependent constant. Its one-sided third difference at the last-but-one section
+//! has its sign turned (`f(i-2) - 3 f(i-1) + 3 f(i) - f(i+1)`, the negative of the change of
+//! curvature it estimates); here it is the backward difference, exact on a cubic like the other
+//! two. Its batched row solves are one solve per row. No
+//! recursion.
+
+use crate::error::{Result, SolidError};
+use crate::math::{Point3, Vec3};
+use crate::nurbs::b_spline_curve::KnotType;
+use crate::nurbs::b_spline_surface::{BSplineSurface, BSplineSurfaceForm, CanonicalSurfaceData};
+use crate::nurbs::crv_fit::p1::{interp_given_params, interp_knot_vector};
+use crate::nurbs::knots::KnotVector;
+use crate::nurbs::math::NOW;
+
+const OP: &str = "sweep::section_blend";
+
+/// Most cross-sections one blend runs through.
+pub const MAX_SECTIONS: usize = 50;
+/// Fewest stations a cross-section is sampled at (a straight line across it).
+pub const MIN_STATIONS: usize = 2;
+/// Most stations a cross-section is sampled at.
+pub const MAX_STATIONS: usize = 257;
+
+/// One station of a cross-section: its point and, at the first and last section, how the blend
+/// leaves it.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct SectionFrame {
+    /// The point.
+    pub p: Point3,
+    /// The direction the blend leaves in, towards the next section (at the last section, back
+    /// into the blend, towards the section before). Its length is ignored.
+    pub leave: Vec3,
+    /// The curvature vector the blend takes along `leave` (zero for a straight start).
+    pub bend: Vec3,
+    /// The arc-length derivative of `bend` along `leave`.
+    pub bend_change: Vec3,
+}
+
+/// The continuity a blend holds at its first or last section.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum EndOrder {
+    /// Position.
+    G0,
+    /// Position and tangent direction.
+    G1,
+    /// And curvature.
+    G2,
+    /// And change of curvature.
+    G3,
+}
+
+impl EndOrder {
+    /// The conditions held: 1 to 4 (position, tangent, curvature, change of curvature).
+    #[must_use]
+    pub const fn conditions(self) -> usize {
+        match self {
+            Self::G0 => 1,
+            Self::G1 => 2,
+            Self::G2 => 3,
+            Self::G3 => 4,
+        }
+    }
+}
+
+fn invalid(reason: &'static str) -> SolidError {
+    SolidError::invalid_input(OP, reason)
+}
+
+/// The derivatives a section holds along the run at each station: `d[k]` is the `(k + 1)`-th,
+/// as many as its conditions less one.
+struct Held {
+    p: Vec<Point3>,
+    d: [Vec<Vec3>; 3],
+}
+
+/// The Bezier control rows at one end of a span of degree `m` over the parameter interval
+/// `delta`, from the end's position `p` and its derivatives `d` (the first `conditions - 1` of
+/// them used), as the span leaves the end (`backward` false: rows `0, 1, ..`) or arrives at it
+/// (`backward` true: rows `m, m - 1, ..`, the odd derivatives read the other way): the leading
+/// rows of a Bezier whose derivatives at that end are `d`. Row `k` comes back at index `k` from
+/// the end.
+///
+/// # Errors
+/// `InvalidInput` for more conditions than the degree carries or than `d` gives.
+pub(crate) fn end_rows(
+    p: Point3,
+    d: &[Vec3],
+    conditions: usize,
+    m: usize,
+    delta: f64,
+    backward: bool,
+) -> Result<Vec<Point3>> {
+    if conditions == 0 || conditions > 4 || conditions > m + 1 || d.len() + 1 < conditions {
+        return Err(invalid(
+            "a span's end carries more conditions than its degree or its data",
+        ));
+    }
+    #[allow(clippy::cast_precision_loss)] // a degree, at most 32
+    let k = m as f64;
+    let sign = if backward { -1.0 } else { 1.0 };
+    let one = delta / k;
+    let two = if m >= 2 {
+        delta * delta / (k * (k - 1.0))
+    } else {
+        0.0
+    };
+    let three = if m >= 3 {
+        delta * delta * delta / (k * (k - 1.0) * (k - 2.0))
+    } else {
+        0.0
+    };
+    let mut rows = vec![p];
+    if conditions >= 2 {
+        let d1 = *d.first().ok_or_else(|| invalid("a missing tangent"))?;
+        let q1 = p + d1 * (sign * one);
+        rows.push(q1);
+        if conditions >= 3 {
+            let d2 = *d.get(1).ok_or_else(|| invalid("a missing curvature"))?;
+            let q2 = d2 * two + q1 * 2.0 - p;
+            rows.push(q2);
+            if conditions >= 4 {
+                let d3 = *d
+                    .get(2)
+                    .ok_or_else(|| invalid("a missing change of curvature"))?;
+                rows.push(d3 * (sign * three) + q2 * 3.0 - q1 * 3.0 + p);
+            }
+        }
+    }
+    Ok(rows)
+}
+
+/// The third derivative a curve needs at an end so that the arc-length derivative of its
+/// curvature vector is `target`, from its first two derivatives `d1`, `d2` there: only its part
+/// square to the tangent holds the condition, the rest is a reparametrisation and is left zero
+/// (SolidCraft's `bridge::third_derivative`).
+///
+/// # Errors
+/// `InvalidInput` for a tangent of no length or a result that is not finite.
+pub(crate) fn third_derivative(d1: Vec3, d2: Vec3, target: Vec3) -> Result<Vec3> {
+    let sigma = d1.length();
+    // the floor on the tangent's length, divided by below: refused, never adjusted
+    if !(sigma.is_finite() && sigma > 0.0) {
+        return Err(invalid(
+            "no room for the change of curvature: the tangent has no length",
+        ));
+    }
+    let t = d1 * (1.0 / sigma);
+    let tp = d2 * (1.0 / sigma) - d1 * (d1.dot(d2) / (sigma * sigma * sigma));
+    let nn = d2 - t * d2.dot(t);
+    let r = tp * (-d2.dot(t)) - t * d2.dot(tp);
+    let x = (target * sigma.powi(5) - r * (sigma * sigma) + nn * (2.0 * d1.dot(d2)))
+        * (1.0 / (sigma * sigma));
+    if !(x.x.is_finite() && x.y.is_finite() && x.z.is_finite()) {
+        return Err(invalid("the change of curvature is not finite"));
+    }
+    Ok(x - t * x.dot(t))
+}
+
+fn finite(v: Vec3) -> bool {
+    v.x.is_finite() && v.y.is_finite() && v.z.is_finite()
+}
+
+/// One exact degree elevation of a Bezier net of rows: the same curve in one row more.
+fn elevate(rows: &[Vec<Point3>]) -> Vec<Vec<Point3>> {
+    let degree = rows.len().saturating_sub(1);
+    #[allow(clippy::cast_precision_loss)] // a degree, at most 32
+    let up = degree as f64 + 1.0;
+    let mut out: Vec<Vec<Point3>> = Vec::new();
+    if let Some(first) = rows.first() {
+        out.push(first.clone());
+    }
+    for i in 1..=degree {
+        if let (Some(before), Some(here)) = (rows.get(i - 1), rows.get(i)) {
+            #[allow(clippy::cast_precision_loss)] // a row index, at most 32
+            let a = i as f64 / up;
+            out.push(
+                before
+                    .iter()
+                    .zip(here)
+                    .map(|(x, y)| *x * a + *y * (1.0 - a))
+                    .collect(),
+            );
+        }
+    }
+    if let Some(last) = rows.last() {
+        out.push(last.clone());
+    }
+    out
+}
+
+/// The blend surface through `sections` (each a cross-section of the same stations, in order),
+/// holding `orders[0]` at the first section and `orders[1]` at the last, `crown` scaling how fast
+/// it leaves each (`-0.9 ..= 3`, 0 the plain blend). See the module's notes for the definition.
+///
+/// # Errors
+/// `InvalidInput` for the refusals the module names; those of the interpolation and the surface's
+/// construction.
+#[allow(clippy::too_many_lines)] // one construction, step by step
+pub fn section_blend(
+    sections: &[Vec<SectionFrame>],
+    orders: [EndOrder; 2],
+    crown: [f64; 2],
+) -> Result<BSplineSurface> {
+    let run = sections.len();
+    if !(2..=MAX_SECTIONS).contains(&run) {
+        return Err(invalid("a blend runs through 2 to 50 cross-sections"));
+    }
+    let samples = sections.first().map_or(0, Vec::len);
+    if !(MIN_STATIONS..=MAX_STATIONS).contains(&samples) {
+        return Err(invalid("a blend's cross-sections take 2 to 257 stations"));
+    }
+    if crown
+        .iter()
+        .any(|c| !(c.is_finite() && (-0.9..=3.0).contains(c)))
+    {
+        return Err(invalid("a blend's crown is between -0.9 and 3"));
+    }
+    for section in sections {
+        if section.len() != samples {
+            return Err(invalid(
+                "every cross-section of a blend has the same stations",
+            ));
+        }
+        if section
+            .iter()
+            .any(|f| !(finite(f.p) && finite(f.leave) && finite(f.bend) && finite(f.bend_change)))
+        {
+            return Err(invalid("a blend's frame is not finite"));
+        }
+    }
+    let point = |i: usize, s: usize| -> Result<Point3> {
+        sections
+            .get(i)
+            .and_then(|sec| sec.get(s))
+            .map(|f| f.p)
+            .ok_or_else(|| invalid("a cross-section is missing a station"))
+    };
+    let frame = |i: usize, s: usize| -> Result<SectionFrame> {
+        sections
+            .get(i)
+            .and_then(|sec| sec.get(s))
+            .copied()
+            .ok_or_else(|| invalid("a cross-section is missing a station"))
+    };
+    for i in 0..run - 1 {
+        for s in 0..samples {
+            // the floor on coincident sections (a zero speed, no tangent to divide by next):
+            // refused, never nudged apart
+            if point(i, s)?.distance(point(i + 1, s)?) <= 0.0 {
+                return Err(invalid(
+                    "two neighbouring cross-sections meet at a station: there is no room for a blend",
+                ));
+            }
+        }
+    }
+    // the conditions at each section: the ends' orders; an interior one four where a fourth
+    // section reaches for the third difference, else three
+    let mut conditions = vec![3usize; run];
+    if let Some(c) = conditions.first_mut() {
+        *c = orders[0].conditions();
+    }
+    if let Some(c) = conditions.last_mut() {
+        *c = orders[1].conditions();
+    }
+    for (i, c) in conditions.iter_mut().enumerate().take(run - 1).skip(1) {
+        if i >= 2 || i + 2 < run {
+            *c = 4;
+        }
+    }
+    let degree = conditions
+        .windows(2)
+        .map(|w| match w {
+            [a, b] => a + b - 1,
+            _ => 0,
+        })
+        .max()
+        .unwrap_or(1)
+        .max(1);
+    #[allow(clippy::cast_precision_loss)] // at most 50 sections
+    let step = 1.0 / (run - 1) as f64;
+
+    // what each section holds along the run
+    let mut held: Vec<Held> = Vec::new();
+    for (i, &c) in conditions.iter().enumerate() {
+        let p: Vec<Point3> = (0..samples).map(|s| point(i, s)).collect::<Result<_>>()?;
+        let mut d: [Vec<Vec3>; 3] = [Vec::new(), Vec::new(), Vec::new()];
+        let first = i == 0;
+        let last = i + 1 == run;
+        for s in 0..samples {
+            let (d1, d2, d3) = if first || last {
+                let f = frame(i, s)?;
+                let (other, crown_here, sign) = if first {
+                    (point(1, s)?, crown[0], 1.0)
+                } else {
+                    (point(i - 1, s)?, crown[1], -1.0)
+                };
+                let length = f.leave.length();
+                // the floor on the tangent's length, divided by below: refused, never defaulted
+                if c >= 2 && !(length.is_finite() && length > 0.0) {
+                    return Err(invalid("a blend's leave direction has no length"));
+                }
+                let leave = if length > 0.0 {
+                    f.leave * (1.0 / length)
+                } else {
+                    f.leave
+                };
+                // a third of the station's chord to its neighbour, the crown, over the interval
+                let speed = f.p.distance(other) / 3.0 * (1.0 + crown_here) / step;
+                let d1 = leave * (sign * speed);
+                let d2 = f.bend * (speed * speed);
+                let d3 = if c >= 4 {
+                    // the last section's frames point back into the blend: read it backwards
+                    if first {
+                        third_derivative(d1, d2, f.bend_change)?
+                    } else {
+                        third_derivative(-d1, d2, f.bend_change)? * -1.0
+                    }
+                } else {
+                    Vec3::ZERO
+                };
+                (d1, d2, d3)
+            } else {
+                let before = point(i - 1, s)?;
+                let here = point(i, s)?;
+                let after = point(i + 1, s)?;
+                let d1 = (after - before) * (1.0 / (2.0 * step));
+                let d2 = (after - here * 2.0 + before) * (1.0 / (step * step));
+                let d3 = if c >= 4 {
+                    let cube = step * step * step;
+                    match (i.checked_sub(2), i + 2 < run) {
+                        (Some(k), true) => {
+                            (point(i + 2, s)? - point(i + 1, s)? * 2.0 + point(i - 1, s)? * 2.0
+                                - point(k, s)?)
+                                * (1.0 / (2.0 * cube))
+                        }
+                        (None, true) => {
+                            (point(i + 2, s)? - point(i + 1, s)? * 3.0 + here * 3.0 - before)
+                                * (1.0 / cube)
+                        }
+                        // (the backward stencil f(i+1) - 3 f(i) + 3 f(i-1) - f(i-2): SolidCraft's
+                        // has its sign turned, see Deviations)
+                        (Some(k), false) => {
+                            (after - here * 3.0 + before * 3.0 - point(k, s)?) * (1.0 / cube)
+                        }
+                        (None, false) => {
+                            return Err(invalid(
+                                "no fourth section for an interior change of curvature",
+                            ))
+                        }
+                    }
+                } else {
+                    Vec3::ZERO
+                };
+                (d1, d2, d3)
+            };
+            if !(finite(d1) && finite(d2) && finite(d3)) {
+                return Err(invalid(
+                    "a section's derivatives along the run are not finite",
+                ));
+            }
+            let [a, b, e] = &mut d;
+            a.push(d1);
+            b.push(d2);
+            e.push(d3);
+        }
+        held.push(Held { p, d });
+    }
+
+    // the spans' control rows, each elevated to the run's degree; a span's first row is the one
+    // before's last
+    let mut rows: Vec<Vec<Point3>> = Vec::new();
+    for j in 0..run - 1 {
+        let (Some(left), Some(right)) = (held.get(j), held.get(j + 1)) else {
+            return Err(invalid("a missing section"));
+        };
+        let (Some(&kl), Some(&kr)) = (conditions.get(j), conditions.get(j + 1)) else {
+            return Err(invalid("a missing section"));
+        };
+        let m = kl + kr - 1;
+        let mut span = vec![vec![Point3::ZERO; samples]; m + 1];
+        for s in 0..samples {
+            let take = |h: &Held| -> Result<(Point3, Vec<Vec3>)> {
+                let p = *h.p.get(s).ok_or_else(|| invalid("a missing station"))?;
+                let d =
+                    h.d.iter()
+                        .map(|v| {
+                            v.get(s)
+                                .copied()
+                                .ok_or_else(|| invalid("a missing station"))
+                        })
+                        .collect::<Result<Vec<_>>>()?;
+                Ok((p, d))
+            };
+            let (pl, dl) = take(left)?;
+            let (pr, dr) = take(right)?;
+            for (k, q) in end_rows(pl, &dl, kl, m, step, false)?
+                .into_iter()
+                .enumerate()
+            {
+                if let Some(slot) = span.get_mut(k).and_then(|r| r.get_mut(s)) {
+                    *slot = q;
+                }
+            }
+            for (k, q) in end_rows(pr, &dr, kr, m, step, true)?
+                .into_iter()
+                .enumerate()
+            {
+                if let Some(slot) = span.get_mut(m - k).and_then(|r| r.get_mut(s)) {
+                    *slot = q;
+                }
+            }
+        }
+        while span.len() < degree + 1 {
+            span = elevate(&span);
+        }
+        rows.extend(span.into_iter().skip(usize::from(j > 0)));
+    }
+
+    // each row interpolated through its stations along v
+    #[allow(clippy::cast_precision_loss)] // at most 257 stations
+    let params: Vec<f64> = (0..samples)
+        .map(|s| s as f64 / (samples - 1) as f64)
+        .collect();
+    let degree_v = 3.min(samples - 1);
+    let knots_v = interp_knot_vector(&params, degree_v)?;
+    let kv = KnotVector::from_slice(&knots_v)?;
+    let count_u = rows.len();
+    let mut net = vec![Point3::ZERO; count_u * samples];
+    for (i, row) in rows.iter().enumerate() {
+        let curve = interp_given_params(row, &params, &kv, degree_v)?;
+        for (s, c) in curve.cpts().iter().take(samples).enumerate() {
+            // (exact tests: NOW is the stored "no weight" mark of a polynomial row, assigned,
+            // never computed, and 1.0 an assigned unit weight; any other weight is a weighted
+            // point)
+            let q = if c.w == NOW || c.w == 1.0 {
+                Point3::new(c.x, c.y, c.z)
+            } else {
+                Point3::new(c.x / c.w, c.y / c.w, c.z / c.w)
+            };
+            if let Some(slot) = net.get_mut(i * samples + s) {
+                *slot = q;
+            }
+        }
+    }
+
+    // the run's knots: clamped, every interior section `degree` times
+    let mut u_knots = vec![0.0];
+    let mut u_mults = vec![degree + 1];
+    for i in 1..run - 1 {
+        #[allow(clippy::cast_precision_loss)] // at most 50 sections
+        u_knots.push(i as f64 * step);
+        u_mults.push(degree);
+    }
+    u_knots.push(1.0);
+    u_mults.push(degree + 1);
+    let (v_knots, v_mults) = unique(&knots_v);
+    BSplineSurface::create_canonical(&CanonicalSurfaceData {
+        u_degree: degree,
+        v_degree: degree_v,
+        control_points: &net,
+        form: BSplineSurfaceForm::Unspecified,
+        u_multiplicities: &u_mults,
+        v_multiplicities: &v_mults,
+        u_knots: &u_knots,
+        v_knots: &v_knots,
+        knot_type: KnotType::Unspecified,
+        weights: None,
+        uv_domain: None,
+    })
+}
+
+/// A knot vector as its distinct knots and their multiplicities.
+fn unique(knots: &[f64]) -> (Vec<f64>, Vec<usize>) {
+    let mut values: Vec<f64> = Vec::new();
+    let mut mults: Vec<usize> = Vec::new();
+    for &u in knots {
+        match (values.last(), mults.last_mut()) {
+            (Some(&last), Some(m)) if last == u => *m += 1,
+            _ => {
+                values.push(u);
+                mults.push(1);
+            }
+        }
+    }
+    (values, mults)
+}

