fix: draw small radii on large bodies round (#515)

Display meshes also bound the angle one facet turns, so bends and small holes on a large body are drawn round instead of as chamfers or squares. Bounded per face, and only the display mesh changes.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

crates/doc/src/eval.rs

@@ -62,12 +62,14 @@ impl ModelBody {
     pub fn definition_name(&self) -> &str {
         self.source_name.as_deref().unwrap_or(&self.name)
     }
-    /// Display mesh (chord tolerance 1/1000 of the body size), computed once.
+    /// Display mesh, computed once: chord tolerance 1/1000 of the body size, and no facet of a
+    /// curved face or edge turning more than [`kernel::DISPLAY_ANGLE`], so that a bend or a
+    /// hole that is small beside the body is still drawn round.
     pub fn mesh(&self) -> Arc<Mesh> {
         self.mesh
             .get_or_init(|| {
                 let tol = (self.body.size() * 1e-3).max(1e-3);
-                Arc::new(self.body.display_mesh(tol).unwrap_or_default())
+                Arc::new(self.body.display_mesh_angular(tol, kernel::DISPLAY_ANGLE).unwrap_or_default())
             })
             .clone()
     }

crates/engine/src/display_mesh_tests.rs

@@ -0,0 +1,153 @@
+//! What the application draws of a large sheet with small bends and holes, and that what
+//! reads the same mesh (bounds, picks, inside tests) answers as before.
+
+use std::f64::consts::{FRAC_PI_2, TAU};
+
+use serde_json::{Value, json};
+use solidcraft_geom::{Mesh, Vec3};
+use solidcraft_kernel::{DISPLAY_ANGLE, FaceSurface, face_surface};
+
+use crate::Session;
+
+fn run(s: &mut Session, id: &str, p: Value) -> Value {
+    match s.execute(id, &p) {
+        Ok(v) => v,
+        Err(e) => panic!("{id} {p}: {e}"),
+    }
+}
+
+const HOLES: [[f64; 2]; 4] = [[30.0, 20.0], [1500.0, 20.0], [2970.0, 980.0], [30.0, 980.0]];
+
+/// A 3000 x 1000 x 2 sheet with bend radius 1, four holes of diameter 4 and a 40 mm flange on
+/// each long side.
+fn large_sheet() -> Session {
+    let mut s = Session::default();
+    run(&mut s, "sheet.manage_rules", json!({"name": "AL2", "thickness": "2 mm", "k_factor": "0.5", "bend_radius": "1 mm", "active": true}));
+    run(&mut s, "sketch.create", json!({"plane": "XY", "name": "Base"}));
+    run(&mut s, "sketch.rectangle.two_point", json!({"p0": [0, 0], "p1": [3000, 1000]}));
+    run(&mut s, "sketch.finish", json!({}));
+    run(&mut s, "sheet.flange", json!({"sketch": "Base"}));
+    run(&mut s, "sketch.create", json!({"plane": "XY", "name": "Holes"}));
+    for c in HOLES {
+        run(&mut s, "sketch.circle.center", json!({"center": c, "diameter": 4}));
+    }
+    run(&mut s, "sketch.finish", json!({}));
+    run(&mut s, "solid.extrude", json!({"sketch": "Holes", "distance": 10, "through_all": true, "operation": "cut"}));
+    run(&mut s, "sheet.flange", json!({"edges": [[1500, 0, 2], [1500, 1000, 2]], "height": 40}));
+    s
+}
+
+/// The widest angle between neighbouring lines of vertices around a cylinder face, and how
+/// many such steps the face has.
+fn steps_around(m: &Mesh, face: usize, origin: Vec3, axis: Vec3) -> (usize, f64) {
+    let u = axis.any_perp();
