A sweep along a path with sharp corners follows the corners: sweeping a rim profile along three lines (an open rectangle) gave a body of volume -0.0006 mm3 with its centre of mass at x = -3.5e9, and no error

kernel::sweep swept segment by segment: a line translates the profile along it, an arc turns it. At a sharp corner the next line runs within the plane the profile has reached, so the profile slid sideways in its own plane and the walls folded into an inside-out, zero-volume shell. Paths whose direction changes at a joint (more than 1e-3 rad) are now swept as a polyline by sweep_path, which mitres the corners; arcs become points within 0.01 mm. Smooth paths (lines and tangent arcs) are swept as before. Pipe uses the same path.

Tests: sweep_round_a_sharp_corner_is_mitred sweeps a 2 x 2 square along an L of two 10 mm lines and checks the volume, 80 mm3 (fails on main).

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

crates/kernel/src/build.rs

@@ -795,13 +795,68 @@ pub enum PathSeg {
     },
 }
 
+impl PathSeg {
+    /// Unit directions of the path where the segment starts and ends.
+    fn tangents(&self) -> Option<(Vec3, Vec3)> {
+        match *self {
+            PathSeg::Line { a, b } => {
+                let t = (b - a).normalized()?;
+                Some((t, t))
+            }
+            PathSeg::Arc { a, center, axis, angle } => {
+                let k = axis.normalized()?;
+                let end = rotate_about(a, center, k, angle);
+                Some((k.cross(a - center).normalized()?, k.cross(end - center).normalized()?))
+            }
+        }
+    }
+
+    /// Points along the segment (an arc within `tol` of its chords), without its start.
+    fn points_after_start(&self, tol: f64) -> Vec<Vec3> {
+        match *self {
+            PathSeg::Line { b, .. } => vec![b],
+            PathSeg::Arc { a, center, axis, angle } => {
+                let Some(k) = axis.normalized() else { return vec![a] };
+                let r = (a - center).len();
+                let step = if r > tol { 2.0 * (1.0 - tol / r).acos() } else { angle.abs() };
+                let n = ((angle.abs() / step.max(1e-6)).ceil() as usize).clamp(1, 512);
+                (1..=n).map(|i| rotate_about(a, center, k, angle * i as f64 / n as f64)).collect()
+            }
+        }
+    }
+}
+
+/// `p` turned by `angle` about the unit axis `k` through `center` (right hand).
+fn rotate_about(p: Vec3, center: Vec3, k: Vec3, angle: f64) -> Vec3 {
+    let v = p - center;
+    let (s, c) = angle.sin_cos();
+    center + v * c + k.cross(v) * s + k * (k.dot(v) * (1.0 - c))
+}
+
 /// Sweep a planar region (outer loop) along a chain of path segments, keeping the profile
-/// perpendicular to the path (lines translate it, arcs rotate it).
+/// perpendicular to the path (lines translate it, arcs rotate it). A path with sharp corners
+/// is swept as a polyline, mitred at the corners.
 pub fn sweep(plane: &Plane, region: &Region2, path: &[PathSeg]) -> Result<Body> {
     region_ok(region)?;
     if path.is_empty() || path.len() > 1000 {
         return Err(KernelError::Invalid("the path needs 1…1000 segments".into()));
     }
+    // Segment by segment the profile only follows a path whose direction runs on across each
+    // joint: at a corner the next line would slide the profile within its own plane.
+    let ends: Vec<(Vec3, Vec3)> =
+        path.iter().map(PathSeg::tangents).collect::<Option<_>>().ok_or_else(|| KernelError::Invalid("a path segment has no direction".into()))?;
+    let corner = ends.windows(2).any(|w| w[0].1.dot(w[1].0) < (1e-3f64).cos());
+    if corner {
+        let first = match path.first() {
+            Some(PathSeg::Line { a, .. } | PathSeg::Arc { a, .. }) => *a,
+            None => return Err(KernelError::Invalid("the path needs 1…1000 segments".into())),
+        };
+        let mut pts = vec![first];
+        for seg in path {
+            pts.extend(seg.points_after_start(1e-2));
+        }
+        return crate::sweep_path::sweep_path(plane, region, &pts);
+    }
     // The outer loop and each hole, swept along the path; the ends are capped with holes.
     let mut starts = vec![wire(plane, &region.outer.ccw())?];
     for h in &region.holes {

crates/kernel/src/tests.rs

@@ -258,6 +258,22 @@ fn loft_and_sweep() {
     assert!(rel(measure(&t).unwrap().volume, expect) < 1e-3, "{} vs {expect}", measure(&t).unwrap().volume);
 }
 
+#[test]
+fn sweep_round_a_sharp_corner_is_mitred() {
+    // A 2 × 2 square centred on an L of two 10 mm lines: lines alone would slide the profile
+    // along the second leg within its own plane (an empty, inside-out body). Mitred, the
+    // volume is the area times the path length.
+    let sq =
+        Region2 { outer: Loop2::polygon(&[Vec2::new(-1.0, -1.0), Vec2::new(1.0, -1.0), Vec2::new(1.0, 1.0), Vec2::new(-1.0, 1.0)]), holes: vec![] };
+    let path = [
+        PathSeg::Line { a: Vec3::ZERO, b: Vec3::new(0.0, 0.0, 10.0) },
+        PathSeg::Line { a: Vec3::new(0.0, 0.0, 10.0), b: Vec3::new(10.0, 0.0, 10.0) },
+    ];
+    let b = sweep(&Plane::XY, &sq, &path).unwrap();
+    let m = measure(&b).unwrap();
+    assert!(rel(m.volume, 80.0) < 1e-9, "{}", m.volume);
+}
+
 #[test]
 fn moving_a_body_with_an_intersection_curve_edge_ends() {
     // A cylinder cut by a tilted box keeps an elliptical intersection curve as an edge. Moving