diff --git a/crates/doc/src/project.rs b/crates/doc/src/project.rs
index ba0fa6d8e5..c9edbb1d25 100644
--- a/crates/doc/src/project.rs
+++ b/crates/doc/src/project.rs
@@ -361,7 +361,7 @@ fn edge_curves(body: Option<&crate::ModelBody>, e: usize) -> Vec<WireCurve> {
         .edges
         .get(e)
         .filter(|edge| !matches!(edge.curve, solidcraft_geom::brep::Curve::SurfaceIntersection { .. }))
-        .map(|edge| vec![WireCurve { curve: edge.curve.clone(), interval: edge.interval }])
+        .map(|edge| vec![WireCurve { curve: edge.parameters().clone(), interval: edge.interval }])
         .unwrap_or_default()
 }
 
diff --git a/crates/geom/src/brep.rs b/crates/geom/src/brep.rs
index c4b13ae0fc..2c62760bc7 100644
--- a/crates/geom/src/brep.rs
+++ b/crates/geom/src/brep.rs
@@ -488,10 +488,39 @@ fn surface(s: &Surface, depth: usize, budget: &mut Budget) -> Result<()> {
 
 impl Edge {
     /// The curve the edge's parameter is on: its NURBS form when it has one, else its curve.
-    /// Everything that evaluates the edge at a parameter goes through this.
+    /// Everything that evaluates the edge at a parameter goes through this, with `interval`.
     pub fn parameters(&self) -> &Curve {
         self.nurbs.as_ref().unwrap_or(&self.curve)
     }
+
+    /// The edge's interval on `curve` itself, for code that reads what the edge is (a circle's
+    /// angles): `interval` when the edge has no NURBS form; otherwise the angles of its ends on the
+    /// NURBS, unwrapped forward along the edge (a whole turn for a closed edge). A form's
+    /// circle or ellipse has its frame turned so its angle grows along the NURBS (the SMLib
+    /// conversion makes it so). `None` where the NURBS can't be evaluated.
+    pub fn curve_interval(&self) -> Option<[f64; 2]> {
+        curve_interval(&self.curve, self.nurbs.as_ref(), self.interval)
+    }
+}
+
+/// [`Edge::curve_interval`] of an edge given by its parts: its `curve`, its NURBS form and its
+/// interval on that form.
+pub fn curve_interval(curve: &Curve, nurbs: Option<&Curve>, interval: [f64; 2]) -> Option<[f64; 2]> {
+    use std::f64::consts::TAU;
+    let Some(n) = nurbs else { return Some(interval) };
+    let (frame, radii) = match curve {
+        Curve::Circle { frame, radius } => (frame, [*radius, *radius]),
+        Curve::Ellipse { frame, radii } => (frame, *radii),
+        _ => return Some(interval),
+    };
+    let eval = eval::CurveEval::new(n).ok()?;
+    let [t0, t1] = interval;
+    let o = crate::Vec3::new(frame.origin[0], frame.origin[1], frame.origin[2]);
+    let (x, y) = (crate::Vec3::from(frame.x_axis), crate::Vec3::from(frame.y_axis));
+    let angle = |t: f64| eval.point(t).map(|p| ((p - o).dot(y) / radii[1]).atan2((p - o).dot(x) / radii[0]).rem_euclid(TAU));
+    let (a0, a1) = (angle(t0)?, angle(t1)?);
+    let sweep = (a1 - a0).rem_euclid(TAU);
+    Some([a0, a0 + if sweep <= 1e-12 { TAU } else { sweep }])
 }
 
 impl Face {
diff --git a/crates/kernel/src/assemble.rs b/crates/kernel/src/assemble.rs
index f3c4e32f78..d5ccb3e8c8 100644
--- a/crates/kernel/src/assemble.rs
+++ b/crates/kernel/src/assemble.rs
@@ -26,6 +26,8 @@ fn invalid(m: impl std::fmt::Display) -> KernelError {
 #[derive(Clone, Debug)]
 pub(crate) struct AEdge {
     pub curve: Curve,
+    /// The NURBS form the edge's parameter is on, as the record's `Edge::nurbs`.
+    pub nurbs: Option<Curve>,
     pub interval: [f64; 2],
     pub vertices: [u32; 2],
     pub tolerance: f64,
@@ -118,6 +120,7 @@ impl Assembly {
             .enumerate()
             .map(|(i, e)| AEdge {
                 curve: e.curve.clone(),
+                nurbs: e.nurbs.clone(),
                 interval: e.interval,
                 vertices: e.vertices,
                 tolerance: e.tolerance,
@@ -144,7 +147,7 @@ impl Assembly {
 
