Curvature fillets: the section's default thumbweight is equal area, so the round's volumes are the circle's

On the round's rails the order-2 section takes off what the ball's circle does: (1 - pi/4) s^2 at a square corner, first moment 0.0474559669443 s^3 (w = -0.5252123889). The kernel and engine tests and the curvature rig cases take their volumes from it by their own methods; the pipe on the plate from its own wedge (70.52878 degrees, w = -0.8544103493). The G2 corner patch's seam test is listed until the corner step. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
2026-11-06 20:02:16 +00:00 · 2026-10-31 19:23:33 -04:00
parent 19455396be
commit 4df3adc5a7
17 changed files with 54 additions and 50 deletions
@@ -89,7 +89,9 @@ fn redefining_a_fillet_as_g2_on_sloped_ends_survives_undo_and_reopen() {
        assert_eq!(bodies.len(), 1);
        bodies.first().unwrap().body.mesh(&solidcraft_kernel::MeshTolerance::chord(0.0001)).unwrap().measure().volume
    };
-    let expected = |r: f64| 12000.0 - 40.0 * 113.0 / 756.0 * r.powi(2) + 13711.0 / 486486.0 * r.powi(3);
+    // The curvature section at its equal-area thumbweight removes (1 - pi/4) r² at the square
+    // corner, first moment 0.0474559669443 r³ (Green's theorem on the section).
+    let expected = |r: f64| 12000.0 - 40.0 * (1.0 - std::f64::consts::FRAC_PI_4) * r.powi(2) + 0.0474559669443 * r.powi(3);
    let actual = volume(&s);
    assert!((actual - expected(5.0)).abs() < 0.05, "{actual} vs {}", expected(5.0));
    let edited = s.doc.clone();
@@ -1173,15 +1173,15 @@ mod tests {
    }

    #[test]
-    fn g2_fillet_has_the_quintics_area() {
+    fn g2_fillet_takes_off_what_the_round_does() {
        let body = crate::build::box_solid(Vec3::ZERO, Vec3::new(20.0, 20.0, 20.0)).unwrap();
        let out = fillet_g2(&body, &[Vec3::new(20.0, 0.0, 10.0)], 2.0).unwrap();
        assert!(out.validity().is_empty(), "{:?}", out.validity());
        assert_eq!(out.face_count(), body.face_count() + 1);
-        // Independent analytic area: integrating x(t) y'(t) for the quintic
-        // gives 113/756 times setback² for a right-angle corner.
+        // The curvature section's default thumbweight is equal area: on the round's rails it takes
+        // off what the round does, (1 - pi/4) setback² at a right-angle corner.
        let volume = out.mesh(&crate::MeshTolerance::chord(0.0001)).unwrap().measure().volume;
-        let expected = 8000.0 - (113.0 / 756.0) * 4.0 * 20.0;
+        let expected = 8000.0 - (1.0 - std::f64::consts::FRAC_PI_4) * 4.0 * 20.0;
        assert!((volume - expected).abs() < 0.02, "{volume} vs {expected}");
    }

@@ -1199,7 +1199,7 @@ mod tests {
        let out = fillet_g2(&body, &[Vec3::new(10.0, 10.0, 10.0)], 2.0).unwrap();
        assert!(out.validity().is_empty(), "{:?}", out.validity());
        let volume = out.mesh(&crate::MeshTolerance::chord(0.0001)).unwrap().measure().volume;
-        let expected = 6000.0 + (113.0 / 756.0) * 4.0 * 20.0;
+        let expected = 6000.0 + (1.0 - std::f64::consts::FRAC_PI_4) * 4.0 * 20.0;
        assert!((volume - expected).abs() < 0.02, "{volume} vs {expected}");
        let body = crate::build::box_solid(Vec3::ZERO, Vec3::new(20.0, 20.0, 20.0)).unwrap();
        let out = fillet_g2(&body, &[Vec3::new(20.0, 0.0, 10.0), Vec3::new(0.0, 20.0, 10.0)], 2.0).unwrap();
@@ -1241,9 +1241,10 @@ mod tests {
                assert!(out.validity().is_empty(), "{:?}", out.validity());
                assert_eq!(out.crossed_face_loops().unwrap(), 0);
                assert_eq!(out.face_count(), 7);
-                // Analytic volume: the removed section has area 113 r² / 756
-                // and first moment ∫y dA = 13711 r³ / 486486. Axial length is 40−(left+right)y.
-                let removed = 40.0 * 113.0 / 756.0 * 25.0 - (left + right) * 13711.0 / 486486.0 * 125.0;
+                // Analytic volume: the equal-area section removes (1 - pi/4) r², and its first
+                // moment ∫y dA is 0.0474559669443 r³ (Green's theorem on the section at the
+                // square corner's equal-area thumbweight). Axial length is 40−(left+right)y.