solidcore/crates/solidcore/src/topology/brep.rs

@@ -64,28 +64,33 @@ pub use p8::{
 };
 pub use p9::{make_vertex_loop, orient_sheet_surfaces};
 
-/// The relative accuracy [`is_outward_solid`] measures the volume's sign at: the sign of a
-/// solid's volume is its whole volume away from zero.
-const SIGN_ACCURACY: f64 = 1e-3;
-
 /// Whether `b` is a valid closed solid facing out (not upstream): one closed manifold solid
 /// ([`is_manifold_solid`]), passed by the kernel's validity check (its pointer check and
-/// `AssertValid`, [`validation::check_brep`] at `Level0`), and its integrated volume positive.
+/// `AssertValid`, [`validation::check_brep`] at `Level0`), and its volume proved positive by
+/// its certified enclosure ([`crate::mass::enclosure::volume_sign`]; an undecided sign is
+/// not).
 ///
 /// The two guard the faceuse orientation together. A body with every face flipped
 /// (`FlipFaceOrientation`, which leaves a face invalid) is still manifold and keeps a
 /// positive volume (the integrator reads the loops and surfaces, not the uses' orientation):
 /// the pointer check is what refuses it. A valid body turned inside out (its loops and
-/// surfaces reversed with its uses) has a negative volume. The sign's margin is the whole
-/// volume, so it is measured at a relative accuracy of `1e-3`.
+/// surfaces reversed with its uses) has a negative volume.
+///
+/// A sign the enclosure leaves undecided (its interval still holds 0 when refinement ends:
+/// a gap between faces as large as the volume, or the cell budget spent) is "not a solid" on
+/// purpose: a solid is what is proved one, so ops' `finish` refuses the body as `NotSolid`.
+/// A body the enclosure cannot read at all is an error, not `false`: a face with no NURBS form
+/// (an offset surface, as the offset of a round keeps; a curve-bounded or in-volume surface),
+/// a face without trim loops, or weights not proved positive.
 ///
 /// A region the kernel is unsure of is [`crate::SolidError::UnsureRegion`], not "not a solid":
 /// the volume's sign would read it as void.
 ///
 /// # Errors
 ///
-/// Those of the manifold test, the validity check and the volume;
-/// [`crate::SolidError::UnsureRegion`].
+/// Those of the manifold test, the validity check and the volume
+/// ([`crate::mass::enclosure::volume_sign`]: [`crate::SolidError::Unsupported`] for a body
+/// it cannot read); [`crate::SolidError::UnsureRegion`].
 pub fn is_outward_solid(
     k: &mut crate::kernel::Kernel,
     b: &mut crate::topology::Brep,
@@ -123,9 +128,10 @@ fn is_valid_and_outward(
         return Ok(false);
     }
     crate::mass::integrator::properties::no_unsure_region(b)?;
-    let volume = crate::mass::integrator::properties::brep_volume_default(k, b, SIGN_ACCURACY)?;
-    // (false for a NaN too)
-    Ok(volume > 0.0)
+    Ok(matches!(
+        crate::mass::enclosure::volume_sign(k, b)?,
+        crate::mass::enclosure::VolumeSign::Positive(_)
+    ))
 }
 
 #[cfg(test)]

solidcore/crates/solidcore/src/topology/brep/local_operation.rs

@@ -34,6 +34,7 @@ use crate::error::{EntityRef, Failure, Result, SolidError};
 use crate::geom::attribute::ObjectKey;
 use crate::geom::axis2_placement::Axis2Placement;
 use crate::kernel::Kernel;
+use crate::mass::enclosure::VolumeSign;
 use crate::math::Vec3;
 use crate::nurbs::b_spline_surface::p1::SurfParamType;
 use crate::nurbs::knots::Side;
@@ -311,8 +312,12 @@ fn local_operation_on(
 /// - the body's pointer check failed, so its geometry was not checked (`AssertValid` is
 ///   skipped then), even where the input's pointer check failed alike;
 /// - the input was a manifold solid and the body is not;
-/// - the body is a manifold solid whose volume is not positive (the input's volume is
-///   not measured).
+/// - the body is a manifold solid whose volume is not proved positive: its certified
+///   enclosure lies below 0, or still holds 0 after its budget
+///   ([`validation::volume_sign`]; the input's volume is not measured). A face whose net
+///   is certified within ε > 0 of its definition (a Gⁿ or law round, a sweep, a Mixed
+///   corner) is read on its net, so the gate decides on the body as stored; widening the
+///   enclosure by ε needs bounds on the definition's `S_u` and `S_v` (#3170).
 ///
 /// The owners the check tests the geometry against are the identities the body's naming
 /// scheme names its entities by ([`validation::standing`]), as `move_faces` sets them.
@@ -357,10 +362,12 @@ fn refuse_unsound(k: &mut Kernel, b: &Brep, input: &validation::Standing) -> Res
         Unsoundness::GeometryUnchecked
     } else if let Some(lost) = validation::lost_manifold(found.manifold, || Ok(input.manifold))? {
         lost
-    } else if found.manifold
-        && validation::volume(k, &mut copy)?.partial_cmp(&0.0) != Some(std::cmp::Ordering::Greater)
-    {
-        Unsoundness::VolumeNotPositive
+    } else if found.manifold {
+        match validation::volume_sign(k, &mut copy)? {
+            VolumeSign::Positive(_) => return Ok(()),
+            VolumeSign::Negative(_) => Unsoundness::VolumeNotPositive,
+            VolumeSign::Undecided(_) => Unsoundness::VolumeUndecided,
+        }
     } else {
         return Ok(());
     };
@@ -2085,6 +2092,36 @@ mod tests {
         );
     }
 
+    /// A body whose volume's sign is not proved is refused as such: the quarter shell R 10,
+    /// t 1e-6 passes the check, but its faces' boundaries lie apart by about its thickness,
+    /// so the strips between them hold 0 in its enclosure whatever its cells become.
+    #[test]
+    fn the_gate_refuses_a_body_whose_sign_it_cannot_prove() {
+        let mut k = Kernel::default();
+        let b = crate::primitive::api_primitives::create_cylindrical_box(
+            &mut k,
+            Point3::ZERO,
+            10.0,
+            10.0,
+            10.0 + 1e-6,
+            0.0,
+            90.0,
+        )
+        .unwrap();
+        let input =
+            validation::standing(&mut k, &mut b.clone_standing_for_self().unwrap()).unwrap();
+        let e = refuse_unsound(&mut k, &b, &input).unwrap_err();
+        assert!(
+            matches!(
+                e.failure().map(|f| &f.reason),
+                Some(crate::error::Reason::Offset(OffsetFailure::Unsound {
+                    what: crate::error::offset::Unsoundness::VolumeUndecided
+                }))
+            ),
+            "{e}"
+        );
+    }
+
     /// A body whose pointer check fails is not checked further (`AssertValid` is skipped):
     /// the gate refuses it even where its input failed the pointer check alike, rather
     /// than finding nothing beyond the input's failures.
@@ -2502,13 +2539,11 @@ mod tests {
     }
 
     /// The same cube, its top given a roof with a ridge: a degree-1 B-spline patch whose
-    /// interior knot is a crease. The roof is a bare net beside the sides, and the reach is
-    /// bounded where it meets them (across the crease too: the net is continuous there), so
-    /// a body is built; it fails more of the check than the cube did (the sides along the
-    /// ridge meet the roof in a kinked line), so the gate refuses it as `Unsound`, and the
-    /// cube is as it came in, with the input's own failures.
+    /// interior knot is a crease. The roof has no exact class, so the reach of the moved
+    /// top has no certified bound: refused as `ReachUncertified` at the top, before any
+    /// body is built, the cube as it came in with the input's own failures.
     #[test]
-    fn a_creased_roof_on_a_defective_input_is_refused_as_unsound() {
+    fn a_creased_roof_on_a_defective_input_is_refused_as_reach_uncertified() {
         use crate::nurbs::b_spline_surface::BSplineSurface;
         use crate::nurbs::math::{CPoint, NOW};
         use crate::nurbs::srf_basic::Surface as Net;
@@ -2529,15 +2564,7 @@ mod tests {
         .unwrap();
         let roof = Surface::from(BSplineSurface::from_gw_nurb(&roof));
         let why = refused_unchanged_or_returned(&mut k, &mut b, &[top], vec![roof]);
-        assert!(
-            matches!(
-                why,
-                Some(OffsetFailure::Unsound {
-                    what: crate::error::offset::Unsoundness::Check { .. }
-                })
-            ),
-            "{why:?}"
-        );
+        assert_eq!(why, Some(OffsetFailure::ReachUncertified { face: top }));
         assert_eq!(failure_classes(&mut k, &b), had);
     }
 

solidcore/crates/solidcore/src/topology/brep/p4.rs

@@ -95,7 +95,7 @@ use crate::geom::extent1d::Extent1d;
 use crate::geom::extent2d::Extent2d;
 use crate::geom::object::{NotifyOperation, ObjectRef};
 use crate::heal::stitch::p1::{DefaultStitchCallback, Stitch, StitchCallback};
-use crate::heal::stitch::p2::MinGapRequest;
+use crate::heal::stitch::p2::{ClosedGap, MinGapRequest};
 use crate::kernel::Kernel;
 use crate::math::{Point2, Vec3, EFF_ZERO};
 use crate::nurbs::b_spline_curve_n_lib::TrimMode;
@@ -1900,6 +1900,61 @@ pub(crate) fn stitch_faces_with_callback<'a, C: StitchCallback>(
     )
 }
 
+/// [`stitch_faces_with_callback`] that additionally returns each gap the stitch
+/// closed, with the tolerance growth its closure applied (not upstream,
+/// solidcore#2975). The caller supplies the rollback boundary; certificate errors
+/// propagate regardless of the legacy edit-status flags.
+///
+/// # Errors
+///
+/// Those of [`stitch_faces`] and geometry enclosure failures (unsupported curve
+/// kinds, invalid data or non-finite bounds).
+pub(crate) fn stitch_faces_with_gap_report(
+    k: &mut Kernel,
+    b: &mut Brep,
+    xsect_tol_3d: f64,
+    faces: Option<&[Option<FaceId>]>,
+    allow_spine_edges: bool,
+    identity: Option<crate::query::brep::BrepIdentity<'_>>,
+) -> Result<(StitchOutcome, Vec<ClosedGap>)> {
+    // lock brep bounding box, until goes out of scope
+    let mut lockit = LockBrepBox::new(k, b)?;
+    let b = lockit.brep();
+
+    // construct Stitch manager with the default keep/delete logic for glue pairs,
+    // recording each closure
+    let mut callback = DefaultStitchCallback::new();
+    let mut stitch = Stitch::new(&mut callback, xsect_tol_3d, true, true);
+    stitch.query_identity = identity;
+    stitch.fast_edge_compare = true;
+    stitch.ignore_problems = true;
+    stitch.squeeze_small_edges = true;
+    stitch.making_manifold_solid = !allow_spine_edges;
+    stitch.remove_laminar_slivers = true;
+    stitch.report_gaps = Some(Vec::new());
+
+    let mut lists = None;
+    if let Some(faces) = faces {
+        let mut vertices = Vec::new();
+        let mut edges = Vec::new();
+        for f in faces.iter().flatten() {
+            vertices.extend(face_vertices(b, *f)?);
+            edges.extend(face_edges(b, *f)?);
+        }
+        lists = Some((vertices, edges));
+    }
+    // pass the stitch call along (SER: its status is returned as is)
+    let outcome = do_stitching(
+        k,
+        b,
+        &mut stitch,
+        lists.as_ref().map(|(v, _)| v.as_slice()),
+        lists.as_ref().map(|(_, e)| e.as_slice()),
+    )?;
+    let gaps = stitch.take_gaps();
+    Ok((outcome, gaps))
+}
+
 // ---- ShrinkGeometry ------------------------------------------------------------------------
 