+    let v = axis.cross(u);
+    let mut a: Vec<f64> = m
+        .triangles
+        .iter()
+        .zip(&m.tri_face)
+        .filter(|(_, f)| **f as usize == face)
+        .flat_map(|(t, _)| t.iter())
+        .map(|k| m.positions[*k as usize] - origin)
+        .map(|d| d.dot(v).atan2(d.dot(u)))
+        .collect();
+    a.sort_by(f64::total_cmp);
+    a.dedup_by(|x, y| (*x - *y).abs() < 1e-7);
+    // Leave out the widest gap: the part of the turn the face does not cover.
+    let n = a.len();
+    let mut gaps: Vec<f64> = (0..n).map(|i| (a[(i + 1) % n] - a[i]).rem_euclid(TAU)).collect();
+    gaps.sort_by(f64::total_cmp);
+    gaps.pop();
+    (gaps.len(), gaps.last().copied().unwrap_or(0.0))
+}
+
+#[test]
+fn a_large_sheet_shows_its_small_bends_and_holes_round() {
+    let s = large_sheet();
+    let st = s.world_state();
+    let b = &st.bodies[0];
+    let m = b.mesh();
+    assert!(b.body.size() * 1e-3 > 3.0, "the chord tolerance is more than any radius here");
+    let (mut bends, mut walls) = (0, 0);
+    for face in 0..b.body.face_count() {
+        let Some(FaceSurface::Cylinder { origin, axis, radius }) = face_surface(&b.body, face) else { continue };
+        let (steps, widest) = steps_around(&m, face, origin, axis);
+        assert!(widest <= DISPLAY_ANGLE * 1.001, "radius {radius}: a facet spans {} degrees", widest.to_degrees());
+        if (radius - 2.0).abs() < 1e-6 {
+            // Half of a hole's wall.
+            walls += 1;
+            assert!(steps >= (TAU / 2.0 / DISPLAY_ANGLE).ceil() as usize, "{steps} facets around half a hole");
+        } else {
+            // A bend's inner (1 mm) or outer (3 mm) side: a quarter turn.
+            bends += 1;
+            assert!((radius - 1.0).abs() < 1e-6 || (radius - 3.0).abs() < 1e-6, "radius {radius}");
+            assert!(steps >= (FRAC_PI_2 / DISPLAY_ANGLE).ceil() as usize, "radius {radius}: {steps} facets across the bend");
+        }
+    }
+    assert_eq!((bends, walls), (4, 8));
+    // The edges the viewport draws: every hole's rim is round, on both sides of the sheet.
+    for [x, y] in HOLES {
+        for z in [0.0, 2.0] {
+            let on = |p: &Vec3| (p.z - z).abs() < 1e-6 && ((p.x - x).hypot(p.y - y) - 2.0).abs() < 1e-6;
+            let rim: Vec<&Vec<Vec3>> = m.edges.iter().filter(|e| e.iter().all(on)).collect();
+            let segments: usize = rim.iter().map(|e| e.len() - 1).sum();
+            assert!(segments >= (TAU / DISPLAY_ANGLE).ceil() as usize, "{segments} segments around the rim at {x}, {y}, {z}");
+            let widest = rim.iter().flat_map(|e| e.windows(2)).map(|w| 2.0 * (w[0].dist(w[1]) / 4.0).asin()).fold(0.0, f64::max);
+            assert!(widest <= DISPLAY_ANGLE * 1.001, "a rim segment spans {} degrees", widest.to_degrees());
+        }
+    }
+    // And the scene the renderers take draws those same polylines.
+    let scene = crate::view::scene(&s, &crate::view::home_camera(&s));
+    let drawn: usize =
+        scene.lines.iter().filter(|l| l.points.iter().all(|p| ((p.x - 30.0).hypot(p.y - 20.0) - 2.0).abs() < 1e-6)).map(|l| l.points.len() - 1).sum();
+    assert!(drawn >= 2 * (TAU / DISPLAY_ANGLE).ceil() as usize, "{drawn} rim segments in the scene");