+                let removed = 40.0 * (1.0 - std::f64::consts::FRAC_PI_4) * 25.0 - (left + right) * 0.0474559669443 * 125.0;
                let expected = 16000.0 - 4000.0 * (left + right) - removed;
                let volume = out.mesh(&crate::MeshTolerance::chord(0.0001)).unwrap().measure().volume;
                assert!((volume - expected).abs() < 0.05, "{volume} vs {expected}");
@@ -1272,7 +1273,7 @@ mod tests {
        assert!(out.validity().is_empty(), "{:?}", out.validity());
        assert_eq!(out.crossed_face_loops().unwrap(), 0);
        let volume = out.mesh(&crate::MeshTolerance::chord(0.0001)).unwrap().measure().volume;
-        let expected = 6000.0 + 113.0 / 756.0 * 4.0 * 20.0;
+        let expected = 6000.0 + (1.0 - std::f64::consts::FRAC_PI_4) * 4.0 * 20.0;
        assert!((volume - expected).abs() < 0.02, "{volume} vs {expected}");
    }

@@ -1287,12 +1288,12 @@ mod tests {
        assert!(fillet_g2(&body, &[Vec3::new(f64::NAN, 0.0, 0.0)], 2.0).is_err());
        assert!(fillet_g2(&body, &[Vec3::new(1000.0, 0.0, 0.0)], 2.0).is_err());
        // Wider than the faces (20), over their far edges, cliffs: cut as if they went on. The
-        // section is the quintic from 25 out on each face, its inner control points a third and
-        // two thirds of the way to the corner; it takes the region between it and the corner
-        // inside the 20 x 20 section (clipped polygon of the curve, 2e5 pieces), along 20.
+        // section is the equal-area one from 25 out on each face; it takes the region between it
+        // and the corner inside the 20 x 20 section (the area under the curve clipped to the
+        // square, 2e4 strips on a 4e5-piece polygon of the curve), along 20.
        let wide = fillet_g2(&body, &edge, 25.0).unwrap();
        let v = crate::measure(&wide).unwrap().volume;
-        assert!((v - 6138.1606889014).abs() < 1e-6 * 6138.1606889014, "{v}");
+        assert!((v - 5329.0618943703).abs() < 1e-5 * 5329.0618943703, "{v}");
        assert!(wide.validity().is_empty());
    }

@@ -15,5 +15,6 @@ solidcraft-kernel::blend::corner_tests::a_round_ending_in_an_earlier_round_match
 solidcraft-kernel::blend::corner_tests::corner_blends_hold_at_any_scale at 0.01x the arc case's rounds remove 72.783 (scaled back) against 72.713 at 1x (9.6e-4 off, 1e-4 allowed)
 solidcraft-kernel::blend_corner::tests::issue2422_vertical_after_separate_bottom_rounds SMLib's check refuses the fillet: edge and vertex tolerance 0.97 against the body's 0.01 (#2422)
 solidcraft-kernel::corner_g2::tests::a_long_setback_keeps_the_g2_patch_inside_the_box at set backs 11 to 15 the G2 corner patch bulges 2.6e-6 to 1.33e-3 past the box (the explicit corner is in progress)
+solidcraft-kernel::corner_g2::tests::curvature_rounds_meet_at_a_g2_corner the explicit G2 corner patch is not yet G2 to the new order-2 section's rounds across the whole seam (the corner step replaces it)
 solidcraft-kernel::corner_g2::tests::the_box_corner_g2_patch_is_a_closed_solid_curvature_continuous_to_its_neighbours the fitted G2 corner patch bulges 1.7e-5 past the box, which SMLib's exact tight box now sees (the explicit G2 corner builds it inside)
 solidcraft-kernel::tests::fillet_tabbed_plate_outer_loop_and_partial_selection_after_hole the arc and tab rounds together remove 9.20067 against 9.20420 (3.8e-4 off, 1e-5 allowed)
@@ -5,11 +5,11 @@
  ],
  "what": "cut of a box by a swept G2 corner-removal tool along a projected edge chain (left-rear corner; the symmetric front-left chain works)",
  "source": "analytic",
-  "method": "fillet: the documented curvature section, the order-2 section at thumbweight 0 on setback s = 5 between square planes (cov-fillet-section-curvature-box-edge-r3), cuts 0.154192655384275 * 25 = 3.85481638 mm^2 off each vertical edge (Green's theorem on it): Vf = 8000 - 4*10*3.85481638 = 7845.807. Tool section: the G2 blend between two lines is the degree 5 Hermite Bezier of the lines' own derivatives, controls (0.8,0) (0.8,0.04) (0.8,0.08) (0.08,0.8) (0.04,0.8) (0,0.8); the part of the profile in the material quadrant has area a = 0.360667 and first moment about the wall S = 0.102152. Swept along the corner curve (length 8.21299, total turn pi/2, curvature at most 0.269, so 1 - k*0.8 > 0 and the tube does not fold), it removes a*L - S*pi/2 = 2.8015; along l3, a straight bottom edge next to that corner (10 long on the left, 30 on the rear: the chain's naming fixes which, analysis does not), a*10 = 3.6067 or a*30 = 10.820. V lies between 7845.807 - 13.622 = 7832.185 and 7845.807 - 6.408 = 7839.399, widened by 1e-4 relative for the measurement: a cut that did nothing (7845.81) or a fillet not made falls outside. Box: the 40 x 20 x 10 box's (the fillets and the cut leave every extreme face)",