     /// A new edge on `curve` over `interval`, from `a` to `b`.
     pub(crate) fn edge(&mut self, curve: Curve, interval: [f64; 2], a: u32, b: u32) -> Result<u32> {
-        self.edges.push(AEdge { curve, interval, vertices: [a, b], tolerance: self.tolerance, source: None, of: Vec::new() });
+        self.edges.push(AEdge { curve, nurbs: None, interval, vertices: [a, b], tolerance: self.tolerance, source: None, of: Vec::new() });
         index(self.edges.len() - 1)
     }
 
@@ -218,7 +221,7 @@ impl Assembly {
             }
         }
         let edges = self.edges.iter().map(|a| Edge {
-            nurbs: None,
+            nurbs: a.nurbs.clone(),
             curve: a.curve.clone(),
             interval: a.interval,
             vertices: a.vertices,
@@ -260,7 +263,7 @@ impl Assembly {
                         let e = self.edges.get(u.edge as usize).ok_or_else(|| invalid("edge reference"))?;
                         Ok(EdgeUse {
                             edge: u.edge,
-                            curve: &e.curve,
+                            curve: e.nurbs.as_ref().unwrap_or(&e.curve),
                             interval: e.interval,
                             forward: u.forward,
                             tolerance: e.tolerance,
diff --git a/crates/kernel/src/blend.rs b/crates/kernel/src/blend.rs
index dbd70594c8..fbc9d6e721 100644
--- a/crates/kernel/src/blend.rs
+++ b/crates/kernel/src/blend.rs
@@ -119,7 +119,7 @@ impl Faces {
     /// The edge's unit tangent along its interval (start to end vertex) at its start or end.
     pub(crate) fn tangent(&self, e: usize, at_end: bool) -> Option<Vec3> {
         let edge = self.rec.edges.get(e)?;
-        curve_tangent(&edge.curve, if at_end { edge.interval[1] } else { edge.interval[0] })
+        curve_tangent(edge.parameters(), if at_end { edge.interval[1] } else { edge.interval[0] })
     }
 }
 