+}
+
+#[test]
+fn what_reads_the_display_mesh_of_a_large_sheet_answers_as_before() {
+    let s = large_sheet();
+    let st = s.world_state();
+    let b = &st.bodies[0];
+    let m = b.mesh();
+    let coarse = b.body.display_mesh((b.body.size() * 1e-3).max(1e-3)).unwrap();
+    // Bounds: the sheet's box is set by flat faces, so the rounder bends move nothing.
+    let (now, before) = (m.bounds(), coarse.bounds());
+    assert!(now.min.dist(before.min) < 1e-9 && now.max.dist(before.max) < 1e-9, "{now:?} {before:?}");
+    let exact = solidcraft_kernel::measure(&b.body).unwrap().bbox;
+    assert!(now.min.dist(exact.min) < 1e-6 && now.max.dist(exact.max) < 1e-6, "{now:?} {exact:?}");
+    // The cost: the sheet takes 2212 triangles against the chord mesh's 92 when measured, a factor of
+    // 24; what grows is the number of round faces and the facets across each, not the size of the body.
+    assert!(
+        m.triangles.len() <= 30 * coarse.triangles.len() && m.triangles.len() < 4000,
+        "{} triangles, {} at the chord tolerance",
+        m.triangles.len(),
+        coarse.triangles.len()
+    );
+    // The same faces and edges, in the same order, between the same faces, with the same ends.
+    assert_eq!(m.edge_faces, coarse.edge_faces);
+    assert_eq!(m.tri_face.iter().max(), coarse.tri_face.iter().max());
+    assert_eq!(m.edges.len(), coarse.edges.len());
+    for (fine, rough) in m.edges.iter().zip(&coarse.edges) {
+        assert!(fine[0].dist(rough[0]) < 1e-9 && fine[fine.len() - 1].dist(rough[rough.len() - 1]) < 1e-9);
+    }
+    // Picks: a point on a round face (on the true cylinder, which a flat strip across a bend
+    // misses by up to 0.9 mm) is found on that face, as is one in the middle of a flat face.
+    let mut round = 0;
+    for face in 0..b.body.face_count() {
+        let Some(FaceSurface::Cylinder { origin, axis, radius }) = face_surface(&b.body, face) else { continue };
+        let corners: Vec<Vec3> =
+            m.triangles.iter().zip(&m.tri_face).filter(|(_, f)| **f as usize == face).flat_map(|(t, _)| t.map(|k| m.positions[k as usize])).collect();
+        let middle = corners.iter().fold(Vec3::ZERO, |a, p| a + *p) / corners.len() as f64;
+        // The middle of the face's corners, pushed out onto the cylinder.
+        let along = origin + axis * (middle - origin).dot(axis);
+        let p = along + (middle - along).normalized().unwrap() * radius;
+        assert_eq!(solidcraft_doc::appearance::face_index_at(b, p), Some(face), "radius {radius} at {p:?}");
+        round += 1;
+    }
+    assert_eq!(round, 12);
+    let top = solidcraft_doc::appearance::face_index_at(b, Vec3::new(1500.0, 500.0, 2.0)).unwrap();
+    assert!(matches!(face_surface(&b.body, top), Some(FaceSurface::Plane { normal, .. }) if normal.dist(Vec3::Z) < 1e-9));
+    // Inside and outside: in the sheet, in a flange's wall, in a hole and above the sheet.
+    assert!(m.contains(Vec3::new(1500.0, 500.0, 1.0)) && m.contains(Vec3::new(1500.0, now.min.y + 1.0, now.max.z - 10.0)));
+    assert!(!m.contains(Vec3::new(30.0, 20.0, 1.0)) && !m.contains(Vec3::new(1500.0, 500.0, 3.0)));
+}