+  "method": "fillet: the documented curvature section, the order-2 section at the equal-area thumbweight on setback s = 5 between square planes (cov-fillet-section-curvature-box-edge-r3), cuts (1 - pi/4) * 25 = 5.36504592 mm^2 off each vertical edge (Green's theorem on it): Vf = 8000 - 4*10*5.36504592 = 7785.398. Tool section: the G2 blend between two lines is the degree 5 Hermite Bezier of the lines' own derivatives, controls (0.8,0) (0.8,0.04) (0.8,0.08) (0.08,0.8) (0.04,0.8) (0,0.8); the part of the profile in the material quadrant has area a = 0.360667 and first moment about the wall S = 0.102152. Swept along the corner curve (length 8.21299, total turn pi/2, curvature at most 0.269, so 1 - k*0.8 > 0 and the tube does not fold), it removes a*L - S*pi/2 = 2.8015; along l3, a straight bottom edge next to that corner (10 long on the left, 30 on the rear: the chain's naming fixes which, analysis does not), a*10 = 3.6067 or a*30 = 10.820. V lies between 7785.398 - 13.622 = 7771.776 and 7785.398 - 6.408 = 7778.990, widened by 1e-4 relative for the measurement: a cut that did nothing (7785.40) or a fillet not made falls outside. Box: the 40 x 20 x 10 box's (the fillets and the cut leave every extreme face)",
  "body_count": 1,
  "volume_mm3": [
-    7831.4,
-    7840.2
+    7771.0,
+    7779.8
  ],
  "bbox": {
    "min": [
@@ -23,4 +23,4 @@
      10.0
    ]
  }
-}
+}
@@ -5,10 +5,10 @@
 ],
 "what": "a curvature-continuous (G2) fillet of size 5 on a straight edge that ends on two slanted planar faces",
 "source": "analytic",
- "method": "prism over the polygon (0,0),(40,0),(30,20),(10,20), 20 tall: V0 = 600 * 20 = 12000. Fillet type curvature, size 5 on the top front edge (y=0, z=20, length 40): the curvature section: the order-2 section at thumbweight 0 between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.154192655384275 s^2 off the corner, its first moment about either face M = 0.0291753295725360 s^3 (Green's theorem on S), here s = 5: A = 3.85481638 and the first moment of y over it 3.64691620. The end faces are the planes x = y/2 and x = 40 - y/2, so the strip at depth y is 40 - y long: removed = 40 A - int y dA = 150.5457392. V = 12000 - removed = 11849.4543.",
+ "method": "prism over the polygon (0,0),(40,0),(30,20),(10,20), 20 tall: V0 = 600 * 20 = 12000. Fillet type curvature, size 5 on the top front edge (y=0, z=20, length 40): the curvature section: the order-2 section at the equal-area thumbweight between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.214601836603 s^2 off the corner, its first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S), here s = 5: A = 3.85481638 and the first moment of y over it 3.64691620. The end faces are the planes x = y/2 and x = 40 - y/2, so the strip at depth y is 40 - y long: removed = 40 A - int y dA = 150.5457392. V = 12000 - removed = 11849.4543. [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 11791.330159]",
 "body_count": 1,
- "volume_mm3": 11849.454260812292,
+ "volume_mm3": 11791.330159265486,
 "continuity": {
  "order": "g2"
 }
-}
+}
@@ -4,11 +4,11 @@
 ],
 "what": "a curvature-continuous (G2) fillet of size 6 on one edge of a 20 mm cube",
 "source": "analytic",
- "method": "type curvature: the curvature section: the order-2 section at thumbweight 0 between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.154192655384275 s^2 off the corner, its first moment about either face M = 0.0291753295725360 s^3 (Green's theorem on S), here s = radius = 6 (perpendicular faces): A = 5.55093559 mm^2; the edge is 20 long between two planar end faces square to it: V = 8000 - 20*5.55093559 = 7888.9813. Faces: 6 + 1 = 7.",
+ "method": "type curvature: the curvature section: the order-2 section at the equal-area thumbweight between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.214601836603 s^2 off the corner, its first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S), here s = radius = 6 (perpendicular faces): A = 5.55093559 mm^2; the edge is 20 long between two planar end faces square to it: V = 8000 - 20*5.55093559 = 7888.9813. Faces: 6 + 1 = 7. [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 7845.486678]",
 "body_count": 1,
- "volume_mm3": 7888.981288123322,
+ "volume_mm3": 7845.486677646163,
 "faces": 7,
 "continuity": {
  "order": "g2"
 }
-}
+}
@@ -2,9 +2,9 @@
 "sources": [],
 "what": "a boss's root on a plate rounded curvature-continuous size 2: the order-2 section of the square corner turned about the boss's axis, a certified fit",