 /// `SmBrep::ShrinkGeometry`: shrinks each face's UV domain to its trim curves (snapped

solidcore/crates/solidcore/src/topology/brep/p5.rs

@@ -78,6 +78,7 @@ use crate::geom::extent1d::Extent1d;
 use crate::geom::extent3d::Extent3d;
 use crate::geom::object::{NotifyOperation, ObjectRef};
 use crate::geom::tol::ZONE_TOL_3D;
+use crate::heal::stitch::p2::ClosedGap;
 use crate::kernel::Kernel;
 use crate::math::{max2, Point3, Vec3};
 use crate::nurbs::b_spline_curve::BSplineCurve;
@@ -2662,6 +2663,103 @@ fn stitch_faces(
     Ok(())
 }
 
+/// [`stitch_faces`] that also returns what the stitch closed: each gap, the
+/// entities, and the tolerance growth its closure applied (`solidcore#2975`).
+///
+/// # Errors
+///
+/// Those of [`stitch_faces`].
+fn stitch_faces_reported(
+    k: &mut Kernel,
+    b: &mut Brep,
+    tolerance: f64,
+    allow_spine: bool,
+    lamina: &mut usize,
+    gaps: &mut Vec<ClosedGap>,
+) -> Result<()> {
+    let (out, pass_gaps) = crate::topology::brep::p4::stitch_faces_with_gap_report(
+        k,
+        b,
+        tolerance,
+        None,
+        allow_spine,
+        None,
+    )?;
+    gaps.extend(pass_gaps);
+    *lamina = usize::try_from(out.lamina_edges)
+        .map_err(|_| SolidError::invalid_input(OP, "lamina edge count"))?;
+    Ok(())
+}
+
+/// [`stitch_and_orient`] that additionally reports what the stitch closed
+/// (`solidcore#2975`): for every gap it closed, the entities it glued, the gap it
+/// enclosed, and the tolerance growth its closure applied. Geometry bounds are
+/// independent of the stitcher's sampled acceptance test and do not feed back
+/// into the construction. A caller decides whether the returned bounds suffice.
+/// On any error the B-rep is restored, including when certification fails after
+/// earlier closures. Errors are never suppressed by legacy status flags.
+///
+/// # Errors
+///
+/// As [`stitch_and_orient`], plus [`SolidError::Unsupported`] for curve kinds
+/// without a proved enclosure and [`SolidError::InvalidInput`] for invalid data
+/// or a non-finite enclosure. No partial report or partial edit is returned.
+pub fn stitch_and_orient_reported(
+    k: &mut Kernel,
+    b: &mut Brep,
+    options: &StitchAndOrientOptions,
+) -> Result<Vec<ClosedGap>> {
+    k.check_cancelled(OP)?;
+    b.with_rollback(
+        |b| stitch_and_orient_reported_inner(k, b, options),
+        Result::is_ok,
+    )
+}
+
+fn stitch_and_orient_reported_inner(
+    k: &mut Kernel,
+    b: &mut Brep,
+    options: &StitchAndOrientOptions,
+) -> Result<Vec<ClosedGap>> {
+    let mut lamina = 0;
+    let mut gaps = Vec::new();
+    let mut tolerance = initial_stitch_tolerance(b.tolerance(), options.stitch_tolerance);
+    stitch_faces_reported(
+        k,
+        b,
+        tolerance,
+        options.allow_spine_edges,
+        &mut lamina,
+        &mut gaps,
+    )?;
+    if lamina > 1 {
+        tolerance = if options.stitch_tolerance <= 0.0 {
+            tolerance * 20.0
+        } else {
+            tolerance * 10.0
+        };
+        stitch_faces_reported(
+            k,
+            b,
+            tolerance,
+            options.allow_spine_edges,
+            &mut lamina,
+            &mut gaps,
+        )?;
+    }
+    plain_edit(k, b, |k, b, env| {
+        orient_trimmed_surfaces(
+            k,
+            b,
+            Some(env),
+            true,
+            options.just_unify.unwrap_or(lamina > 0),
+            options.faces_to_swap.as_deref(),
+        )
+    })?;
+    Ok(gaps)
+}
+
 /// `SmBrep::OrientTrimmedSurfaces(bNormalsOutward, bJustUnifyNormals, pFacesToSwapUV)`
 /// ([`crate::topology::brep::p3::orient_trimmed_surfaces`]), notifying as
 /// [`with_p3_notifications`].

solidcore/crates/solidcore/src/topology/brep/validation.rs

@@ -34,7 +34,7 @@ pub use coincidence::{contains_coincident_topology, CoincidenceResult};
 pub(crate) use pointers::validate_geometry;
 pub use pointers::validate_pointers;
 pub(crate) use soundness::lost_manifold;
-pub use soundness::{soundness, standing, volume, Soundness, Standing};
+pub use soundness::{soundness, standing, volume_sign, Soundness, Standing};
 
 use crate::error::{EntityRef, Result, SolidError};
 use crate::geom::assert_array::{AssertArray, AssertReport, ObjectKey, ReportSpec};

solidcore/crates/solidcore/src/topology/brep/validation/soundness.rs

@@ -1,7 +1,7 @@
 //! (not upstream) A body's soundness: its check at `SM_LEVEL_2`, and for a closed body,
 //! whether it is a manifold solid of positive volume. The local operation measures its
 //! input's [`standing`] (the check with the body's own owner naming, and the manifold
-//! test) and its result's, and the result's [`volume`] only to test it is positive
+//! test) and its result's, and the result's [`volume_sign`] only to test it is positive
 //! ([`crate::topology::brep::local_operation::local_operation`]); the goldens soundness
 //! probe (`goldens::soundness`) measures result bodies with [`soundness`] (the geometry's
 //! recorded owners).
@@ -15,10 +15,7 @@ use crate::kernel::Kernel;
 use crate::topology::Brep;
 
 use super::assert_valid::{check_brep_with_keys, BrepCheck, CheckLevel};
-
-/// The relative accuracy the volume is integrated at: its sign is a verdict on the body,
-/// which a closed solid's whole volume holds away from zero.
-const VOLUME_ACCURACY: f64 = 1e-6;
+use crate::mass::enclosure::VolumeSign;
 
 /// What [`soundness`] measured of one body.
 #[derive(Debug, Clone)]
@@ -28,16 +25,17 @@ pub struct Soundness {
     pub check: BrepCheck,
     /// Whether the body is a manifold solid ([`crate::topology::brep::is_manifold_solid`]).
     pub manifold: bool,
-    /// Its volume, when it is a manifold solid.
-    pub volume: Option<f64>,
+    /// Its volume's sign, when it is a manifold solid ([`volume_sign`]).
+    pub volume: Option<VolumeSign>,
 }
 
 impl Soundness {
     /// Whether the check is clean and, when the body is a manifold solid, its volume is
-    /// positive (a NaN volume is not).
+    /// proved positive (an undecided sign is not).
     #[must_use]
     pub fn sound(&self) -> bool {
-        self.check.is_valid() && (!self.manifold || self.volume.is_some_and(|v| v > 0.0))
+        self.check.is_valid()
+            && (!self.manifold || matches!(self.volume, Some(VolumeSign::Positive(_))))
     }
 }
 
@@ -99,7 +97,11 @@ pub fn soundness(k: &mut Kernel, b: &mut Brep) -> Result<Soundness> {
     };
     let check = check_brep_with_keys(k, b, CheckLevel::Level2, &keys)?;
     let manifold = crate::topology::brep::p2::is_manifold_solid(b)?;
-    let volume = if manifold { Some(volume(k, b)?) } else { None };
+    let volume = if manifold {
+        Some(volume_sign(k, b)?)
+    } else {
+        None
+    };
     Ok(Soundness {
         check,
         manifold,
@@ -111,7 +113,7 @@ pub fn soundness(k: &mut Kernel, b: &mut Brep) -> Result<Soundness> {
 /// geometry's owner the identity `b`'s naming scheme names the entity by
 /// ([`Brep::owner_identity`], as the operations that bind geometry set it), so a curve or
 /// surface owned under another entity's identity fails the owner tests; then the manifold
-/// test. Its volume is not measured ([`volume`]).
+/// test. Its volume is not measured ([`volume_sign`]).
 ///
 /// As for [`soundness`], the check edits what it measures: measure a private copy.
 ///
@@ -151,11 +153,15 @@ pub(crate) fn lost_manifold(
     Ok(Some(crate::error::offset::Unsoundness::NotManifoldSolid))
 }
 
-/// The volume of the manifold solid `b`, integrated at [`VOLUME_ACCURACY`].
+/// The sign of the manifold solid `b`'s volume, from its certified enclosure
+/// ([`crate::mass::enclosure::volume_sign`]): positive or negative where the enclosure
+/// proves it, undecided where it still holds 0 after its budget. A face whose net is
+/// certified within ε > 0 of its definition is read on its net: the sign is the stored
+/// body's (#3170 widens it by ε).
 ///
 /// # Errors
 ///
-/// Those of [`crate::mass::integrator::properties::brep_volume_default`].
-pub fn volume(k: &mut Kernel, b: &mut Brep) -> Result<f64> {
-    crate::mass::integrator::properties::brep_volume_default(k, b, VOLUME_ACCURACY)
+/// Those of [`crate::mass::enclosure::volume_sign`].
+pub fn volume_sign(k: &Kernel, b: &mut Brep) -> Result<VolumeSign> {
+    crate::mass::enclosure::volume_sign(k, b)
 }

solidcore/crates/solidcore/src/topology/proto_topology/p2.rs

@@ -107,6 +107,10 @@
 //!   `Kernel::fixes.imprint_extends_edge_to_proto_vertex`, [`ProtoTopologyManager::imprint_edge_definition`]
 //!   first fits each end of the definition's interval to its proto vertex (`imprint_ends`: the SMLib
 //!   fork's thread-groove fixes, tangency-labs/smlib b43876f, a8caccd).
+//! - **Not upstream: one trim interval** (WR-767, tangency-labs/solidcore#3214).
+//!   [`ProtoTopologyManager::create_proto_edge`] trims the 3D curve and its uv curves to the
+//!   one interval none of their trims snaps (`exact_pieces::common_trim_interval`); upstream
+//!   trims them in turn with one interval, and the edge can end past its 3D curve.
 //! - `UpdateEdges` trims a definition at the split point; its alternative of splitting
 //!   the proto edge (`SmProtoEdge::Split`) sits behind `static constexpr SmBoolean
 //!   cbiDoSplit = FALSE` and is not ported.
@@ -140,6 +144,7 @@ use crate::math::{max2, max3, max4, min2, Point2, Point3, Vec3, EFF_ZERO};
 use crate::nurbs::b_spline_curve_n_lib::TrimMode;
 use crate::nurbs::b_spline_surface_n_lib::p2::OrientType;
 use crate::query::face::p2::proto_vertex_containment_radius;
+use crate::surface::surface::exact_pieces::{common_trim_interval, trim_unsnapped};
 use crate::topology::brep::p5::{make_edge_in_face_in, EdgeInFace};
 use crate::topology::VertexId;
 
@@ -2211,26 +2216,54 @@ impl<O: ClassObject> ProtoTopologyManager<O> {
         let p3d_curve = cc1.curve();
         let _ = cc2.curve() == p3d_curve;
 
-        // Create a copy of the input curve and trim it to this CurveInterval.
+        // Create a copy of the input curve and of its uv curves (copy statuses ignored), and
+        // trim them to this CurveInterval.
         let mut copy = curve_of(brep, p3d_curve)?.copy(k)?;
-        let mut domain = ci1.interval;
-        copy.trim(k, &mut domain, TrimMode::Notify)?;
-
-        // See about uv curves (copy statuses ignored; the trims' passed on with
-        // `ssi_proto_topology_statuses_pass_on`, fork bcc6f01).
-        let pass = k.fixes.ssi_proto_topology_statuses_pass_on;
         let mut uv1 = None;
         if let Some(c) = cc1.uv_curve1() {
             uv1 = ignore_soft(curve_of(brep, Some(c))?.copy(k))?;
-            if let Some(u) = uv1.as_mut() {
-                ignore_soft(passed_on(u.trim(k, &mut domain, TrimMode::Notify), pass)?)?;
-            }
         }
         let mut uv2 = None;
         if let Some(c) = cc2.uv_curve1() {
             uv2 = ignore_soft(curve_of(brep, Some(c))?.copy(k))?;
-            if let Some(u) = uv2.as_mut() {
-                ignore_soft(passed_on(u.trim(k, &mut domain, TrimMode::Notify), pass)?)?;
+        }
+
+        // The uv curves' trim statuses are ignored, and passed on with
+        // `ssi_proto_topology_statuses_pass_on` (fork bcc6f01). Not upstream (WR-767): the
+        // 3D curve and the uv curves whose trims accept the interval are trimmed to the one
+        // interval none of their trims snaps ([`common_trim_interval`]). Upstream trims them
+        // in turn with one interval, each trim snapping it onto a knot of its own curve, and
+        // the edge takes the interval the last trim left: a uv curve's knot a few ulps from
+        // the 3D curve's trim parameter leaves the edge's interval outside its 3D curve's
+        // (`SmEdge` test 2). A uv curve whose trim refuses the interval is trimmed alone, as
+        // upstream.
+        let pass = k.fixes.ssi_proto_topology_statuses_pass_on;
+        let mut joins = [false; 2];
+        for (u, join) in [&uv1, &uv2].into_iter().zip(&mut joins) {
+            if let Some(u) = u {
+                let mut probe = ci1.interval;
+                let trimmed = u.copy(k)?.trim(k, &mut probe, TrimMode::IntervalOnly);
+                *join = ignore_soft(passed_on(trimmed, pass)?)?.is_some();
+            }
+        }
+        let joined: Vec<&Curve> = std::iter::once(&copy)
+            .chain(
+                [&uv1, &uv2]
+                    .into_iter()
+                    .zip(joins)
+                    .filter_map(|(u, join)| u.as_ref().filter(|_| join)),
+            )
+            .collect();
+        let domain = common_trim_interval(k, &joined, ci1.interval, OP_CREATE_PE)?;
+        trim_unsnapped(k, &mut copy, domain, OP_CREATE_PE)?;
+        for (u, join) in [&mut uv1, &mut uv2].into_iter().zip(joins) {
+            if let Some(u) = u.as_mut() {
+                let trimmed = if join {
+                    trim_unsnapped(k, u, domain, OP_CREATE_PE)
+                } else {
+                    u.trim(k, &mut domain.clone(), TrimMode::Notify)
+                };
+                ignore_soft(passed_on(trimmed, pass)?)?;
             }
         }
 