crates/engine/src/lib.rs

@@ -793,6 +793,8 @@ mod construct_tests;
 #[cfg(test)]
 mod delete_face_tests;
 #[cfg(test)]
+mod display_mesh_tests;
+#[cfg(test)]
 mod extent_tests;
 #[cfg(test)]
 mod hole_face_tests;

crates/kernel/src/body.rs

@@ -148,17 +148,38 @@ pub struct FaceInfo {
 
 type MeshedShell = truck_topology::Shell<mt::Point3, PolylineCurve<mt::Point3>, Option<PolygonMesh>>;
 
+/// The most one facet of the display mesh turns (radians): a curved face or edge is divided
+/// until no facet spans more of it than this, however small its radius is beside the body.
+/// 20 degrees: a quarter turn is drawn with at least five facets, a full circle with at least 18.
+pub const DISPLAY_ANGLE: f64 = std::f64::consts::PI / 9.0;
+
+/// The sag, as a fraction of the chord tolerance, below which the angle no longer divides a
+/// facet: at [`DISPLAY_ANGLE`] and the application's tolerance of 1/1000 of the body, a radius
+/// under about 1/15000 of the body gets fewer facets than the angle asks for, and one under
+/// a millionth of it only those of the chord tolerance.
+const DISPLAY_ANGLE_FLOOR: f64 = 1e-3;
+
+/// The finest angle a display mesh is divided by (one degree).
+const MIN_DISPLAY_ANGLE: f64 = std::f64::consts::PI / 180.0;
+
 /// Triangulate each shell (not the solid: truck's solid constructor panics on the open or
 /// non-manifold shells an import can produce). Boundaries that lie on their surface only within
 /// tolerance (imports, boolean results) are projected onto it.
 fn mesh_shells(solid: &Solid, tol: f64) -> Vec<MeshedShell> {
+    mesh_shells_within(solid, Deflection::chord(tol))
+}
+
+/// [`mesh_shells`] divided by a chord tolerance and, when it has one, a bound on the angle a
+/// facet spans. Each edge is divided once for both its faces, so the faces still share its
+/// points.
+fn mesh_shells_within(solid: &Solid, deflection: Deflection) -> Vec<MeshedShell> {
     solid
         .boundaries()
         .iter()
         // The robust search tries the exact one first, so exact geometry costs nothing extra; a
         // face can also come back as an empty mesh rather than none (boolean results with
         // approximate intersection curves), so always use it.
-        .map(|sh| sh.robust_triangulation(tol))
+        .map(|sh| sh.robust_triangulation_within(deflection))
         .collect()
 }
 
@@ -838,13 +859,24 @@ impl Body {
     /// Like [`Body::tessellate`]; with `refine`, triangles that cut through curved faces are
     /// split until within `tol` of the surface (for measuring).
     pub fn tessellate_with(&self, tol: f64, refine: bool) -> Result<Mesh> {
+        self.tessellate_within(tol, f64::INFINITY, refine)
+    }
+
+    /// [`Body::tessellate_with`] in which no facet turns more than `angle` radians either
+    /// (infinite: the chord tolerance alone).
+    fn tessellate_within(&self, tol: f64, angle: f64, refine: bool) -> Result<Mesh> {
         let tol = if tol.is_finite() && tol > 0.0 { tol } else { 0.05 };
         let tol = tol.max(self.size() * 1e-6);
         if let Some(m) = &self.mesh {
             return Ok(m.to_mesh());
         }
+        let deflection = if angle.is_finite() && angle > 0.0 {
+            Deflection { chord: tol, angle: angle.max(MIN_DISPLAY_ANGLE), floor: tol * DISPLAY_ANGLE_FLOOR }
+        } else {
+            Deflection::chord(tol)
+        };
         guard("tessellate", || {
-            let meshed = mesh_shells(&self.solid, tol);
+            let meshed = mesh_shells_within(&self.solid, deflection);
             let mut out = Mesh::default();
             let solid_faces: Vec<&mt::Face> = self.solid.face_iter().collect();
             for (fi, face) in meshed.iter().flat_map(|s| s.face_iter()).enumerate() {
@@ -941,7 +973,20 @@ impl Body {
 