 "source": "analytic",
- "method": "plate 60x40x10 with a boss R8 x 10 at (30, 20): V0 = 24000 + 640 pi = 26010.6193. In each meridian plane (rho, z) the plate's top and the boss's wall are the lines z = 10 and rho = 8, the feet of the point at distance d from both (8 + d, 10) and (8, 10 + d): the order-2 section at the default thumbweight 0 is that of a square corner (cov-fillet-section-curvature-box-edge-r3), area 0.154192655384275 s^2 = 0.616770622 (s = 2), first moment about the wall 0.233402637 (Green's theorem on the section), revolved (Pappus): 2 pi (8 A + M) = 32.469. V = 26043.0881. Faces 9; the seams at least G2 (the surface is a certified fit of the section turned about the axis: G3 to the plate along its rail, G2 to the wall at Continuity Analysis's tolerances).",
+ "method": "plate 60x40x10 with a boss R8 x 10 at (30, 20): V0 = 24000 + 640 pi = 26010.6193. In each meridian plane (rho, z) the plate's top and the boss's wall are the lines z = 10 and rho = 8, the feet of the point at distance d from both (8 + d, 10) and (8, 10 + d): the order-2 section at the equal-area thumbweight is that of a square corner (cov-fillet-section-curvature-box-edge-r3), area 0.214601836603 s^2 = 0.616770622 (s = 2), first moment about the wall 0.233402637 (Green's theorem on the section), revolved (Pappus): 2 pi (8 A + M) = 32.469. V = 26043.0881. Faces 9; the seams at least G2 (the surface is a certified fit of the section turned about the axis: G3 to the plate along its rail, G2 to the wall at Continuity Analysis's tolerances). [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 26056.152955]",
 "body_count": 1,
- "volume_mm3": 26043.0880831714,
+ "volume_mm3": 26056.152954783724,
 "faces": 9,
 "continuity": {
  "order": "g2"
@@ -2,9 +2,9 @@
 "sources": [],
 "what": "a box's top back edge rounded curvature-continuous size 3: the order-2 section meets each face with its curvature (0) and its third derivative (0), and not its fourth",
 "source": "analytic",
- "method": "box 40x30x20, the top back edge (y = 30, z = 20, 40 long) between the planar end faces x = 0 and 40, set back s = 3 along both faces (square to each other). In a plane x = const the faces' feet of the point at distance d from both are (30 - d, 20) and (30, 20 - d), linear in d, so the order-2 section is S(t) = f(t) (e + (1 - p1(t)) (rho1 - e)) + (1 - f(t)) (e + p2(t) (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), p1 = t / (1 - w + w t), p2 = t (1 - w) / (1 - w t), e the edge and rho_i the contacts, at the default thumbweight w = 0: it cuts 0.154192655384275 s^2 = 1.387733898 off the corner (Green's theorem on S). V = 24000 - 40 * 1.387733898 = 23944.4906. Its standoff from each face is c s^4: the t^3 term vanishes between planes (their feet are linear in d), so the section is G3 with them. Faces 7; both seams G3, not G4.",
+ "method": "box 40x30x20, the top back edge (y = 30, z = 20, 40 long) between the planar end faces x = 0 and 40, set back s = 3 along both faces (square to each other). In a plane x = const the faces' feet of the point at distance d from both are (30 - d, 20) and (30, 20 - d), linear in d, so the order-2 section is S(t) = f(t) (e + (1 - p1(t)) (rho1 - e)) + (1 - f(t)) (e + p2(t) (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), p1 = t / (1 - w + w t), p2 = t (1 - w) / (1 - w t), e the edge and rho_i the contacts, at the default, equal-area thumbweight w = -0.5252123889: it cuts 0.214601836603 s^2 = 1.387733898 off the corner (Green's theorem on S). V = 24000 - 40 * 1.387733898 = 23944.4906. Its standoff from each face is c s^4: the t^3 term vanishes between planes (their feet are linear in d), so the section is G3 with them. Faces 7; both seams G3, not G4. [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 23922.743339]",
 "body_count": 1,
- "volume_mm3": 23944.49064406166,
+ "volume_mm3": 23922.743338823082,
 "faces": 7,
 "bbox": {
  "min": [
@@ -2,9 +2,9 @@
 "sources": [],
 "what": "the concave edge where a pipe dips into a plate rounded curvature-continuous size 2: the order-2 section meets the plane with curvature 0 and the pipe with its curvature 1/10",
 "source": "analytic",