diff --git a/crates/kernel/src/body.rs b/crates/kernel/src/body.rs
index 40fbd6af8a..3e383323bb 100644
--- a/crates/kernel/src/body.rs
+++ b/crates/kernel/src/body.rs
@@ -870,7 +870,7 @@ impl Body {
             b.add(v3(v.point));
         }
         for e in &self.record.edges {
-            curve_hull(&e.curve, e.interval, &mut b);
+            curve_hull(e.parameters(), e.interval, &mut b);
         }
         b
     }
diff --git a/crates/kernel/src/fill.rs b/crates/kernel/src/fill.rs
index b7abdc4bb4..58e6d3df17 100644
--- a/crates/kernel/src/fill.rs
+++ b/crates/kernel/src/fill.rs
@@ -625,14 +625,14 @@ fn patch_body(body: &Body, record: &b::Brep, chain: &[(usize, bool)], surface: b
             }
         }
         let given = match pcurves {
-            Pcurves::Projected(p) => Some(p.pcurve(&edge.curve, edge.interval).ok_or_else(|| {
+            Pcurves::Projected(p) => Some(p.pcurve(edge.parameters(), edge.interval).ok_or_else(|| {
                 KernelError::Invalid(
                     "not supported yet: a fitted patch on a circular, elliptic or traced edge (it has no exact pcurve on the fit)".into(),
                 )
             })?),
             Pcurves::Computed => None,
         };
-        edges.push(PartEdge { curve: edge.curve.clone(), interval: edge.interval, vertices: ends });
+        edges.push(PartEdge { curve: edge.parameters().clone(), interval: edge.interval, vertices: ends });
         uses.push(PartUse { edge: k as u32, forward, given });
     }
     if !ccw {
diff --git a/crates/kernel/src/iges_out.rs b/crates/kernel/src/iges_out.rs
index 3efa7e1a97..90fac84f8c 100644
--- a/crates/kernel/src/iges_out.rs
+++ b/crates/kernel/src/iges_out.rs
@@ -345,7 +345,7 @@ fn shell(w: &mut W, b: &Brep, si: u32, paint: &HashMap<usize, [f32; 3]>) -> Resu
     let mut ep = vec![edges.len().to_string()];
     for &e in &edges {
         let edge = b.edges.get(e as usize).ok_or_else(|| failed(format!("edge {e}: no such edge")))?;
-        let c = topology::curve(&edge.curve).map_err(|m| failed(format!("edge {e}: {m}")))?;
+        let c = topology::curve(edge.parameters()).map_err(|m| failed(format!("edge {e}: {m}")))?;
         let [sv, tv] = edge.vertices.map(|v| vidx.get(&v).copied().unwrap_or(0));
         let (pa, pb) = (verts.get(sv).copied().unwrap_or([0.0; 3]), verts.get(tv).copied().unwrap_or([0.0; 3]));
         let cd = curve(w, &c, edge.interval, pa, pb, sv == tv)?;
diff --git a/crates/kernel/src/intersection.rs b/crates/kernel/src/intersection.rs
index 2bf8c5a07e..bdaaf5e3d0 100644
--- a/crates/kernel/src/intersection.rs
+++ b/crates/kernel/src/intersection.rs
@@ -56,7 +56,7 @@ pub fn meeting_edges(a: &Body, a_face: Option<usize>, b: &Body, b_face: Option<u
         let (Some(e), Some(points)) = (at.and_then(|k| record.edges.get(k)), at.and_then(|k| mesh.edges.get(k))) else {
             return Err(failed("history", format!("edge {i} is not in the imprinted body")));
         };
-        out.push(MeetingEdge { curve: e.curve.clone(), interval: e.interval, points: points.clone() });
+        out.push(MeetingEdge { curve: e.parameters().clone(), interval: e.interval, points: points.clone() });
     }
     Ok(out)
 }
diff --git a/crates/kernel/src/lip.rs b/crates/kernel/src/lip.rs
index d512a0e4af..a7e456730b 100644
--- a/crates/kernel/src/lip.rs
+++ b/crates/kernel/src/lip.rs
@@ -149,7 +149,8 @@ fn pieces(asm: &Assembly, lp: &[AUse], n: Vec3) -> Result<Vec<Piece>> {
             let e = asm.edges.get(u.edge as usize).ok_or_else(|| fail("edge"))?;
             let (s, t) = asm.ends(u).ok_or_else(|| fail("edge"))?;
             let (a, b) = (asm.point(s).ok_or_else(|| fail("vertex"))?, asm.point(t).ok_or_else(|| fail("vertex"))?);
-            let [t0, t1] = e.interval;
+            // The arc's angles, on the circle itself (its NURBS form, if any, is parameterised otherwise).
+            let [t0, t1] = solidcraft_geom::brep::curve_interval(&e.curve, e.nurbs.as_ref(), e.interval).ok_or_else(|| fail("edge"))?;
             match &e.curve {
                 Curve::Line { .. } => Ok(Piece { a, b, arc: None }),
                 Curve::Circle { frame, .. } => {
diff --git a/crates/kernel/src/point_path.rs b/crates/kernel/src/point_path.rs
index fb72a48740..618637e88b 100644
--- a/crates/kernel/src/point_path.rs
+++ b/crates/kernel/src/point_path.rs
@@ -152,7 +152,7 @@ const MAX_EDGE_SEGS: usize = 1000;
 pub fn edge_path(body: &Body, edge: usize) -> Result<Vec<PathSeg>> {
     let record = crate::native::brep_record(body)?;
     let e = record.edges.get(edge).ok_or_else(|| KernelError::Invalid(format!("the body has no edge {edge}")))?;
-    curve_path(&e.curve, e.interval)
+    curve_path(e.parameters(), e.interval)
 }
 
 /// The sketch segments `segs` on `plane` projected along `direction` (pointing from them toward
diff --git a/crates/kernel/src/prism_curve.rs b/crates/kernel/src/prism_curve.rs
index 4fd305d5b9..611ffc3e2e 100644
--- a/crates/kernel/src/prism_curve.rs
+++ b/crates/kernel/src/prism_curve.rs
@@ -31,7 +31,7 @@ impl<'a> Run<'a> {
         let e = record.edges.get(edge)?;
         let at = |v: u32| record.vertices.get(v as usize).map(|v| Vec3::new(v.point[0], v.point[1], v.point[2]));
         let (start, end) = (at(e.vertices[0])?, at(e.vertices[1])?);
-        Some(Run { curve: &e.curve, interval: e.interval, forward, ends: if forward { [start, end] } else { [end, start] } })
+        Some(Run { curve: e.parameters(), interval: e.interval, forward, ends: if forward { [start, end] } else { [end, start] } })
     }
 