solidcore/crates/solidcore/tests/contact_between_bodies.rs

@@ -0,0 +1,200 @@
+//! #3144: whether two bodies meet, decided by a certified bracket of their boundary distance
+//! (`query::contact`), against closed forms: boxes touching on a face, apart by 1e-9,
+//! overlapping in a face, an edge resting on a face, interpenetrating, one inside the other,
+//! far apart; spheres apart and crossing; a cylinder crossing a box's face and one against a
+//! side along a line; a peg through a hole that it clears.
+
+#![allow(clippy::unwrap_used, clippy::panic, clippy::float_cmp)] // test
+
+use solidcore::boolean::api_brep::boolean_difference;
+use solidcore::geom::certified::Verdict;
+use solidcore::kernel::Kernel;
+use solidcore::primitive::api_primitives::{create_box, create_cylinder, create_sphere};
+use solidcore::query::contact::{boundary_distance, meets};
+use solidcore::topology::brep::mirror::transform_matrix;
+use solidcore::{Brep, Point3};
+
+fn k() -> Kernel {
+    Kernel {
+        fixes: solidcore::kernel::UpstreamFixes::all(),
+        ..Kernel::default()
+    }
+}
+
+fn cube(k: &mut Kernel, at: [f64; 3], size: f64) -> Brep {
+    create_box(k, Point3::new(at[0], at[1], at[2]), size, size, size).unwrap()
+}
+
+/// `b` turned by `angle` about the x axis, then moved by `by`.
+fn turned_about_x(k: &mut Kernel, b: &mut Brep, angle: f64, by: [f64; 3]) {
+    let (c, s) = (angle.cos(), angle.sin());
+    // row vectors (`p' = p A + t`): A's rows are the images of x, y and z, t the fourth row
+    let m = [
+        [1.0, 0.0, 0.0, 0.0],
+        [0.0, c, s, 0.0],
+        [0.0, -s, c, 0.0],
+        [by[0], by[1], by[2], 1.0],
+    ];
+    transform_matrix(k, b, &m, true).unwrap();
+}
+
+/// Asserts the verdict at `tol`, the bracket shown on failure.
+fn verdict_is(k: &Kernel, a: &mut Brep, b: &mut Brep, tol: f64, want: Verdict) {
+    let c = meets(k, a, b, tol).unwrap();
+    assert!(c.lower <= c.upper, "{c:?}");
+    assert_eq!(c.verdict, want, "at {tol}: {c:?}");
+}
+
+/// The bracket of the boundary distance, asserted to hold `exact`.
+fn holds(k: &Kernel, a: &mut Brep, b: &mut Brep, exact: f64) {
+    let c = boundary_distance(k, a, b, 1e-6).unwrap();
+    assert_eq!(c.verdict, Verdict::Yes, "{c:?}");
+    assert!(c.lower <= exact && exact <= c.upper, "{exact} not in {c:?}");
+    assert!(c.upper - c.lower <= 1e-6 * c.upper.max(1.0), "{c:?}");
+}
+
+#[test]
+fn boxes_touching_on_a_face_meet_at_any_tolerance() {
+    let mut k = k();
+    let mut a = cube(&mut k, [0.0; 3], 1.0);
+    let mut b = cube(&mut k, [1.0, 0.0, 0.0], 1.0);
+    let c = meets(&k, &mut a, &mut b, 1e-12).unwrap();
+    assert_eq!(c.verdict, Verdict::Yes, "{c:?}");
+    let [p, q] = c.witness.unwrap();
+    assert!(
+        p.distance(q) <= 1e-12 && (p.x - 1.0).abs() <= 1e-12,
+        "{c:?}"
+    );
+}
+
+#[test]
+fn boxes_apart_by_a_nanometre_meet_only_at_a_tolerance_past_it() {
+    let mut k = k();
+    // the gap as the doubles have it
+    let gap = (1.0 + 1e-9) - 1.0;
+    let mut a = cube(&mut k, [0.0; 3], 1.0);
+    let mut b = cube(&mut k, [1.0 + 1e-9, 0.0, 0.0], 1.0);
+    verdict_is(&k, &mut a, &mut b, 1e-8, Verdict::Yes);
+    verdict_is(&k, &mut a, &mut b, 1e-10, Verdict::No);
+    holds(&k, &mut a, &mut b, gap);
+}
+
+#[test]
+fn boxes_overlapping_in_a_face_meet() {
+    let mut k = k();
+    let mut a = cube(&mut k, [0.0; 3], 1.0);
+    let mut b = cube(&mut k, [1.0, 0.5, 0.5], 1.0);
+    verdict_is(&k, &mut a, &mut b, 1e-12, Verdict::Yes);
+}
+
+#[test]
+fn an_edge_resting_on_a_face_meets_it() {
+    let mut k = k();
+    let mut a = cube(&mut k, [0.0; 3], 1.0);
+    // a cube centred on the x axis, turned 45 degrees about it (either way: it is square), is
+    // a diamond whose lowest edge is at z = -sqrt(2)/2; moved onto a's top face
+    let mut b = cube(&mut k, [0.0, -0.5, -0.5], 1.0);
+    let half = std::f64::consts::FRAC_1_SQRT_2;
+    turned_about_x(
+        &mut k,
+        &mut b,
+        std::f64::consts::FRAC_PI_4,
+        [0.0, 0.5, 1.0 + half],
+    );
+    let c = meets(&k, &mut a, &mut b, 1e-12).unwrap();
+    assert_eq!(c.verdict, Verdict::Yes, "{c:?}");
+    let [p, _] = c.witness.unwrap();
+    assert!((p.z - 1.0).abs() <= 1e-9, "{c:?}");
+}
+
+#[test]
+fn interpenetrating_boxes_meet() {
+    let mut k = k();
+    let mut a = cube(&mut k, [0.0; 3], 1.0);
+    let mut b = cube(&mut k, [0.5; 3], 1.0);
+    verdict_is(&k, &mut a, &mut b, 1e-12, Verdict::Yes);
+}
+
+#[test]
+fn a_box_inside_another_meets_it_and_their_walls_are_one_apart() {
+    let mut k = k();
+    let mut a = cube(&mut k, [0.0; 3], 3.0);
+    let mut b = cube(&mut k, [1.0; 3], 1.0);
+    verdict_is(&k, &mut a, &mut b, 1e-3, Verdict::Yes);
+    verdict_is(&k, &mut b, &mut a, 1e-3, Verdict::Yes);
+    holds(&k, &mut a, &mut b, 1.0);
+}
+
+#[test]
+fn boxes_far_apart_do_not_meet_and_their_gap_is_bracketed() {
+    let mut k = k();
+    let mut a = cube(&mut k, [0.0; 3], 1.0);
+    let mut b = cube(&mut k, [5.0, 0.0, 0.0], 1.0);
+    verdict_is(&k, &mut a, &mut b, 0.1, Verdict::No);
+    holds(&k, &mut a, &mut b, 4.0);
+}
+
+#[test]
+fn spheres_apart_are_their_centres_gap_less_their_radii() {
+    let mut k = k();
+    let mut a = create_sphere(&mut k, Point3::new(0.0, 0.0, 0.0), 1.0).unwrap();
+    let mut b = create_sphere(&mut k, Point3::new(3.0, 0.0, 0.0), 1.0).unwrap();
+    verdict_is(&k, &mut a, &mut b, 0.5, Verdict::No);
+    verdict_is(&k, &mut a, &mut b, 2.0, Verdict::Yes);
+    holds(&k, &mut a, &mut b, 1.0);
+}
+
+#[test]
+fn crossing_spheres_meet_where_their_surfaces_cross() {
+    let mut k = k();
+    let mut a = create_sphere(&mut k, Point3::new(0.0, 0.0, 0.0), 1.0).unwrap();
+    let mut b = create_sphere(&mut k, Point3::new(1.5, 0.0, 0.0), 1.0).unwrap();
+    let c = meets(&k, &mut a, &mut b, 1e-9).unwrap();
+    assert_eq!(c.verdict, Verdict::Yes, "{c:?}");
+    // the witness is on the circle where they cross: x = 0.75, |p| = 1
+    let [p, _] = c.witness.unwrap();
+    assert!((p.x - 0.75).abs() <= 1e-6, "{c:?}");
+}
+
+#[test]
+fn a_cylinder_crossing_a_box_face_meets_the_box() {
+    let mut k = k();
+    let mut a = cube(&mut k, [0.0; 3], 1.0);
+    let mut b = create_cylinder(&mut k, Point3::new(0.5, 0.5, 0.5), 0.3, 1.0).unwrap();
+    verdict_is(&k, &mut a, &mut b, 1e-9, Verdict::Yes);
+}
+
+/// A cylinder touching a box side along a line meets it; moved 0.25 off, its bracket holds
+/// 0.25 and the verdicts either side of it are exact.
+///
+/// The bracket is not 1e-6 wide here: trimmed rim pieces stall `lower` at 0.25 - 0.0013 (the
+/// end caps' pieces at the rim straddle the circular trim, and each hull carries a sliver of
+/// the cap's plane outside the disk toward the box; their subdivision runs out of pairs
+/// first). The bracket contains the truth; verdicts outside [0.2487, 0.25] are exact. The
+/// width asserted is what the pair budget certifies, not a target.
+#[test]
+fn a_cylinder_against_a_box_side_meets_it_along_a_line() {
+    let mut k = k();
+    let mut a = cube(&mut k, [0.0; 3], 1.0);
+    let mut b = create_cylinder(&mut k, Point3::new(1.5, 0.5, 0.0), 0.5, 1.0).unwrap();
+    verdict_is(&k, &mut a, &mut b, 1e-9, Verdict::Yes);
+    let mut far = create_cylinder(&mut k, Point3::new(1.75, 0.5, 0.0), 0.5, 1.0).unwrap();
+    verdict_is(&k, &mut a, &mut far, 0.24, Verdict::No);
+    verdict_is(&k, &mut a, &mut far, 0.26, Verdict::Yes);
+    let c = boundary_distance(&k, &mut a, &mut far, 1e-6).unwrap();
+    assert!(c.lower <= 0.25 && 0.25 <= c.upper, "{c:?}");
+    assert!(c.lower >= 0.2487 && c.upper - 0.25 <= 1e-12, "{c:?}");
+}
+
+#[test]
+fn a_peg_through_a_hole_it_clears_does_not_meet_the_plate() {
+    let mut k = k();
+    // a 4 x 4 x 1 plate with a hole of radius 1 through its middle, and a peg of radius 0.75
+    // down the hole's axis: the peg clears the hole's wall by 0.25
+    let plate = create_box(&mut k, Point3::new(0.0, 0.0, 0.0), 4.0, 4.0, 1.0).unwrap();
+    let hole = create_cylinder(&mut k, Point3::new(2.0, 2.0, -1.0), 1.0, 3.0).unwrap();
+    let mut plate = boolean_difference(&mut k, plate, hole).unwrap();
+    let mut peg = create_cylinder(&mut k, Point3::new(2.0, 2.0, -2.0), 0.75, 5.0).unwrap();
+    verdict_is(&k, &mut plate, &mut peg, 0.1, Verdict::No);
+    holds(&k, &mut plate, &mut peg, 0.25);
+}

solidcore/crates/solidcore/tests/extend_short_arc_long_rulings.rs

@@ -1,8 +1,8 @@
-//! A cylinder wall of a short arc far from the origin, extended 1500 mm along its rulings and
-//! round its axis. The iso that certifies the turn is interpolated between rulings 3 m long.
-//! At 500 mm the certificate took its rounding at the iso's own size and refused; at 1500 mm a
-//! weight ratio per row, differing by the continuation's rounding, took the iso out of its
-//! plane by 1.8e-10. Every point of the result stays on the cylinder, radius 80 about its axis.
+//! A cylinder wall of a short arc far from the origin, extended 500 and 1500 mm along its
+//! rulings and round its axis. The iso that certifies the turn is interpolated between rulings
+//! up to 3 m long: a weight ratio per row, differing by the continuation's rounding, took it out
+//! of its plane by 1.8e-10, and the certificate refused the extension as not exact. Every point
+//! of the result stays on the cylinder, radius 80 about its axis.
 #![allow(
     clippy::unwrap_used,
     clippy::expect_used,
@@ -16,9 +16,11 @@ use solidcore::kernel::UpstreamFixes;
 use solidcore::math::{Point2, Point3, Vec3};
 use solidcore::primitive::api_curves as curves;
 use solidcore::primitive::api_primitives::create_box;
+use solidcore::surface::cone::p1::Cone;
 use solidcore::surface::extend::Continuity;
 use solidcore::surface::implicit::AnalyticSupport;
 use solidcore::surface::side::BoxSide;
+use solidcore::surface::surface::Surface;
 use solidcore::sweep::api_brep::create_linear_sweep;
 use solidcore::topology::brep::p1 as bp1;
 use solidcore::{Brep, Kernel};
@@ -108,3 +110,46 @@ fn a_short_arc_extends_along_long_rulings_on_its_cylinder() {
         }
     }
 }
+
+/// A cylinder of radius 1, 60 degrees round and 1 high at the origin, extended along its
+/// rulings and round its axis by up to 1e5: the frame's size stays the source's (about 1)
+/// while the rows grow to the extension, so this is where a limit at the iso's own size
+/// could fall under its rounding. Every point stays on the cylinder.
+#[test]
+fn a_small_arc_extends_far_beyond_its_size_on_its_cylinder() {
+    let k = Kernel::default();
+    let wall = Surface::from(Cone::new_cylinder_bounded(
+        Vec3::new(0.0, 0.0, 0.0),
+        Vec3::new(1.0, 0.0, 0.0),
+        Vec3::new(0.0, 1.0, 0.0),
+        1.0,
+        0.0,
+        60.0,
+        1.0,
+        false,
+        false,
+        false,
+    ));
+    for d in [1e2, 1e3, 1e4, 1e5] {
+        let grown = wall
+            .extended_sides_keeping_parameters(&k, &BoxSide::ALL, Continuity::Ruled, d)
+            .unwrap_or_else(|e| panic!("{d}: {e}"))
+            .surface;
+        let dom = grown.natural_uv_domain_with_nurb(&k).unwrap();
+        let (u, v) = (dom.u_interval(), dom.v_interval());
+        for i in 0..=8 {
+            for j in 0..=8 {
+                let uv = Point2::new(
+                    u.min() + u.length() * f64::from(i) / 8.0,
+                    v.min() + v.length() * f64::from(j) / 8.0,
+                );
+                let x = grown.evaluate_point(&k, uv).unwrap();
+                let r = x.x.hypot(x.y);
+                assert!(
+                    (r - 1.0).abs() < 1e-9 * (1.0 + x.z.abs()),
+                    "{d} {i} {j} {r}"
+                );
+            }
+        }
+    }
+}