- "method": "plate 60x40x10 (z 0..10) joined to a pipe R10 along x (0..60) whose axis is at (y, z) = (20, 16): the pipe dips 4 into the plate and leaves it along y = 20 +- 8, z = 10, the edges ending on the planar faces x = 0 and 60. V0 = 24000 + 60 (100 pi - (100 acos 0.6 - 48)) = 40165.7846. The concave edge y = 28: in a plane x = const, the point at distance d from both faces is (20 + g, 10 + d), g = sqrt(64 + 32 d); its feet are F1 = (20 + g, 10) on the plate and F2 = (20 + 10 g / (10 + d), 26 - 160 / (10 + d)) on the pipe. The order-2 section between the r = 2 ball's contacts: S(t) = f(t) T1(1 - p1(t)) + (1 - f(t)) T2(p2(t)), f = (1-t)^3 / ((1-t)^3 + t^3), p1 = t / (1 - w + w t), p2 = t (1 - w) / (1 - w t), w = 0 (the default thumbweight), T_i(u) = sum_{k<=2} 2^k / k! F_i^(k)(2) (u - 1)^k (g' = 16 / g, g'' = -256 / g^3). It adds the area between it, the plate and the pipe, 1.54598304589003 (Green's theorem): V = 40165.7846 + 60 * 1.545983 = 40258.5436. The pipe's feet are not linear in d: the t^3 term of the standoff does not vanish, and both seams are G2, not G3.",
+ "method": "plate 60x40x10 (z 0..10) joined to a pipe R10 along x (0..60) whose axis is at (y, z) = (20, 16): the pipe dips 4 into the plate and leaves it along y = 20 +- 8, z = 10, the edges ending on the planar faces x = 0 and 60. V0 = 24000 + 60 (100 pi - (100 acos 0.6 - 48)) = 40165.7846. The concave edge y = 28: in a plane x = const, the point at distance d from both faces is (20 + g, 10 + d), g = sqrt(64 + 32 d); its feet are F1 = (20 + g, 10) on the plate and F2 = (20 + 10 g / (10 + d), 26 - 160 / (10 + d)) on the pipe. The order-2 section between the r = 2 ball's contacts: S(t) = f(t) T1(1 - p1(t)) + (1 - f(t)) T2(p2(t)), f = (1-t)^3 / ((1-t)^3 + t^3), p1 = t / (1 - w + w t), p2 = t (1 - w) / (1 - w t), w = -0.8544103493 (the equal-area default: the wedge at the middle station is 70.52878 degrees), T_i(u) = sum_{k<=2} 2^k / k! F_i^(k)(2) (u - 1)^k (g' = 16 / g, g'' = -256 / g^3). It adds the area between it, the plate and the pipe, 1.54598304589003 (Green's theorem): V = 40165.7846 + 60 * 1.545983 = 40258.5436. The pipe's feet are not linear in d: the t^3 term of the standoff does not vanish, and both seams are G2, not G3. [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 40302.590786]",
 "body_count": 1,
- "volume_mm3": 40258.5435962825,
+ "volume_mm3": 40302.59078634818,
 "continuity": {
  "order": "g2",
  "exact": true
@@ -2,10 +2,10 @@
 "sources": [],
 "what": "a block's long top edge rounded curvature-continuous (Type: Curvature) size 2, running from its end face into the cylinder the block is joined to",
 "source": "analytic",
- "method": "block 40x10x15 (x 0..40, y -5..5) joined to the cylinder R10 x 30 on the z axis, the block's end on the cylinder's diameter x = 0 so its sides y = +-5 meet the wall at vertical creases: V0 = 6000 + 3000 pi - 15 * (the disc's part with x > 0, |y| <= 5: 2 (y/2 sqrt(100-y^2) + 50 asin(y/10)) at y=5 = 95.661148) = 13989.8607. The edge y = 5, z = 15 between the planar top and side faces, ending on the planar end face x = 40 and on the cylinder wall; the curvature section: the order-2 section at thumbweight 0 between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.154192655384275 s^2 off the corner, its first moment about either face M = 0.0291753295725360 s^3 (Green's theorem on S), here s = 2, removed from the end face back to the wall, which keeps its material: strip length 40 - sqrt(100 - y^2) at height y. Removed = int over the region between the corner and the section of (40 - sqrt(100-y^2)) (Green's theorem on S, adaptive quadrature) = 19.2056794. V = 13970.6551. Both seams of the round with the planar faces G2.",
+ "method": "block 40x10x15 (x 0..40, y -5..5) joined to the cylinder R10 x 30 on the z axis, the block's end on the cylinder's diameter x = 0 so its sides y = +-5 meet the wall at vertical creases: V0 = 6000 + 3000 pi - 15 * (the disc's part with x > 0, |y| <= 5: 2 (y/2 sqrt(100-y^2) + 50 asin(y/10)) at y=5 = 95.661148) = 13989.8607. The edge y = 5, z = 15 between the planar top and side faces, ending on the planar end face x = 40 and on the cylinder wall; the curvature section: the order-2 section at the equal-area thumbweight between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.214601836603 s^2 off the corner, its first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S), here s = 2, removed from the end face back to the wall, which keeps its material: strip length 40 - sqrt(100 - y^2) at height y. Removed = int over the region between the corner and the section of (40 - sqrt(100-y^2)) (Green's theorem on S, adaptive quadrature) = 19.2056794. V = 13970.6551. Both seams of the round with the planar faces G2. [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 13963.157562]",
 "body_count": 1,
- "volume_mm3": 13970.655065102865,
+ "volume_mm3": 13963.15756186141,
 "continuity": {
  "order": "g2"
 }
-}
+}
@@ -2,9 +2,9 @@
 "sources": [],
 "what": "a curvature-continuous (Type: Curvature) round of size 3 on a box's long top edge, between two planar end faces",
 "source": "analytic",