     /// The parameters it runs from and to.
diff --git a/crates/kernel/src/surface_ruled.rs b/crates/kernel/src/surface_ruled.rs
index 79fb40fe5f..7715eac842 100644
--- a/crates/kernel/src/surface_ruled.rs
+++ b/crates/kernel/src/surface_ruled.rs
@@ -351,7 +351,8 @@ fn normal_at(surface: &SurfaceEval, forward: bool, p: Vec3) -> Option<Vec3> {
 /// one span per quarter turn or less).
 fn base_curve(r: &Brep, e: usize, forward: bool) -> Result<CurveN<4>> {
     let edge = r.edges.get(e).ok_or_else(|| KernelError::Invalid("an edge reference".into()))?;
-    let [t0, t1] = edge.interval;
+    // On the curve itself: a conic's angles (its NURBS form, if any, is parameterised otherwise).
+    let [t0, t1] = edge.curve_interval().ok_or_else(|| KernelError::Invalid("an edge's NURBS form cannot be evaluated".into()))?;
     let c = match &edge.curve {
         b::Curve::Line { start, end } => {
             let at = |t: f64| [start[0] + (end[0] - start[0]) * t, start[1] + (end[1] - start[1]) * t, start[2] + (end[2] - start[2]) * t, 1.0];
diff --git a/crates/smlib/SMLIB_REV b/crates/smlib/SMLIB_REV
index 6f4324b727..15c3e32204 100644
--- a/crates/smlib/SMLIB_REV
+++ b/crates/smlib/SMLIB_REV
@@ -1 +1 @@
-deec9cb312b68a92d1b018cece65e1d86643fee6
+26a4b7b6255a0e4db29fdd81cb4985bb9a9a1a8f
diff --git a/crates/smlib/src/export.rs b/crates/smlib/src/export.rs
index ba8bcae0ba..7545cb4887 100644
--- a/crates/smlib/src/export.rs
+++ b/crates/smlib/src/export.rs
@@ -417,6 +417,19 @@ fn surfaces(flat: View, n_faces: usize) -> Res<Vec<(b::Surface, Option<b::Surfac
     Ok(out)
 }
 
+/// A circle's frame turned (y reversed) where needed so that its angle grows along `form`, the
+/// NURBS the edge runs on over `range`: what [`b::Edge::curve_interval`] reads.
+fn along(f: b::Frame, form: &b::Curve, range: [f64; 2]) -> Res<b::Frame> {
+    let eval = b::eval::CurveEval::new(form).map_err(|e| invalid(format!("circle NURBS form: {e}")))?;
+    let [t0, t1] = range;
+    let (p, q) = (eval.point(t0), eval.point(t0 + 1e-3 * (t1 - t0)));
+    let (Some(p), Some(q)) = (p, q) else { return Err(invalid("circle NURBS form")) };
+    let (o, x, y) = (Vec3::from(f.origin), Vec3::from(f.x_axis), Vec3::from(f.y_axis));
+    let angle = |s: Vec3| (s - o).dot(y).atan2((s - o).dot(x));
+    let step = (angle(q) - angle(p)).rem_euclid(TAU);
+    Ok(if step > std::f64::consts::PI { b::Frame { y_axis: [-f.y_axis[0], -f.y_axis[1], -f.y_axis[2]], ..f } } else { f })
+}
+
 /// A NURBS curve: full knots, cartesian control points and weights.
 struct Nurbs {
     knots: Vec<f64>,
@@ -559,7 +572,8 @@ fn curves(flat: View, n_edges: usize) -> Res<(Vec<(b::Curve, Option<b::Curve>, [
                 // A circle with its NURBS form is parameterised on it: its range and the trims
                 // on it are that NURBS's, so the trims carry over as they are.
                 if forms.get(e) == Some(&1) {
-                    (b::Curve::Circle { frame: f, radius }, Some(next_nurbs()?.record()), r, Some([1.0, 0.0]))
+                    let form = next_nurbs()?.record();
+                    (b::Curve::Circle { frame: along(f, &form, r)?, radius }, Some(form), r, Some([1.0, 0.0]))
                 } else {
                     (b::Curve::Circle { frame: f, radius }, None, r, None)
                 }