     /// Display mesh: like [`Body::tessellate`], with seam edges flagged.
     pub fn display_mesh(&self, tol: f64) -> Result<Mesh> {
-        let mut m = self.tessellate(tol)?;
+        self.flagged(self.tessellate(tol)?)
+    }
+
+    /// Display mesh whose curved faces and edges look curved whatever the body's size: like
+    /// [`Body::display_mesh`], and no facet turns more than `angle` radians (see
+    /// [`DISPLAY_ANGLE`]). A chord tolerance that follows the body's size is larger than the
+    /// sagitta of a small radius on a large body (a sheet-metal bend, a small hole), which the
+    /// tolerance alone leaves as one flat facet.
+    pub fn display_mesh_angular(&self, tol: f64, angle: f64) -> Result<Mesh> {
+        self.flagged(self.tessellate_within(tol, angle, false)?)
+    }
+
+    /// A tessellation with its edges flagged for display (seams, tangent joins, protected creases).
+    fn flagged(&self, mut m: Mesh) -> Result<Mesh> {
         if self.is_mesh() {
             return Ok(m);
         }
@@ -1221,6 +1266,10 @@ mod lump_tests;
 #[path = "refine_cache_tests.rs"]
 mod refine_cache_tests;
 
+#[cfg(test)]
+#[path = "display_mesh_tests.rs"]
+mod display_mesh_tests;
+
 #[cfg(test)]
 #[path = "regularization_protection_tests.rs"]
 mod regularization_protection_tests;