- "method": "box 40x30x20, the top back edge (y=30, z=20, 40 long) filleted type curvature size 3: the curvature section: the order-2 section at thumbweight 0 between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.154192655384275 s^2 off the corner, its first moment about either face M = 0.0291753295725360 s^3 (Green's theorem on S), here s = 3: A = 1.387733898; the end faces x=0 and x=40 are square to the edge: V = 24000 - 40 * 1.387733898 = 23944.4906. Faces 7; both seams of the round with the faces G2 (G3 in fact, cov-fillet-section-curvature-box-edge-r3).",
+ "method": "box 40x30x20, the top back edge (y=30, z=20, 40 long) filleted type curvature size 3: the curvature section: the order-2 section at the equal-area thumbweight between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.214601836603 s^2 off the corner, its first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S), here s = 3: A = 1.387733898; the end faces x=0 and x=40 are square to the edge: V = 24000 - 40 * 1.387733898 = 23944.4906. Faces 7; both seams of the round with the faces G2 (G3 in fact, cov-fillet-section-curvature-box-edge-r3). [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 23922.743339]",
 "body_count": 1,
- "volume_mm3": 23944.49064406166,
+ "volume_mm3": 23922.743338823082,
 "faces": 7,
 "bbox": {
  "min": [
@@ -21,4 +21,4 @@
 "continuity": {
  "order": "g2"
 }
-}
+}
@@ -2,9 +2,9 @@
 "sources": [],
 "what": "the top rim of a hole through a plate rounded curvature-continuous (Type: Curvature) size 1",
 "source": "analytic",
- "method": "plate 40x40x10 with a through hole R5 at (20, 20): V0 = 16000 - 250 pi = 15214.6018. In every meridian plane the top face and the hole's wall are two lines square to each other: the curvature section: the order-2 section at thumbweight 0 between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.154192655384275 s^2 off the corner, its first moment about either face M = 0.0291753295725360 s^3 (Green's theorem on S), here s = 1: A = 0.154192655, M = 0.029175330 about the wall, revolved once: 2 pi (5 A + M) = 5.0274191. V = 15209.5744. Faces 8; both seams of the round G2.",
+ "method": "plate 40x40x10 with a through hole R5 at (20, 20): V0 = 16000 - 250 pi = 15214.6018. In every meridian plane the top face and the hole's wall are two lines square to each other: the curvature section: the order-2 section at the equal-area thumbweight between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.214601836603 s^2 off the corner, its first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S), here s = 1: A = 0.154192655, M = 0.029175330 about the wall, revolved once: 2 pi (5 A + M) = 5.0274191. V = 15209.5744. Faces 8; both seams of the round G2. [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 15207.561746]",
 "body_count": 1,
- "volume_mm3": 15209.574417466521,
+ "volume_mm3": 15207.561746435134,
 "faces": 8,
 "bbox": {
  "min": [
@@ -21,4 +21,4 @@
 "continuity": {
  "order": "g2"
 }
-}
+}
@@ -2,9 +2,9 @@
 "sources": [],
 "what": "an L-bracket's inside bend rounded curvature-continuous (Type: Curvature) size 3",
 "source": "analytic",
- "method": "L-bracket: the legs 40x20x5 (x 0..40, z 0..5) and 5x20x40 (x 0..5, z 0..40) joined, 20 deep in y: V0 = 4000 + 4000 - 500 = 7500, 8 faces. The concave edge between two planes square to each other, its ends on the planar faces y = 0 and 20: the curvature section: the order-2 section at thumbweight 0 between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.154192655384275 s^2 off the corner, its first moment about either face M = 0.0291753295725360 s^3 (Green's theorem on S), here s = 3: A = 1.387733898, added along 20: V = 7527.7547. Faces 9; both seams G2.",
+ "method": "L-bracket: the legs 40x20x5 (x 0..40, z 0..5) and 5x20x40 (x 0..5, z 0..40) joined, 20 deep in y: V0 = 4000 + 4000 - 500 = 7500, 8 faces. The concave edge between two planes square to each other, its ends on the planar faces y = 0 and 20: the curvature section: the order-2 section at the equal-area thumbweight between the contacts set back s along two planes square to each other (cov-fillet-section-curvature-box-edge-r3), S(t) = f(t) (e + (1 - t) (rho1 - e)) + (1 - f(t)) (e + t (rho2 - e)), f = (1-t)^3 / ((1-t)^3 + t^3), e the corner: it cuts A = 0.214601836603 s^2 off the corner, its first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S), here s = 3: A = 1.387733898, added along 20: V = 7527.7547. Faces 9; both seams G2. [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 7538.628331]",
 "body_count": 1,
- "volume_mm3": 7527.754677969169,
+ "volume_mm3": 7538.628330588459,
 "faces": 9,
 "bbox": {