solidcore/crates/solidcore/tests/far_sphere_recognised.rs

@@ -0,0 +1,213 @@
+//! A sphere's NURBS form is recognised as its sphere far from the origin, at any radius and
+//! orientation, and the half-meridian test allows the angles' rounding at the points' size,
+//! no more (#3131). A sphere of radius 2.5 at 1e5 reads 180 + 6.7e-10 degrees, past the fixed
+//! half-meridian tolerance, and was not recognised.
+#![allow(
+    clippy::unwrap_used,
+    clippy::expect_used,
+    clippy::panic,
+    clippy::indexing_slicing
+)] // test helpers
+
+use solidcore::blend::fillet_section::station::as_b_spline;
+use solidcore::curve::curve::Curve;
+use solidcore::geom::axis2_placement::Axis2Placement;
+use solidcore::geom::extent2d::Extent2d;
+use solidcore::math::{Point3, Vec3};
+use solidcore::nurbs::b_spline_curve::{BSplineCurve, NurbCircleParam};
+use solidcore::nurbs::b_spline_surface::BSplineSurface;
+use solidcore::nurbs::math::gamma;
+use solidcore::nurbs::srf_basic::Surface as Net;
+use solidcore::primitive::api_primitives::create_sphere;
+use solidcore::surface::implicit::AnalyticSupport;
+use solidcore::surface::sphere::Sphere;
+use solidcore::surface::surf_of_revolution::SurfOfRevolution;
+use solidcore::surface::surface::Surface;
+use solidcore::topology::brep::p1 as bp1;
+use solidcore::Kernel;
+
+/// The allowance the recogniser adds, as a position: `4 gamma_K (1 + |corners| + 2 r)`,
+/// `K = 16 (2 + 2 + 2)` for a form of degrees (2, 2) (written out so that a change to the
+/// allowance fails). In degrees it is this over `r`, turned to degrees.
+fn allowance_position(form: &BSplineSurface, r: f64) -> f64 {
+    let d = form.natural_uv_domain();
+    let corners = form
+        .evaluate_point(d.min())
+        .unwrap()
+        .max_dimension()
+        .max(form.evaluate_point(d.max()).unwrap().max_dimension());
+    4.0 * gamma(16 * 6) * (1.0 + corners + 2.0 * r)
+}
+
+/// The NURBS form of a sphere of radius `r` at `c`, turned by `turn` degrees about the axis
+/// (1, 1, 1) when it is not 0, and its label.
+fn form_at(k: &mut Kernel, c: Point3, r: f64, turn: f64) -> (BSplineSurface, AnalyticSupport) {
+    let b = create_sphere(k, Point3::new(0.0, 0.0, 0.0), r).unwrap();
+    let f = bp1::faces(&b, None).unwrap()[0];
+    let mut s = b
+        .face(f)
+        .unwrap()
+        .surface
+        .as_ref()
+        .unwrap()
+        .copy(k)
+        .unwrap();
+    // turned about (1, 1, 1) by `turn`, then moved to `c`
+    let a = turn.to_radians();
+    let n = Vec3::new(1.0, 1.0, 1.0) * (1.0 / 3.0_f64.sqrt());
+    let rot = |v: Vec3| v * a.cos() + n.cross(v) * a.sin() + n * (n.dot(v) * (1.0 - a.cos()));
+    let mut place = Axis2Placement::default();
+    place
+        .set_canonical(
+            c,
+            rot(Vec3::new(1.0, 0.0, 0.0)),
+            rot(Vec3::new(0.0, 1.0, 0.0)),
+        )
+        .unwrap();
+    s.transform(k, &place, None).unwrap();
+    let form = as_b_spline(k, &s).unwrap().unwrap().into_owned();
+    (form, AnalyticSupport::of(&s).unwrap())
+}
+
+/// Recognised at radii 1e-3 to 1e3, 0 to 1e7 from the origin (at most 1e9 radii out), on the
+/// axes and turned off them, with its radius and centre within the allowance as a position.
+#[test]
+fn a_far_sphere_is_recognised_on_its_own_numbers() {
+    let mut k = Kernel::default();
+    for r in [1e-3, 1.0, 2.5, 1e3] {
+        for off in [0.0, 1e3, 1e5, 1e6, 1e7] {
+            // a sphere of radius 1e-3 at 1e7, ten orders apart: upstream's iso-circle test
+            // fails with a status there (1001), before any angle is read; unchanged here
+            if off > 1e9 * r {
+                continue;
+            }
+            for turn in [0.0, 37.0] {
+                let c = Point3::new(off, off, off + 10.0);
+                let (form, _) = form_at(&mut k, c, r, turn);
+                let found = Sphere::is_nurb_surface_sphere(&k, &form, 1.0)
+                    .unwrap()
+                    .unwrap_or_else(|| panic!("not recognised: r {r} at {off}, turned {turn}"));
+                let AnalyticSupport::Sphere { placement, radius } =
+                    AnalyticSupport::of(&Surface::from(found)).unwrap()
+                else {
+                    panic!("not a sphere");
+                };
+                let tol = allowance_position(&form, r);
+                assert!((radius - r).abs() <= tol, "r {r} at {off}: radius {radius}");
+                assert!(
+                    (placement.origin() - c).length() <= tol,
+                    "r {r} at {off}: centre {:e} past {tol:e}",
+                    (placement.origin() - c).length()
+                );
+            }
+        }
+    }
+}
+
+/// A half meridian of `180 + extra` degrees, radius `r`, at `c`: a circle arc from -90 to
+/// `90 + extra` degrees in the plane y = c.y, turned a quarter turn about the vertical.
+fn long_meridian(k: &Kernel, c: Point3, r: f64, extra: f64) -> BSplineSurface {
+    let mut frame = Axis2Placement::default();
+    frame
+        .set_canonical(c, Vec3::new(1.0, 0.0, 0.0), Vec3::new(0.0, 0.0, 1.0))
+        .unwrap();
+    let generator = BSplineCurve::create_circle_segment(
+        3,
+        &frame,
+        r,
+        -90.0,
+        90.0 + extra,
+        NurbCircleParam::Quadratic,
+    )
+    .unwrap();
+    let mut sor = SurfOfRevolution::new(
+        k,
+        Curve::from(generator),
+        c,
+        Vec3::new(1.0, 0.0, 0.0),
+        Vec3::new(0.0, 1.0, 0.0),
+        Extent2d::from_bounds(0.0, -90.0, 90.0, 90.0 + extra),
+        false,
+    )
+    .unwrap();
+    sor.make_nurb(k).unwrap();
+    as_b_spline(k, &Surface::from(sor))
+        .unwrap()
+        .unwrap()
+        .into_owned()
+}
+
+/// The half meridian is allowed `1e-12` degrees (upstream) plus the angles' rounding at the
+/// points' size. A meridian `d` past 180 degrees also folds the generator's STEP interval
+/// against the sphere's latitudes by `2 d` (a point past the pole reads latitude `90 - d`),
+/// held to the same allowance. So a meridian 0.4 of the allowance past is recognised (both
+/// tests pass; halve the allowance and the fold, 0.8 of it, is refused) and one twice the
+/// allowance past is refused, at the origin and at 1e5. A doubled allowance is caught by
+/// `sphere.rs`'s own unit test of `meridian_rounding` against its closed form.
+#[test]
+fn the_half_meridian_is_allowed_its_rounding_and_no_more() {
+    let k = Kernel::default();
+    let r = 2.5;
+    for off in [0.0, 1e5] {
+        let c = Point3::new(off, off, off + 10.0);
+        let exact = long_meridian(&k, c, r, 0.0);
+        let allowed = 1e-12 + (allowance_position(&exact, r) / r).to_degrees();
+        let over = long_meridian(&k, c, r, 2.0 * allowed);
+        assert!(
+            Sphere::is_nurb_surface_sphere(&k, &over, 1.0)
+                .unwrap()
+                .is_none(),
+            "at {off}: 180 + {:e} degrees recognised",
+            2.0 * allowed
+        );
+        let under = long_meridian(&k, c, r, 0.4 * allowed);
+        assert!(
+            Sphere::is_nurb_surface_sphere(&k, &under, 1.0)
+                .unwrap()
+                .is_some(),
+            "at {off}: 180 + {:e} degrees refused",
+            0.4 * allowed
+        );
+    }
+}
+
+/// A form or a label 1e-3 off the sphere is refused at every offset to 1e6: the label by
+/// `lies_on` (`AnalyticSupport::build`), the form by the iso-circle tests. Neither reaches
+/// the angle allowance; they show the allowance did not open what those tests close. At 1e7
+/// the iso-circle tests' own tolerance, `100 SM_EFF_ZERO (1 + |corners|)` (about 2e-3),
+/// admits a 1e-3 move: upstream's, unchanged here.
+#[test]
+fn a_form_or_label_1e3_off_is_refused_to_1e6() {
+    let mut k = Kernel::default();
+    for off in [0.0, 1e3, 1e4, 1e5, 1e6] {
+        let c = Point3::new(off, off, off + 10.0);
+        let (form, support) = form_at(&mut k, c, 2.5, 0.0);
+        let AnalyticSupport::Sphere { placement, radius } = support else {
+            panic!("a sphere");
+        };
+        let off_label = AnalyticSupport::Sphere {
+            placement,
+            radius: radius + 1e-3,
+        };
+        assert!(off_label.build(&k, form.copy()).is_err(), "label at {off}");
+        let net = form.gw_nurb().unwrap();
+        let mut cpts = net.cpts();
+        let (i, j) = (cpts.len() / 2, cpts[0].len() / 2);
+        let w = cpts[i][j].w;
+        cpts[i][j].x += 1e-3
+            * if w == solidcore::nurbs::math::NOW {
+                1.0
+            } else {
+                w
+            };
+        let (p, q) = net.degrees();
+        let moved = Net::new(cpts, p, q, net.u_knots().to_vec(), net.v_knots().to_vec()).unwrap();
+        let moved = BSplineSurface::from_gw_nurb(&moved);
+        assert!(
+            Sphere::is_nurb_surface_sphere(&k, &moved, 1.0)
+                .unwrap()
+                .is_none(),
+            "form at {off}"
+        );
+    }
+}

solidcore/crates/solidcore/tests/issue_2343_curved_setback.rs

@@ -1363,3 +1363,82 @@ fn d_prism_asked_past_the_rails_names_the_setback_that_fits() {
         }
     }
 }
+
+/// The least distance from the prism's axis of the top face's spring curve at the corner of
+/// [`d_prism_eight_case`] when every setback is `s`, by its closed form: the top is a plane,
+/// so the spring curve is the parabola (P, X, Q) itself, P on the chord's rail x = 7, `s`
+/// along the chord from V, Q on the arc's rail rho = 8, `s` along the arc from V, and X where
+/// the rails' tangents there cross. The least over 20000 even steps of the parabola's
+/// parameter (each a few millionths long).
+fn top_spring_least_rho(s: f64) -> f64 {
+    let p = (7.0, 6.0 - s);
+    let psi = 6.0f64.atan2(8.0) + s / 10.0;
+    let q = (8.0 * psi.cos(), 8.0 * psi.sin());
+    let along = (7.0 - q.0) / psi.sin();
+    let x = (7.0, q.1 - along * psi.cos());
+    (0..=20000)
+        .map(|i| {
+            let t = f64::from(i) / 20000.0;
+            let (a, b, c) = ((1.0 - t) * (1.0 - t), 2.0 * t * (1.0 - t), t * t);
+            (a * p.0 + b * x.0 + c * q.0).hypot(a * p.1 + b * x.1 + c * q.1)
+        })
+        .fold(f64::INFINITY, f64::min)
+}
+
+/// #2343 (d), "a thin flat strip beside a cylinder": the bored D prism (bore R 6.9) asked 8.5
+/// at V. By the closed form above its top face's spring curve dips into the bore from asked
+/// 7.8068; main built asked 7.8 (the spring curve 6e-4 clear of the bore) and refused 8 to
+/// 9.5 late, "a round kept round a feature does not close on the body", naming nothing. The
+/// corner checks what it takes out of the top: refused as `SetbackTooLong` at V, naming the
+/// largest setback on 8.5's grid of thousandths whose spring curve stays on the face, 0.918 x
+/// 8.5 = 7.803 (3.3e-4 clear of the bore; the next, 7.8115, 4.1e-4 into it). Asked that, the
+/// corner builds, graded as the corners above.
+#[test]
+fn bored_d_prism_spring_curve_leaving_the_top_names_the_setback_that_keeps_it() {
+    let (bore, asked, step) = (6.9, 8.5, 8.5 / 1000.0);
+    let (mut k, mut b, edges, case) = d_prism_eight_case(Some(bore), 14);
+    let v = vertex_at(&b, case.v);
+    let r = round_asked(
+        &mut k,
+        &mut b,
+        &edges,
+        &[1.0, 1.5, 2.0],
+        case.v,
+        Some(asked),
+    );
+    assert_eq!(r.event, Some(BlendCornerEvent::Setback), "{}", r.reason);
+    assert!(!r.ok, "asked {asked}: built");
+    let named = match r.refusal {
+        Some(BlendRefusal::SetbackTooLong { vertex, largest }) => {
+            assert_eq!(vertex, v);
+            largest
+        }
+        other => panic!("{other:?}, {}", r.reason),
+    };
+    // on the grid, its spring curve clear of the bore, the next one's not
+    let grid = (named / step).round();
+    assert!((grid * step - named).abs() <= 1e-12, "{named} off the grid");
+    assert!(
+        top_spring_least_rho(named) > bore,
+        "{named}: {}",
+        top_spring_least_rho(named)
+    );
+    assert!(
+        top_spring_least_rho(named + step) < bore,
+        "{}: {}",
+        named + step,
+        top_spring_least_rho(named + step)
+    );
+    let (mut k, mut b, edges, case) = d_prism_eight_case(Some(bore), 14);
+    let r = round_asked(
+        &mut k,
+        &mut b,
+        &edges,
+        &[1.0, 1.5, 2.0],
+        case.v,
+        Some(named),
+    );
+    assert!(r.ok, "asked {named}: {}", r.reason);
+    graded(&mut k, &mut b, &case, 3);
+    kept_definitions(&k, &b, &case, 3);
+}

solidcore/crates/solidcore/tests/issue_2972_volume_sign_enclosure.rs

@@ -0,0 +1,322 @@
+//! Regression tests for tangency-labs/solidcore#2972: a body's volume sign is read from a
+//! certified enclosure `[lo, hi]` of its volume, not from a quadrature estimate.
+//!
+//! - A thin quarter shell (radius 1e4, thickness 1e-3, length 10) is a valid solid whose
+//!   volume, 157.08, lies below the estimate's error at the sign test's accuracy (the
+//!   estimate at 1e-3 reads -180.05): its enclosure holds the closed form and is positive,
+//!   and `is_outward_solid` calls it a solid.
+//! - A box with one edge rounded (radius 3) is enclosed to a millionth of its volume,
+//!   around the closed form `24000 - 40 * 9 * (1 - pi / 4)`, on the default kernel and with
+//!   the rounds' definitions on.
+//! - A box, and the same box with its material outside (every face's material side
+//!   swapped), decide positive and negative with enclosures holding +120 and -120; a
+//!   sphere (seam and poles) holds `4/3 pi r^3`.
+//! - The same box with one side's surface moved out by 1e-3 and its trims kept: the faces
+//!   no longer meet, and the closed surface the enclosure bounds (the faces and the strips
+//!   across their gaps) holds 120 + 30e-3, which the faces alone do not.
+//! - Two unit cubes touching along an edge (their union: four face sides at that edge,
+//!   paired by sense) are enclosed around 2.
+//! - A G2 round of the box edge (its net rational of degree 7 across, whose weights an
+//!   interval proves positive only over small boxes) decides, around the round's volume:
+//!   as a bare net, and as a procedural blend whose net is certified within a bound above 0
+//!   of its definition, read on its net (#3170 widens by that bound).
+//! - The quarter shell R 10, t 1e-6 passes the check, but its faces' boundaries lie apart
+//!   by about its thickness: the sign is undecided, early (the strips between them hold 0
+//!   whatever the cells become), and `is_outward_solid` reads that as "not a solid". A box
+//!   with an offset-surface face cannot be read at all: an error, not a sign.
+//! - `nurb_fillet.smb` (a sphere with a pocket) decides positive: its sphere face's loop
+//!   closes along the pole, from trim ends a unit in the last place off the net's last
+//!   knot, a segment whose 3D length is of the order of rounding.
+#![allow(clippy::unwrap_used, clippy::panic)]
+
+use solidcore::blend::fillet_executive::api::fillet_edges;
+use solidcore::blend::fillet_section::section::GN_THUMBWEIGHT_EQUAL_AREA;
+use solidcore::boolean::api_brep::boolean_union;
+use solidcore::geom::axis2_placement::Axis2Placement;
+use solidcore::kernel::{KernelOptions, UpstreamFixes};
+use solidcore::mass::enclosure::{
+    enclose_volume, volume_sign, VolumeEnclosure, VolumeSign, CELL_BUDGET,
+};
+use solidcore::math::{Point3, Vec3, PI};
+use solidcore::primitive::api_primitives::{create_box, create_cylindrical_box, create_sphere};
+use solidcore::query::api_queries::edge_closest_point;
+use solidcore::surface::offset_surface::OffsetSurface;
+use solidcore::surface::surface::Surface;
+use solidcore::topology::brep::is_outward_solid;
+use solidcore::topology::brep::p1::{faces, regions};
+use solidcore::topology::brep::validation::{check_brep, CheckLevel};
+use solidcore::SolidError;
+use solidcore::{Brep, Kernel};
+
+/// The quarter shell between radii `r` and `r + t` about Z, length 10.
+fn quarter_shell(k: &mut Kernel, r: f64, t: f64) -> Brep {
+    create_cylindrical_box(k, Point3::new(0.0, 0.0, 0.0), 10.0, r, r + t, 0.0, 90.0).unwrap()
+}
+
+fn shell_volume(r: f64, t: f64) -> f64 {
+    PI / 4.0 * ((r + t) * (r + t) - r * r) * 10.0
+}
+
+/// The box 40 x 30 x 20 with its edge through (20, 30, 20) rounded at radius 3.
+fn rounded_box(k: &mut Kernel) -> Brep {
+    rounded_box_by(k, 1, 1, 1.0)
+}
+
+/// [`rounded_box`] with `fillet_edges`' section kind, order and thumbweight.
+fn rounded_box_by(k: &mut Kernel, kind: u32, order: u32, weight: f64) -> Brep {
+    let mut b = create_box(k, Point3::new(0.0, 0.0, 0.0), 40.0, 30.0, 20.0).unwrap();
+    let q = Point3::new(20.0, 30.0, 20.0);
+    let e = b
+        .edge_list()
+        .iter()
+        .copied()
+        .find(|&e| edge_closest_point(k, &b, e, q).is_ok_and(|c| c.closest.distance < 1e-9))
+        .unwrap();
+    fillet_edges(k, &mut b, &[e], 3.0, kind, order, weight).unwrap();
+    b
+}
+
+/// Every fix on but the G2 one, as SolidCraft runs: the round is an exact round, a
+/// definition with bound 0.
+fn definitions_kernel() -> Kernel {
+    let mut k = Kernel::new(&KernelOptions::default());
+    let mut f = UpstreamFixes::default();
+    for &name in UpstreamFixes::NAMES {
+        if name != "geometric_g2_continuity" {
+            *f.flag_mut(name).unwrap() = true;
+        }
+    }
+    k.fixes = f;
+    k
+}
+
+fn holds(e: &VolumeEnclosure, v: f64) -> bool {
+    e.lo <= v && v <= e.hi
+}
+
+#[test]
+fn a_thin_shell_below_the_estimates_error_decides_positive() {
+    for (r, t) in [(1e4, 1e-3), (10.0, 1e-4)] {
+        let mut k = Kernel::default();
+        let mut b = quarter_shell(&mut k, r, t);
+        let v = shell_volume(r, t);
+        match volume_sign(&k, &mut b).unwrap() {
+            VolumeSign::Positive(e) => assert!(holds(&e, v), "r {r} t {t}: {e:?} misses {v}"),
+            other => panic!("r {r} t {t}: {other:?}, volume {v}"),
+        }
+        // the solid test reads the same sign: on the estimate (-180.05 at r 1e4) it was false
+        let mut b = quarter_shell(&mut k, r, t);
+        assert!(is_outward_solid(&mut k, &mut b).unwrap(), "r {r} t {t}");
+    }
+}
+
+#[test]
+fn a_rounded_box_is_enclosed_around_its_closed_form() {
+    let v = 24000.0 - 40.0 * 9.0 * (1.0 - PI / 4.0);
+    for (name, mut k) in [
+        ("default", Kernel::default()),
+        ("definitions", definitions_kernel()),
+    ] {
+        let mut b = rounded_box(&mut k);
+        let e = enclose_volume(&k, &mut b, 1e-6 * v).unwrap();
+        assert!(holds(&e, v), "{name}: {e:?} misses {v}");
+        assert!(e.width() <= 1e-6 * v, "{name}: {e:?} wider than 1e-6 V");
+        let mut b = rounded_box(&mut k);
+        let s = volume_sign(&k, &mut b).unwrap();
+        assert!(
+            matches!(s, VolumeSign::Positive(e) if holds(&e, v)),
+            "{name}: {s:?}"
+        );
+    }
+}
+
+#[test]
+fn a_box_and_its_inside_out_twin_decide_their_signs() {
+    let mut k = Kernel::default();
+    let mut b = create_box(&mut k, Point3::new(1.0, 2.0, 3.0), 4.0, 5.0, 6.0).unwrap();
+    let e = enclose_volume(&k, &mut b, 1e-9).unwrap();
+    assert!(holds(&e, 120.0) && e.width() <= 1e-9, "{e:?}");
+    // the material outside: every face's material side is the other one
+    for r in regions(&b, None).unwrap() {
+        let g = b.region_mut(r).unwrap();
+        g.is_void = 1 - g.is_void;
+    }
+    match volume_sign(&k, &mut b).unwrap() {
+        VolumeSign::Negative(e) => assert!(holds(&e, -120.0), "{e:?}"),
+        other => panic!("{other:?}"),
+    }
+}
+
+#[test]
+fn a_sphere_is_enclosed_across_its_seam_and_poles() {
+    let mut k = Kernel::default();
+    let mut b = create_sphere(&mut k, Point3::new(0.0, 0.0, 0.0), 2.0).unwrap();
+    let v = 4.0 / 3.0 * PI * 8.0;
+    let e = enclose_volume(&k, &mut b, 1e-6).unwrap();
+    assert!(holds(&e, v) && e.width() <= 1e-6, "{e:?} misses {v}");
+}
+
+#[test]
+fn a_gap_between_faces_is_closed_by_its_strips() {
+    let mut k = Kernel::default();
+    let mut b = create_box(&mut k, Point3::new(1.0, 2.0, 3.0), 4.0, 5.0, 6.0).unwrap();
+    // the side x = 5 (5 x 6) moved out by delta, its trims and its neighbours kept
+    let delta = 1e-3;
+    let side = faces(&b, None)
+        .unwrap()
+        .into_iter()
+        .find(|&f| {
+            let face = b.face(f).unwrap();
+            let s = face.surface.as_ref().unwrap();
+            s.evaluate_point(&k, face.uv_domain.mid())
+                .is_ok_and(|p| (p.x - 5.0).abs() < 1e-12)
+        })
+        .unwrap();
+    let mut shift = Axis2Placement::default();
+    shift.translate(Vec3::new(delta, 0.0, 0.0));
+    b.face_mut(side)
+        .unwrap()
+        .surface
+        .as_mut()
+        .unwrap()
+        .transform(&k, &shift, None)
+        .unwrap();
+    let v = 120.0 + 30.0 * delta;
+    let e = enclose_volume(&k, &mut b, 1.0).unwrap();
+    assert!(holds(&e, v) && e.counts.strips > 0, "{e:?} misses {v}");
+    assert!(matches!(
+        volume_sign(&k, &mut b).unwrap(),
+        VolumeSign::Positive(_)
+    ));
+}
+
+/// `upstream/TestFiles/pt_TestFiles/Solids/nurb_fillet.smb`, read and healed; `None` where
+/// the upstream test files are not present.
+fn nurb_fillet(k: &mut Kernel) -> Option<Brep> {
+    use solidcore::geom::attribute::{AttributeStore, ObjectKey};
+    use solidcore::geom::object::ObjectRef;
+    use solidcore::topology::brep::p10::TopologyEnv;
+    use solidcore::topology::brep::p7::read_from_file;
+    use solidcore::topology::database_io::FileType;
+    use solidcore::topology::topology::NotifyRecords;
+    use solidcore::EntityRef;
+    let path = std::path::Path::new(env!("CARGO_MANIFEST_DIR"))
+        .join("../../upstream/TestFiles/pt_TestFiles/Solids/nurb_fillet.smb");
+    let Ok(bytes) = std::fs::read(&path) else {
+        assert!(
+            std::env::var_os("SOLIDCORE_REQUIRE_UPSTREAM").is_none(),
+            "SOLIDCORE_REQUIRE_UPSTREAM is set and the upstream test file is missing: {}",
+            path.display()
+        );
+        return None;
+    };
+    let mut b = Brep::new_with_infinite_region().unwrap();
+    let mut records = NotifyRecords::new();
+    let mut attributes = AttributeStore::default();
+    let key = |_: EntityRef| ObjectRef {
+        key: ObjectKey(0),
+        type_code: 0,
+    };
+    let mut env = TopologyEnv {
+        all_attributes: &[],
+        attributes: &mut attributes,
+        key_of: &key,
+        records: &mut records,
+        next_key: 1 << 50,
+    };
+    read_from_file(k, &mut b, bytes, FileType::Ascii, false, &mut env).unwrap();
+    b.use_arena_naming().unwrap();
+    Some(b)
+}
+
+#[test]
+fn a_sphere_closed_along_its_pole_decides() {
+    let mut k = Kernel::default();
+    let Some(mut b) = nurb_fillet(&mut k) else {
+        return;
+    };
+    let s = volume_sign(&k, &mut b).unwrap();
+    assert!(matches!(s, VolumeSign::Positive(_)), "{s:?}");
+}
+
+#[test]
+fn solids_touching_along_an_edge_pair_their_sides() {
+    let mut k = Kernel::default();
+    let a = create_box(&mut k, Point3::new(0.0, 0.0, 0.0), 1.0, 1.0, 1.0).unwrap();
+    let c = create_box(&mut k, Point3::new(1.0, 1.0, 0.0), 1.0, 1.0, 1.0).unwrap();
+    let mut b = boolean_union(&mut k, a, c).unwrap();
+    let e = enclose_volume(&k, &mut b, 1e-9).unwrap();
+    assert!(holds(&e, 2.0) && e.width() <= 1e-9, "{e:?}");
+}
+
+#[test]
+fn a_g2_round_decides_around_its_volume() {
+    // the G^n section's flag and the one its plane rails need: the round a bare net
+    let mut bare = Kernel::default();
+    bare.fixes.fillet_gn_section_generator = true;
+    bare.fixes.fillet_surface_plane_curve_on_plane_equation = true;
+    let v = 24000.0 - 40.0 * 9.0 * (1.0 - PI / 4.0);
+    for (name, mut k, certified) in [
+        ("bare net", bare, false),
+        ("definition", definitions_kernel(), true),
+    ] {
+        let mut b = rounded_box_by(&mut k, 2, 2, GN_THUMBWEIGHT_EQUAL_AREA);
+        // with the definitions on, the round is a procedural blend whose net is certified
+        // within a bound above 0: it is read on its net
+        let bounds: Vec<f64> = faces(&b, None)
+            .unwrap()
+            .into_iter()
+            .filter_map(|f| {
+                let s = b.face(f).unwrap().surface.as_ref().unwrap();
+                s.procedural_blend().map(|d| d.bound())
+            })
+            .collect();
+        if certified {
+            assert!(bounds.iter().any(|&e| e > 0.0), "{name}: {bounds:?}");
+        } else {
+            assert!(bounds.is_empty(), "{name}: {bounds:?}");
+        }
+        let e = enclose_volume(&k, &mut b, 1e-3 * v).unwrap();
+        assert!(
+            holds(&e, v) && e.width() <= 1e-3 * v,
+            "{name}: {e:?} misses {v}"
+        );
+        let mut b = rounded_box_by(&mut k, 2, 2, GN_THUMBWEIGHT_EQUAL_AREA);
+        let s = volume_sign(&k, &mut b).unwrap();
+        assert!(matches!(s, VolumeSign::Positive(_)), "{name}: {s:?}");
+    }
+}
+
+#[test]
+fn a_gap_as_large_as_the_volume_leaves_the_sign_undecided() {
+    let mut k = Kernel::default();
+    let shell = |k: &mut Kernel| quarter_shell(k, 10.0, 1e-6);
+    let mut b = shell(&mut k);
+    let c = check_brep(&mut k, &mut b, CheckLevel::Level2).unwrap();
+    assert!(c.lines().is_empty(), "{:?}", c.lines());
+    let v = shell_volume(10.0, 1e-6);
+    let mut b = shell(&mut k);
+    match volume_sign(&k, &mut b).unwrap() {
+        // undecided long before the budget: the strips settle
+        VolumeSign::Undecided(e) => {
+            assert!(holds(&e, v) && e.counts.cells < CELL_BUDGET / 4, "{e:?}");
+        }
+        other => panic!("{other:?}"),
+    }
+    // undecided is "not a solid" on purpose
+    let mut b = shell(&mut k);
+    assert!(!is_outward_solid(&mut k, &mut b).unwrap());
+}
+
+#[test]
+fn a_face_without_a_nurbs_form_is_an_error_not_a_sign() {
+    let mut k = Kernel::default();
+    let mut b = create_box(&mut k, Point3::new(0.0, 0.0, 0.0), 4.0, 5.0, 6.0).unwrap();
+    // one side's plane as an offset surface at distance 0: the same box
+    let f = faces(&b, None).unwrap()[0];
+    let base = b.face(f).unwrap().surface.as_ref().unwrap().clone();
+    let off = OffsetSurface::new(&k, 0.0, base, true, 0).unwrap();
+    b.face_mut(f).unwrap().surface = Some(Surface::from(off));
+    let r = volume_sign(&k, &mut b);
+    assert!(matches!(r, Err(SolidError::Unsupported { .. })), "{r:?}");
+}