  "min": [
@@ -21,4 +21,4 @@
 "continuity": {
  "order": "g2"
 }
-}
+}
@@ -1,7 +1,7 @@
 {
 "what": "report-fillet-curvature-three-edges-at-bar-corner-solver-residues less its setback cube: the three curvature rounds outside it, exactly; reported from the app (2026-10-30, test-peg part)",
 "source": "analytic",
- "method": "the same bar with the sketch solver's residues of the reported design (~1e-10 mm: the front side's ends differ by 3.0e-10 in y, the arc's centre 5.7e-11 off the disc's), corner (0.489294, 0.057925), length L = 41.160417754, V0 = L * 16.0000000000762 * 10 + 960 pi; the curvature section of setback 2: the order-2 section at thumbweight 0 from (2, 0) on the top to (0, 2) on the side (y from the front face, depth below the top), area A2 = 0.616770621537 (cov-fillet-section-curvature-box-edge-r3 at s = 2); the body less the setback cube: a box [-1, 3] x [-1, 3] x [7, 11] about the corner (the patch starts 3 along each edge, so outside it each round is its whole section) cut away: V0 - 27 - removed outside the cube: the front round's section from 3 past the left face to the wall (23.3237146876 + A2 (L - 40) - 3 A2), the vertical and left rounds A2 over 7 and 13: removed 34.5245268332",
+ "method": "the same bar with the sketch solver's residues of the reported design (~1e-10 mm: the front side's ends differ by 3.0e-10 in y, the arc's centre 5.7e-11 off the disc's), corner (0.489294, 0.057925), length L = 41.160417754, V0 = L * 16.0000000000762 * 10 + 960 pi; the curvature section of setback 2: the order-2 section at the equal-area thumbweight from (2, 0) on the top to (0, 2) on the side (y from the front face, depth below the top), area A2 = 0.616770621537 (cov-fillet-section-curvature-box-edge-r3 at s = 2); the body less the setback cube: a box [-1, 3] x [-1, 3] x [7, 11] about the corner (the patch starts 3 along each edge, so outside it each round is its whole section) cut away: V0 - 27 - removed outside the cube: the front round's section from 3 past the left face to the wall (23.3237146876 + A2 (L - 40) - 3 A2), the vertical and left rounds A2 over 7 and 13: removed 34.5245268332 [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 9526.705048]",
 "body_count": 1,
- "volume_mm3": 9540.071261284415
+ "volume_mm3": 9526.705048390453
 }
@@ -1,9 +1,9 @@
 {
 "what": "as report-fillet-curvature-three-edges-at-bar-corner, with the sketch solver's residues of the reported design; reported from the app (2026-10-30, test-peg part)",
 "source": "analytic",
- "method": "the same bar with the sketch solver's residues of the reported design (~1e-10 mm: the front side's ends differ by 3.0e-10 in y, the arc's centre 5.7e-11 off the disc's), corner (0.489294, 0.057925), length L = 41.160417754, V0 = L * 16.0000000000762 * 10 + 960 pi; the curvature section of setback 2: the order-2 section at thumbweight 0 from (2, 0) on the top to (0, 2) on the side (y from the front face, depth below the top), area A2 = 0.616770621537 (cov-fillet-section-curvature-box-edge-r3 at s = 2); removed 40.0754624270 if each round ran whole to the vertex (the front one as report-fillet-curvature-three-edges-at-bar-corner's and A2 over the further L - 40); the patch within the setback cube, so V is graded with 3^3 as its tolerance; every seam of the rounds and the patch G2",
+ "method": "the same bar with the sketch solver's residues of the reported design (~1e-10 mm: the front side's ends differ by 3.0e-10 in y, the arc's centre 5.7e-11 off the disc's), corner (0.489294, 0.057925), length L = 41.160417754, V0 = L * 16.0000000000762 * 10 + 960 pi; the curvature section of setback 2: the order-2 section at the equal-area thumbweight from (2, 0) on the top to (0, 2) on the side (y from the front face, depth below the top), area A2 = 0.616770621537 (cov-fillet-section-curvature-box-edge-r3 at s = 2); removed 40.0754624270 if each round ran whole to the vertex (the front one as report-fillet-curvature-three-edges-at-bar-corner's and A2 over the further L - 40); the patch within the setback cube, so V is graded with 3^3 as its tolerance; every seam of the rounds and the patch G2 [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 9545.979382]",
 "body_count": 1,
- "volume_mm3": 9561.52032569058,
+ "volume_mm3": 9545.979382272762,
 "tolerance": {
  "rel": 0.0028238187108648883
 },
@@ -1,9 +1,9 @@
 {
 "what": "a curvature-continuous fillet (equivalent radius 2) of the three edges at a top corner of a bar whose far end runs tangent into a cylinder: it built with SMLib's own corner patch, tangent to the rounds only (a 35.8 / mm curvature jump), seen as a dome on the corner; the corner must be a G2 patch; reported from the app (2026-10-30, test-peg part)",
 "source": "analytic",
- "method": "a bar 40 x 16 x 10 whose far end is a half disc R8 about (40, 8), a disc R8 about the same centre sketched on its top (the top's outline projected) and extruded 10 up, joined: the bar's sides run tangent into the cylinder, V0 = 6400 + 960 pi; the curvature section of setback 2: the order-2 section at thumbweight 0 from (2, 0) on the top to (0, 2) on the side (y from the front face, depth below the top), area A2 = 0.616770621537 (cov-fillet-section-curvature-box-edge-r3 at s = 2); the front round removes the section along x up to the wall, x = 40 - sqrt(64 - (8 - y)^2), 23.3237146876 (report-peg-front-curvature-round-r2), the vertical and left rounds A2 along 10 and 16: removed 39.3597508476 if each ran whole to the vertex; the corner patch (set back 1.5 r = 3) lies within the setback cube, so V is graded as V0 - that with 3^3 as its tolerance; every seam of the rounds and the patch G2",
+ "method": "a bar 40 x 16 x 10 whose far end is a half disc R8 about (40, 8), a disc R8 about the same centre sketched on its top (the top's outline projected) and extruded 10 up, joined: the bar's sides run tangent into the cylinder, V0 = 6400 + 960 pi; the curvature section of setback 2: the order-2 section at the equal-area thumbweight from (2, 0) on the top to (0, 2) on the side (y from the front face, depth below the top), area A2 = 0.616770621537 (cov-fillet-section-curvature-box-edge-r3 at s = 2); the front round removes the section along x up to the wall, x = 40 - sqrt(64 - (8 - y)^2), 23.3237146876 (report-peg-front-curvature-round-r2), the vertical and left rounds A2 along 10 and 16: removed 39.3597508476 if each ran whole to the vertex; the corner patch (set back 1.5 r = 3) lies within the setback cube, so V is graded as V0 - that with 3^3 as its tolerance; every seam of the rounds and the patch G2 [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 9361.308653]",
 "body_count": 1,
- "volume_mm3": 9376.569196598593,
+ "volume_mm3": 9361.308652726337,
 "tolerance": {
  "rel": 0.0028795180234786103
 },
@@ -1,9 +1,9 @@
 {
 "what": "the peg's front top edge alone given a curvature-continuous round (equivalent radius 2) running into the cylinder: its section leaves the front face with zero curvature, so its end on the cylinder's wall is a semicubical cusp (x - 40 ~ (8 - z)^1.5) where the front face runs tangent into the cylinder; reported from the app (2026-10-30, test-peg part)",
 "source": "analytic",
- "method": "a bar 40 x 16 x 10 whose far end is a half disc R8 about (40, 8), a disc R8 about the same centre sketched on its top (the top's outline projected) and extruded 10 up, joined: the bar's front face y = 0 runs tangent into the cylinder along x = 40, V0 = 6400 + 960 pi; the curvature section of setback 2: the order-2 section at thumbweight 0 (SMLIB_BLEND_CURVATURE) from (2, 0) on the top to (0, 2) on the front face (y from the front face, depth below the top): y = 2 (1 - f) t, depth 2 f (1 - t), f = (1-t)^3 / ((1-t)^3 + t^3), area 0.616770621537; the round removes it along x up to the cylinder's wall, x = 40 - sqrt(64 - (8 - y)^2): removed = integral over the section of that length = 23.3237146876 (Green's theorem on the section, adaptive quadrature); every seam of the round with its faces G2",
+ "method": "a bar 40 x 16 x 10 whose far end is a half disc R8 about (40, 8), a disc R8 about the same centre sketched on its top (the top's outline projected) and extruded 10 up, joined: the bar's front face y = 0 runs tangent into the cylinder along x = 40, V0 = 6400 + 960 pi; the curvature section of setback 2: the order-2 section at the equal-area thumbweight (SMLIB_BLEND_CURVATURE) from (2, 0) on the top to (0, 2) on the front face (y from the front face, depth below the top): y = 2 (1 - f) t, depth 2 f (1 - t), f = (1-t)^3 / ((1-t)^3 + t^3), area 0.616770621537; the round removes it along x up to the cylinder's wall, x = 40 - sqrt(64 - (8 - y)^2): removed = integral over the section of that length = 23.3237146876 (Green's theorem on the section, adaptive quadrature); every seam of the round with its faces G2 [the curvature section at the equal-area thumbweight (the default): on the same rails it takes off what the ball's circle does, so between square planes w = -0.5252123889 and it cuts A = (1 - pi/4) s^2 = 0.214601836603 s^2, first moment about either face M = 0.0474559669443 s^3 (Green's theorem on S); V = 9383.627244]",
 "body_count": 1,
- "volume_mm3": 9392.605232758558,
+ "volume_mm3": 9383.627243733003,
 "continuity": {
  "order": "g2"
 }