solidcore/crates/solidcore/tests/issue_2975_stitch_gap_report.rs

@@ -0,0 +1,308 @@
+//! tangency-labs/solidcore#2975: the stitch reports, for every gap it closes, a
+//! certified bound on the gap and the tolerance growth its closure applied; an exact
+//! match's closure applies no growth.
+
+#![allow(
+    clippy::unwrap_used,
+    clippy::expect_used,
+    clippy::panic,
+    clippy::indexing_slicing
+)]
+
+use solidcore::geom::extent2d::Extent2d;
+use solidcore::geom::tol::USE_DEFAULT;
+use solidcore::math::{Point2, Vec3};
+use solidcore::surface::plane::Plane;
+use solidcore::surface::surface::Surface;
+use solidcore::topology::brep::p2::ArenaNotifyState;
+use solidcore::topology::brep::p3::new_brep;
+use solidcore::topology::brep::p5::{stitch_and_orient_reported, StitchAndOrientOptions};
+use solidcore::topology::brep::p8::{create_face_from_surface, FaceBuildEnv};
+use solidcore::topology::brep_cache::{arena_identity, CacheObject};
+use solidcore::topology::topology_traverser::Marks;
+use solidcore::{Brep, Kernel};
+
+/// Compare stored tolerance accounting independently of the reported bound.
+fn check_accounting(entry: &solidcore::heal::stitch::p2::ClosedGap) {
+    let increase = (entry.tolerance_after - entry.tolerance_before).max(0.0);
+    assert!(
+        entry.growth.is_finite() && entry.growth >= increase,
+        "{entry:?}"
+    );
+    if entry.tolerance_after <= entry.tolerance_before {
+        assert_eq!(entry.growth, 0.0);
+    }
+}
+
+/// Adds one square planar face on the plane `z = 0` over the 1 x 1 domain whose low
+/// corner is `x` on x and `y` on y.
+fn add_square(k: &mut Kernel, b: &mut Brep, x: f64, y: f64) {
+    let surface = Surface::from(Plane::from_normal(
+        Vec3::new(0.0, 0.0, 0.0),
+        Vec3::new(0.0, 0.0, 1.0),
+    ));
+    let mut state = ArenaNotifyState::new(b);
+    let mut env = state.env(None);
+    let mut marks = Marks::default();
+    let this_face = |face| arena_identity(CacheObject::Face(face));
+    let mut fenv = FaceBuildEnv {
+        env: &mut env,
+        marks: &mut marks,
+        this_face: &this_face,
+    };
+    let domain = Extent2d::from_points(Point2::new(x, y), Point2::new(x + 1.0, y + 1.0));
+    create_face_from_surface(k, b, Some(surface), &domain, &mut fenv).unwrap();
+}
+
+#[test]
+fn a_known_gap_reports_its_bound_and_the_growth_its_closure_applied() {
+    let gap = 1e-5;
+    let mut k = Kernel::default();
+    let mut b = new_brep(&mut k, USE_DEFAULT, USE_DEFAULT).unwrap();
+    add_square(&mut k, &mut b, 0.0, 0.0);
+    add_square(&mut k, &mut b, 1.0 + gap, 0.0);
+
+    let gaps = stitch_and_orient_reported(&mut k, &mut b, &StitchAndOrientOptions::default())
+        .expect("the stitch runs");
+    for entry in &gaps {
+        check_accounting(entry);
+    }
+    // The two corners glue: each reports the gap it held (the known offset the two
+    // squares put between them) and the growth the glue applied — the survivor's
+    // tolerance rose by the same amount, the glue's rule keeping the closed distance
+    // inside the surviving tolerance (solidcore#2975).
+    let corners: Vec<_> = gaps
+        .iter()
+        .filter(|entry| {
+            matches!(
+                entry.kind,
+                solidcore::heal::stitch::p2::ClosedGapKind::Vertex { .. }
+            )
+        })
+        .collect();
+    assert_eq!(corners.len(), 2, "{gaps:?}");
+    for entry in corners {
+        assert!(entry.gap >= (1.0 + gap) - 1.0, "{entry:?}");
+        assert!(
+            (entry.gap - gap).abs() <= 1e-9 * gap.max(1.0),
+            "reported {entry:?} against the known {gap:.1e}"
+        );
+        assert!(
+            (entry.growth - gap).abs() <= 1e-9 * gap.max(1.0),
+            "growth {entry:?} against the known {gap:.1e}"
+        );
+    }
+    // Gluing the vertices does not move the two underlying edge curves. Their
+    // whole-curve gap is still the original horizontal separation.
+    let shared = gaps
+        .iter()
+        .find(|entry| {
+            matches!(
+                entry.kind,
+                solidcore::heal::stitch::p2::ClosedGapKind::Edge { .. }
+            )
+        })
+        .expect("the shared edge closure");
+    assert!(
+        shared.gap >= (1.0 + gap) - 1.0 && shared.gap < gap + 1e-12,
+        "{shared:?}"
+    );
+}
+
+#[test]
+fn an_exact_match_reports_no_growth() {
+    let mut k = Kernel::default();
+    let mut b = new_brep(&mut k, USE_DEFAULT, USE_DEFAULT).unwrap();
+    add_square(&mut k, &mut b, 1.0, 0.0);
+    add_square(&mut k, &mut b, 0.0, 0.0);
+
+    let gaps = stitch_and_orient_reported(&mut k, &mut b, &StitchAndOrientOptions::default())
+        .expect("the stitch runs");
+    assert_eq!(
+        gaps.len(),
+        3,
+        "two endpoint glues and their shared edge: {gaps:?}"
+    );
+    for gap in gaps {
+        // Independently enclosing the two analytic line evaluations adds a
+        // conservative rounding floor, even though the geometric boundary agrees.
+        assert!(
+            gap.gap.is_finite() && (0.0..=1e-12).contains(&gap.gap),
+            "{gap:?}"
+        );
+        check_accounting(&gap);
+        assert!(
+            gap.growth == 0.0,
+            "the exact match's closure applied no growth: {gap:?}"
+        );
+    }
+}
+
+#[test]
+fn an_interior_vertex_split_reports_the_original_curve_gap() {
+    use solidcore::heal::stitch::p2::ClosedGapKind;
+    let mut k = Kernel::default();
+    let mut b = new_brep(&mut k, USE_DEFAULT, USE_DEFAULT).unwrap();
+    let gap = 1e-5;
+    add_square(&mut k, &mut b, 0.0, 0.0);
+    add_square(&mut k, &mut b, 0.5, 1.0 + gap);
+    let records =
+        stitch_and_orient_reported(&mut k, &mut b, &StitchAndOrientOptions::default()).unwrap();
+    let splits: Vec<_> = records
+        .iter()
+        .filter(|r| matches!(r.kind, ClosedGapKind::Split { .. }))
+        .collect();
+    assert_eq!(
+        splits.len(),
+        2,
+        "both ends of the partial shared boundary: {records:?}"
+    );
+    for entry in splits {
+        assert!(
+            entry.gap >= (1.0 + gap) - 1.0 && entry.gap < gap + 1e-12,
+            "{entry:?}"
+        );
+        check_accounting(entry);
+    }
+}
+
+/// Two adjacent squares, with one shared edge represented by an exact cubic
+/// Hermite line. Stitching can compare it; this certificate does not support it.
+fn unsupported_shared_edge() -> (Kernel, Brep) {
+    use solidcore::curve::hermite_curve::HermiteCurve;
+    let mut k = Kernel::default();
+    let mut b = new_brep(&mut k, USE_DEFAULT, USE_DEFAULT).unwrap();
+    add_square(&mut k, &mut b, 0.0, 0.0);
+    add_square(&mut k, &mut b, 1.0, 0.0);
+    b.refresh_cached_topology();
+    let ends: Vec<_> = b
+        .edge_list()
+        .iter()
+        .copied()
+        .map(|e| {
+            let data = b.edge(e).unwrap();
+            let c = data.curve.as_ref().unwrap();
+            let a = c.evaluate_point(&k, data.interval.min()).unwrap();
+            let z = c.evaluate_point(&k, data.interval.max()).unwrap();
+            (e, a, z)
+        })
+        .collect();
+    let edge = ends
+        .iter()
+        .find(|(e, a, z)| {
+            ends.iter()
+                .any(|(other, p, q)| e != other && ((a == p && z == q) || (a == q && z == p)))
+        })
+        .expect("the exactly shared boundary")
+        .0;
+    let data = b.edge(edge).unwrap();
+    let old = data.curve.as_ref().unwrap();
+    let a = old.evaluate_point(&k, data.interval.min()).unwrap();
+    let z = old.evaluate_point(&k, data.interval.max()).unwrap();
+    let mut curve: solidcore::curve::curve::Curve = HermiteCurve::new(a, z - a, z, z - a, 3).into();
+    curve.set_owner(
+        old.owner(),
+        Some(solidcore::topology::brep::p2::brep_ref(&b)),
+    );
+    b.edge_mut(edge).unwrap().curve = Some(curve);
+    b.edge_mut(edge).unwrap().interval =
+        solidcore::geom::extent1d::Extent1d::from_min_max(0.0, 1.0);
+    (k, b)
+}
+
+/// A deterministic binary record checks topology, geometry and stored tolerances;
+/// explicit id-list assertions below also cover the original arena handles.
+fn binary(k: &Kernel, b: &Brep) -> Vec<u8> {
+    use solidcore::geom::attribute::{AttributeStore, ObjectKey};
+    use solidcore::topology::brep_data_write::FromBrepEnv;
+    use solidcore::topology::topology::NotifyRecords;
+    let attributes = AttributeStore::new();
+    let records = NotifyRecords::new();
+    let env = FromBrepEnv {
+        attributes: &attributes,
+        records: &records,
+        key_of: &solidcore::topology::loopuse::notify_ref,
+        curve_key: &|_| ObjectKey(0),
+        uv_curve_key: &|_| ObjectKey(0),
+        surface_key: &|_| ObjectKey(0),
+    };
+    solidcore::topology::api_files::write_brep_to_file(k, Some(b), &env, false).unwrap()
+}
+
+#[test]
+fn certificate_failure_propagates_and_rolls_back_earlier_closures_with_flags_off_or_on() {
+    use solidcore::heal::stitch::p1::{DefaultStitchCallback, Stitch};
+    use solidcore::heal::stitch::p2::{ClosedGapKind, MinGapRequest};
+    use solidcore::SolidError;
+
+    // The unwrapped stitch demonstrates that failure really occurs AFTER the two
+    // vertex glues. This is not merely a no-edit input-validation test.
+    let (mut k, mut b) = unsupported_shared_edge();
+    let mut callback = DefaultStitchCallback::new();
+    let mut stitch = Stitch::new(&mut callback, b.tolerance() * 4.0, true, true);
+    stitch.fast_edge_compare = true;
+    stitch.report_gaps = Some(Vec::new());
+    let failure = stitch
+        .do_stitching(&mut k, &mut b, None, None, MinGapRequest::default())
+        .unwrap_err();
+    assert!(
+        matches!(
+            failure,
+            SolidError::Unsupported {
+                operation: "heal::stitch::bounds",
+                ..
+            }
+        ),
+        "{failure:?}"
+    );
+    let records = stitch.report_gaps.as_ref().unwrap();
+    assert_eq!(
+        records
+            .iter()
+            .filter(|r| matches!(r.kind, ClosedGapKind::Vertex { .. }))
+            .count(),
+        2,
+        "{records:?}"
+    );
+    b.refresh_cached_topology();
+    assert_eq!(
+        b.vertex_list().len(),
+        6,
+        "the direct stitch has already edited the operand"
+    );
+
+    for statuses in [false, true] {
+        let (mut k, mut b) = unsupported_shared_edge();
+        k.fixes.brep_edit_statuses_pass_on = statuses;
+        let before = binary(&k, &b);
+        let ids = (
+            b.face_list().to_vec(),
+            b.edge_list().to_vec(),
+            b.vertex_list().to_vec(),
+        );
+        let result = stitch_and_orient_reported(&mut k, &mut b, &StitchAndOrientOptions::default());
+        assert!(
+            matches!(
+                result,
+                Err(SolidError::Unsupported {
+                    operation: "heal::stitch::bounds",
+                    ..
+                })
+            ),
+            "flag={statuses}: {result:?}"
+        );
+        assert_eq!(
+            binary(&k, &b),
+            before,
+            "flag={statuses}: the full operand must be restored"
+        );
+        assert_eq!(
+            (
+                b.face_list().to_vec(),
+                b.edge_list().to_vec(),
+                b.vertex_list().to_vec()
+            ),
+            ids
+        );
+    }
+}

solidcore/crates/solidcore/tests/issue_2978_local_reach_beside_nets.rs

@@ -1,318 +0,0 @@
-//! The local operation's reach beside bare B-spline nets: planes moved beside the walls of
-//! `Solids/extrusion.smb`, two of which are extrusions with no analytic label (of a cubic
-//! B-spline and of a rational curve of lines and an arc; the reader makes its other faces
-//! planes and cylinders), build sound bodies of their closed-form volumes instead of being
-//! refused as `ReachUncertified`; so does the base of `Solids/pyramid.smb` moved up,
-//! beside sides stored as bare B-spline nets; and
-//! the planes moved over the curved nets of `Solids/nurb_fillet.smb` (the cases whose
-//! extension can leave a body that is no manifold solid) are built sound or refused with
-//! the input left as it came in, never returned unsound.
-//!
-//! Each case is a goldens case of `topology.brep_local_operation`, made as its runner makes
-//! it: a face's surface replaced by the plane through the point at the middle of its UV
-//! domain, moved `offset` along the surface's normal there, the normal tilted by `tilt`.
-//!
-//! The solids are the upstream test files, read when the pinned upstream checkout is
-//! present (the tests are skipped otherwise, as in CI's test job).
-#![allow(
-    clippy::unwrap_used,
-    clippy::expect_used,
-    clippy::panic,
-    clippy::indexing_slicing
-)] // test helpers
-
-#[path = "support/offset_fixture.rs"]
-mod offset_fixture;
-
-use offset_fixture::Notifications;
-use solidcore::geom::attribute::{AttributeStore, ObjectKey};
-use solidcore::geom::object::ObjectRef;
-use solidcore::mass::integrator::properties::{face_area, face_centroid};
-use solidcore::math::{Point3, Vec3};
-use solidcore::nurbs::knots::Side;
-use solidcore::surface::plane::Plane;
-use solidcore::surface::surface::Surface;
-use solidcore::topology::brep::local_operation::local_operation;
-use solidcore::topology::brep::p1 as bp1;
-use solidcore::topology::brep::p10::TopologyEnv;
-use solidcore::topology::brep::p7::read_from_file;
-use solidcore::topology::brep::validation::volume;
-use solidcore::topology::database_io::FileType;
-use solidcore::topology::face::p2 as face_ops;
-use solidcore::topology::topology::NotifyRecords;
-use solidcore::topology::FaceId;
-use solidcore::{Brep, EntityRef, Kernel};
-
-/// The upstream test file `Solids/<name>`, or `None` without the upstream checkout.
-fn solid(k: &mut Kernel, name: &str) -> Option<Brep> {
-    let path = std::path::Path::new(env!("CARGO_MANIFEST_DIR"))
-        .join("../../upstream/TestFiles/pt_TestFiles/Solids")
-        .join(name);
-    let Ok(bytes) = std::fs::read(&path) else {
-        assert!(
-            std::env::var_os("SOLIDCORE_REQUIRE_UPSTREAM").is_none(),
-            "SOLIDCORE_REQUIRE_UPSTREAM is set and the upstream test file is missing: {}",
-            path.display()
-        );
-        eprintln!("unavailable upstream test file: {}", path.display());
-        return None;
-    };
-    let mut b = Brep::new_with_infinite_region().unwrap();
-    let mut records = NotifyRecords::new();
-    let mut attributes = AttributeStore::default();
-    let key = |_: EntityRef| ObjectRef {
-        key: ObjectKey(0),
-        type_code: 0,
-    };
-    let mut env = TopologyEnv {
-        all_attributes: &[],
-        attributes: &mut attributes,
-        key_of: &key,
-        records: &mut records,
-        next_key: 1 << 50,
-    };
-    read_from_file(k, &mut b, bytes, FileType::Ascii, false, &mut env).unwrap();
-    b.use_arena_naming().unwrap();
-    Some(b)
-}
-
-/// The plane the goldens runner gives face `index` (`GetFaces` order): through the point
-/// at the middle of its UV domain moved `offset` along the normal there, the normal plus
-/// `tilt`: the face, and the plane's origin and normal.
-fn plane_for(
-    k: &Kernel,
-    b: &Brep,
-    index: usize,
-    offset: f64,
-    tilt: [f64; 3],
-) -> (FaceId, (Point3, Vec3)) {
-    let face = bp1::faces(b, None).unwrap()[index];
-    let surface = face_ops::surface(b, face).unwrap().unwrap();
-    let uv = b.face(face).unwrap().uv_domain.evaluate(0.5, 0.5);
-    let p = surface.evaluate_point(k, uv).unwrap();
-    let n = surface
-        .evaluate_normal(k, uv, Side::Left, Side::Left)
-        .unwrap();
-    let origin = Point3::new(p.x + n.x * offset, p.y + n.y * offset, p.z + n.z * offset);
-    let normal = Vec3::new(n.x + tilt[0], n.y + tilt[1], n.z + tilt[2]);
-    (face, (origin, normal))
-}
-
-/// `b`'s faces `moves` (index, offset, tilt) given their planes by a local operation; the
-/// planes' origins and normals.
-fn moved(
-    k: &mut Kernel,
-    b: &mut Brep,
-    moves: &[(usize, f64, [f64; 3])],
-) -> solidcore::Result<Vec<(Point3, Vec3)>> {
-    let (faces, planes): (Vec<FaceId>, Vec<(Point3, Vec3)>) = moves
-        .iter()
-        .map(|&(i, offset, tilt)| plane_for(k, b, i, offset, tilt))
-        .unzip();
-    let surfaces = planes
-        .iter()
-        .map(|&(o, n)| Surface::from(Plane::from_normal(o, n)))
-        .collect();
-    let mut notifications = Notifications::new(b);
-    local_operation(k, b, &faces, surfaces, &mut notifications.context())?;
-    Ok(planes)
-}
-
-/// The face of `b` whose surface's point at the middle of its domain is at height `z`, and
-/// whose normal there is along z (a cap of the extrusion).
-fn cap_at(k: &Kernel, b: &Brep, z: f64) -> FaceId {
-    let caps: Vec<FaceId> = bp1::faces(b, None)
-        .unwrap()
-        .into_iter()
-        .filter(|&f| {
-            let s = face_ops::surface(b, f).unwrap().unwrap();
-            let uv = b.face(f).unwrap().uv_domain.evaluate(0.5, 0.5);
-            let p = s.evaluate_point(k, uv).unwrap();
-            let n = s.evaluate_normal(k, uv, Side::Left, Side::Left).unwrap();
-            (p.z - z).abs() < 1e-9 && n.x.abs() < 1e-9 && n.y.abs() < 1e-9
-        })
-        .collect();
-    assert_eq!(caps.len(), 1, "{caps:?}");
-    caps[0]
-}
-
-/// The integrators' accuracy, and the agreement asked of two integrals at it.
-const ACCURACY: f64 = 1e-6;
-const AGREE: f64 = 1e-5;
-
-/// Walls of the extrusion (z from 0 to 10) moved onto planes, the caps kept: the result
-/// is the prism over its bottom cap, ten times the cap's area, and sound, and each new wall
-/// stands on its plane (at least four of the body's vertices on it, two at each cap).
-fn walls_moved_build_their_prism(moves: &[(usize, f64, [f64; 3])]) {
-    let mut k = Kernel::default();
-    let Some(mut b) = solid(&mut k, "extrusion.smb") else {
-        return;
-    };
-    let faces = bp1::faces(&b, None).unwrap().len();
-    let planes = moved(&mut k, &mut b, moves).unwrap();
-    for (o, n) in planes {
-        let n = n * (1.0 / n.length());
-        let on: Vec<f64> = b
-            .vertex_list()
-            .iter()
-            .map(|&v| solidcore::topology::vertex::point(&b, v).unwrap())
-            .filter(|p| (*p - o).dot(n).abs() <= b.tolerance())
-            .map(|p| p.z)
-            .collect();
-        let at = |z: f64| {
-            on.iter()
-                .filter(|&&h| (h - z).abs() <= b.tolerance())
-                .count()
-        };
-        assert!(at(0.0) >= 2 && at(10.0) >= 2, "{on:?}");
-    }
-    assert!(solidcore::topology::brep::p2::is_manifold_solid(&b).unwrap());
-    assert_eq!(bp1::faces(&b, None).unwrap().len(), faces);
-    let v = volume(&mut k, &mut b).unwrap();
-    let bottom = cap_at(&k, &b, 0.0);
-    let want = 10.0 * face_area(&k, &mut b, bottom, ACCURACY).unwrap();
-    assert!((v - want).abs() <= AGREE * want, "{v} vs {want}");
-}
-
-/// gen0000: the quarter cylinder wall (face 4) given its tangent plane moved out 1.14, and
-/// the cubic wall (face 2) its tangent plane at its middle. Each new plane meets the caps,
-/// the flat wall beside them and the rational wall (face 5, an extrusion), whose ruled
-/// extension past its end the moved planes reach.
-#[test]
-fn two_walls_given_planes_out_build_the_prism_of_their_profile() {
-    walls_moved_build_their_prism(&[(4, 1.143_604_136_567_873_7, [0.0; 3]), (2, 0.0, [0.0; 3])]);
-}
-
-/// gen0021: the same two walls, both moved out (0.20 and 0.55).
-#[test]
-fn two_walls_moved_out_build_the_prism_of_their_profile() {
-    walls_moved_build_their_prism(&[
-        (4, 0.202_101_138_781_204_4, [0.0; 3]),
-        (2, 0.548_365_023_570_791_1, [0.0; 3]),
-    ]);
-}
-
-/// gen0048: the cubic wall (face 2) given its tangent plane at its middle.
-#[test]
-fn a_cubic_wall_given_its_tangent_plane_builds_the_prism_of_its_profile() {
-    walls_moved_build_their_prism(&[(2, 0.0, [0.0; 3])]);
-}
-
-/// gen0041: the top cap (face 1) moved down 0.16 and tilted. The walls keep their surfaces
-/// and meet it along their rulings (the two extrusions as nets); the body is the solid over the
-/// bottom cap under the tilted plane, whose volume is the cap's area times the plane's
-/// height over the cap's centroid (the height is linear), and sound.
-#[test]
-fn a_top_moved_down_and_tilted_holds_its_height_over_the_centroid() {
-    let mut k = Kernel::default();
-    let Some(mut b) = solid(&mut k, "extrusion.smb") else {
-        return;
-    };
-    let bottom = cap_at(&k, &b, 0.0);
-    let (area, centroid) = face_centroid(&k, &mut b, bottom, ACCURACY).unwrap();
-    let tilt = [
-        -0.095_716_453_310_687_6,
-        0.014_193_158_954_830_198,
-        -0.155_603_183_282_545_88,
-    ];
-    let planes = moved(&mut k, &mut b, &[(1, -0.163_195_178_504_810_47, tilt)]).unwrap();
-    assert!(solidcore::topology::brep::p2::is_manifold_solid(&b).unwrap());
-    // the plane's height over the centroid: (x − o)·n = 0 solved for z
-    let (o, n) = planes[0];
-    let height = o.z - ((centroid.x - o.x) * n.x + (centroid.y - o.y) * n.y) / n.z;
-    let want = area * height;
-    let v = volume(&mut k, &mut b).unwrap();
-    assert!((v - want).abs() <= AGREE * want, "{v} vs {want}");
-}
-
-/// gen0076: the base of `Solids/pyramid.smb` (a plane) moved up 1.31 toward the apex. Two
-/// of the sides are nets off their planes by the rounding of their stored points (single
-/// precision: 1.9e-6); the base meets them on their nets. What is left is the pyramid above
-/// the new base, similar to the old one: the volume times `((h − d) / h)³`, `h` the apex's
-/// height over the old base, `d` the move.
-#[test]
-fn a_pyramid_base_moved_up_leaves_the_similar_pyramid_above_it() {
-    let mut k = Kernel::default();
-    let Some(mut b) = solid(&mut k, "pyramid.smb") else {
-        return;
-    };
-    let before = volume(&mut k, &mut b).unwrap();
-    let h = b
-        .vertex_list()
-        .iter()
-        .map(|&v| solidcore::topology::vertex::point(&b, v).unwrap().z)
-        .fold(f64::NEG_INFINITY, f64::max);
-    let planes = moved(&mut k, &mut b, &[(0, 1.308_567_886_431_627_2, [0.0; 3])]).unwrap();
-    assert!(solidcore::topology::brep::p2::is_manifold_solid(&b).unwrap());
-    let d = planes[0].0.z;
-    assert!(d > 1.3 && d < 1.31, "{d}");
-    let want = before * ((h - d) / h).powi(3);
-    let v = volume(&mut k, &mut b).unwrap();
-    assert!((v - want).abs() <= AGREE * want, "{v} vs {want}");
-}
-
-/// The cases of `Solids/nurb_fillet.smb` that can leave a non-manifold body once the plane
-/// beside its curved nets has a reach: built only as a manifold solid of positive volume,
-/// or refused with the input as it came in (its volume, faces and edges).
-fn sound_or_refused_unchanged(moves: &[(usize, f64, [f64; 3])]) {
-    let mut k = Kernel::default();
-    let Some(mut b) = solid(&mut k, "nurb_fillet.smb") else {
-        return;
-    };
-    let before = (
-        volume(&mut k, &mut b).unwrap(),
-        bp1::faces(&b, None).unwrap().len(),
-        b.edge_list().len(),
-    );
-    match moved(&mut k, &mut b, moves) {
-        Ok(_) => {
-            assert!(solidcore::topology::brep::p2::is_manifold_solid(&b).unwrap());
-            assert!(volume(&mut k, &mut b).unwrap() > 0.0);
-        }
-        Err(e) => {
-            let after = (
-                volume(&mut k, &mut b).unwrap(),
-                bp1::faces(&b, None).unwrap().len(),
-                b.edge_list().len(),
-            );
-            assert_eq!(after, before, "{e}");
-        }
-    }
-}
-
-/// `nurb_fillet_face0_same` (and its `attributed_` twin): face 0 given its tangent plane.
-#[test]
-fn a_curved_net_given_its_tangent_plane_is_sound_or_refused_unchanged() {
-    sound_or_refused_unchanged(&[(0, 0.0, [0.0; 3])]);
-}
-
-/// `nurb_fillet_face4_same` (and its `attributed_` twin): face 4 given its tangent plane.
-#[test]
-fn another_curved_net_given_its_tangent_plane_is_sound_or_refused_unchanged() {
-    sound_or_refused_unchanged(&[(4, 0.0, [0.0; 3])]);
-}
-
-/// `fc0004`: faces 16 and 0 given tilted planes, 16's moved in 1.21.
-#[test]
-fn two_curved_nets_given_tilted_planes_are_sound_or_refused_unchanged() {
-    sound_or_refused_unchanged(&[
-        (
-            16,
-            -1.212_618_021_690_697_2,
-            [
-                -0.227_499_561_725_195_12,
-                -0.119_235_175_885_283_43,
-                0.212_040_256_859_765_76,
-            ],
-        ),
-        (
-            0,
-            0.0,
-            [
-                0.195_822_407_983_586_08,
-                -0.180_816_552_666_528_46,
-                -0.250_316_266_099_896_8,
-            ],
-        ),
-    ]);
-}

solidcore/crates/solidcore/tests/kernel_cases/booleans/13462-rod-cut-by-two-counter-wound-channel-coils.json

@@ -0,0 +1,595 @@
+{
+  "area": "booleans",
+  "bodies": {
+    "b14": {
+      "keeping_splines": false,
+      "trusted": true
+    },
+    "b4": {
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+      "outputs": [
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+      "params": {}
+    },
+    {
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+      "op": "copy",
+      "outputs": [
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+      ],
+      "params": {}
+    },
+    {
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+      ],
+      "op": "copy",
+      "outputs": [
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+      ],
+      "params": {}
+    },
+    {
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+      ],
+      "op": "copy",
+      "outputs": [
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+      ],
+      "params": {}
+    },
+    {
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+        "b8"
+      ],
+      "op": "tagged",
+      "outputs": [
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+      ],
+      "params": {
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+    },
+    {
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+        "b10"
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+      "op": "tagged",
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+    },
+    {
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+        "b11",
+        "b12"
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+      "op": "boolean",
+      "outputs": [
+        "b13"
+      ],
+      "params": {
+        "op": "subtract"
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+    },
+    {
+      "inputs": [
+        "b14"
+      ],
+      "op": "copy",
+      "outputs": [
+        "b15"
+      ],
+      "params": {}
+    },
+    {
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+        "b15"
+      ],
+      "op": "copy",
+      "outputs": [
+        "b16"
+      ],
+      "params": {}
+    },
+    {
+      "inputs": [
+        "b5"
+      ],
+      "op": "copy",
+      "outputs": [
+        "b17"
+      ],
+      "params": {}
+    },
+    {
+      "inputs": [
+        "b17"
+      ],
+      "op": "copy",
+      "outputs": [
+        "b18"
+      ],
+      "params": {}
+    },
+    {
+      "inputs": [
+        "b16"
+      ],
+      "op": "tagged",
+      "outputs": [
+        "b19"
+      ],
+      "params": {
+        "operand": 0
+      }
+    },
+    {
+      "inputs": [
+        "b18"
+      ],
+      "op": "tagged",
+      "outputs": [
+        "b20"
+      ],
+      "params": {
+        "operand": 1
+      }
+    },
+    {
+      "inputs": [
+        "b19",
+        "b20"
+      ],
+      "op": "boolean",
+      "outputs": [
+        "b21"
+      ],
+      "params": {
+        "op": "subtract"
+      }
+    }
+  ],
+  "case": "13462-rod-cut-by-two-counter-wound-channel-coils",
+  "expected": {
+    "body_count": 1,
+    "method": "Each horizontal section of a screw sweep of a profile D in a plane normal to the axis is one rotated copy of D. With D_in = D n disk(16.5), A_in its area, one sweep removes A_in*|p|; the two sweeps' sections at one height are D_in turned by +t and -t, whose overlap integrates over the turn to (|p|/2pi)*Int s(r)^2 r dr, s(r) the angle D_in covers on the circle of radius r. s(r) found exactly from the circle's crossings with the profile's lines and axis-centred arcs, integrated by adaptive Gauss-Kronrod: A_in = 4.214046963094, Int s^2 r dr = 1.279023422464. V = pi*16.5^2*124 - 2*A_in*30 + (30/2pi)*Int s^2 r dr. The one-sweep form agrees with a single cut to 3e-12. Tolerance 1e-6: the sweeps' walls are within 3e-3 of the screw surfaces (|p|*1e-4), which moves the two sweeps' overlap by about 2e-3 mm^3 (1.6e-8 here)",
+    "source": "analytic",
+    "sources": [
+      "tangency-labs/solidcraft#13462",
+      "tangency-labs/solidcore#3214"
+    ],
+    "tolerance": {
+      "rel": 1e-06
+    },
+    "volume_mm3": 105810.29046175262,
+    "what": "a rod (r 16.5, 124 long) cut by two one-turn screw sweeps of one channel profile, one right-handed and one left-handed, pitch 30, both starting on the rod's top face: the channel's two radial walls meet the rod's surface, so each sweep's rail on it is a helix there and the two rails cross. The cut's new edge along a crossing rail took an interval its UV curve's trim had snapped 2.4e-12 past its 3D curve's end ('SmEdge test 2, Bad Domain')"
+  },
+  "expressible": true,
+  "operation_expressible": true,
+  "outcome": {
+    "ran": true,
+    "raw_counts": {
+      "edges": 60,
+      "faces": 30,
+      "vertices": 32
+    }
+  },
+  "records": "13462-rod-cut-by-two-counter-wound-channel-coils.bodies.json.gz",
+  "result": [
+    {
+      "body": "Rod",
+      "made": "b21"
+    }
+  ],
+  "rig": {
+    "error": null,
+    "known_failing": null,
+    "measured": {
+      "area_mm2": 14815.578874890229,
+      "body_count": 1,
+      "edges": 55,
+      "faces": 25,
+      "vertices": 32,
+      "volume_mm3": 105810.28872357338
+    },
+    "refused_with": null,
+    "status": "pass"
+  },
+  "sources": [
+    "tangency-labs/solidcraft#13462",
+    "tangency-labs/solidcore#3214"
+  ],
+  "traced_ops": [
+    "extrude",
+    "screw_sweep",
+    "screw_sweep",
+    "copy",
+    "copy",
+    "copy",
+    "copy",
+    "tagged",
+    "tagged",
+    "boolean",
+    "copy",
+    "copy",
+    "copy",
+    "copy",
+    "tagged",
+    "tagged",
+    "boolean"
+  ],
+  "ungraded": [],
+  "what": "a rod (r 16.5, 124 long) cut by two one-turn screw sweeps of one channel profile, one right-handed and one left-handed, pitch 30, both starting on the rod's top face: the channel's two radial walls meet the rod's surface, so each sweep's rail on it is a helix there and the two rails cross. The cut's new edge along a crossing rail took an interval its UV curve's trim had snapped 2.4e-12 past its 3D curve's end ('SmEdge test 2, Bad Domain')",
+  "why_not": []
+}