crates/kernel/src/display_mesh_tests.rs

@@ -0,0 +1,350 @@
+//! The display mesh of a large body with small radii: bends and holes look round, the mesh
+//! stays closed, and the cost stays bounded.
+
+use std::collections::HashMap;
+use std::f64::consts::{FRAC_PI_2, PI, TAU};
+
+use solidcraft_geom::{Loop2, Mesh, Plane, Region2, Seg2, Vec2, Vec3};
+
+use super::{Body, DISPLAY_ANGLE};
+use crate::{FaceSurface, extrude, face_surface};
+
+/// The chord tolerance the application draws a body with.
+fn display_tol(b: &Body) -> f64 {
+    (b.size() * 1e-3).max(1e-3)
+}
+
+fn rect(w: f64, h: f64) -> Loop2 {
+    Loop2::polygon(&[Vec2::new(0.0, 0.0), Vec2::new(w, 0.0), Vec2::new(w, h), Vec2::new(0.0, h)])
+}
+
+/// A `length` long angle of 2 mm sheet: a 100 mm leg along X, a 90 degree bend of inner
+/// radius 1 (outer 3) about the line x = y = 3, and a 40 mm leg along Y, extruded along Z.
+fn bent_sheet(length: f64) -> Body {
+    let line = |a: (f64, f64), b: (f64, f64)| Seg2::Line { a: Vec2::new(a.0, a.1), b: Vec2::new(b.0, b.1) };
+    let c = Vec2::new(3.0, 3.0);
+    let outline = Loop2 {
+        segs: vec![
+            line((100.0, 0.0), (100.0, 2.0)),
+            line((100.0, 2.0), (3.0, 2.0)),
+            Seg2::Arc { center: c, radius: 1.0, start: 1.5 * PI, sweep: -FRAC_PI_2 },
+            line((2.0, 3.0), (2.0, 40.0)),
+            line((2.0, 40.0), (0.0, 40.0)),
+            line((0.0, 40.0), (0.0, 3.0)),
+            Seg2::Arc { center: c, radius: 3.0, start: PI, sweep: FRAC_PI_2 },
+            line((3.0, 0.0), (100.0, 0.0)),
+        ],
+    };
+    assert!(outline.signed_area() > 0.0);
+    extrude(&Plane::XY, &[Region2 { outer: outline, holes: vec![] }], 0.0, length).unwrap().pop().unwrap()
+}
+
+/// A 3000 x 1000 x 2 plate with round holes of `radius` at `centres`.
+fn plate_with_holes(centres: &[Vec2], radius: f64) -> Body {
+    let holes = centres.iter().map(|c| Loop2::circle(*c, radius).reversed()).collect();
+    extrude(&Plane::XY, &[Region2 { outer: rect(3000.0, 1000.0), holes }], 0.0, 2.0).unwrap().pop().unwrap()
+}
+
+/// The faces of a body on cylinders of this radius.
+fn cylinder_faces(b: &Body, radius: f64) -> Vec<(usize, Vec3, Vec3)> {
+    (0..b.face_count())
+        .filter_map(|i| match face_surface(b, i)? {
+            FaceSurface::Cylinder { origin, axis, radius: r } if (r - radius).abs() < 1e-6 => Some((i, origin, axis)),
+            _ => None,
+        })
+        .collect()
+}
+
+/// Distance of a point from an axis.
+fn radial(p: Vec3, origin: Vec3, axis: Vec3) -> f64 {
+    let d = p - origin;
+    (d - axis * d.dot(axis)).len()
+}
+
+/// How a face on a cylinder is divided around its axis: the angles (radians, sorted, from the
+/// first) at which it has vertices.
+fn angles_around(m: &Mesh, face: usize, origin: Vec3, axis: Vec3) -> Vec<f64> {
+    let u = axis.any_perp();
+    let v = axis.cross(u);
+    let mut a: Vec<f64> = m
+        .triangles
+        .iter()
+        .zip(&m.tri_face)
+        .filter(|(_, f)| **f as usize == face)
+        .flat_map(|(t, _)| t.iter())
+        .filter_map(|k| m.positions.get(*k as usize))
+        .map(|p| (*p - origin).dot(v).atan2((*p - origin).dot(u)))
+        .collect();
+    a.sort_by(f64::total_cmp);
+    // Start at the widest gap, so an arc that crosses ±π stays in one piece.
+    let n = a.len();
+    let gap = |i: usize| (a[(i + 1) % n] - a[i]).rem_euclid(TAU);
+    let start = (0..n).max_by(|i, j| gap(*i).total_cmp(&gap(*j))).map_or(0, |i| (i + 1) % n);
+    let first = a[start];
+    let mut out: Vec<f64> = (0..n).map(|i| (a[(start + i) % n] - first).rem_euclid(TAU)).collect();
+    out.dedup_by(|x, y| (*x - *y).abs() < 1e-7);
+    out
+}
+
+/// The most a triangle of `face` lies inside the cylinder it is on (its corners are on it).
+fn sag(m: &Mesh, face: usize, origin: Vec3, axis: Vec3, radius: f64) -> f64 {
+    let mut worst = 0.0f64;
+    for (t, _) in m.triangles.iter().zip(&m.tri_face).filter(|(_, f)| **f as usize == face) {
+        let [a, b, c] = m.tri(t).unwrap();
+        for p in [a, b, c] {
+            assert!((radial(p, origin, axis) - radius).abs() < 1e-6, "a corner off the cylinder");
+        }
+        for p in [(a + b) * 0.5, (b + c) * 0.5, (c + a) * 0.5, (a + b + c) / 3.0] {
+            worst = worst.max((radius - radial(p, origin, axis)).abs());
+        }
+    }
+    worst
+}
+
+/// Triangle sides that are not shared by exactly two triangles once corners closer than `eps`
+/// are joined (a closed mesh has none).
+fn open_sides(m: &Mesh, eps: f64) -> usize {
+    let cell = |p: &Vec3| ((p.x / eps).floor() as i64, (p.y / eps).floor() as i64, (p.z / eps).floor() as i64);
+    let mut grid: HashMap<(i64, i64, i64), Vec<usize>> = HashMap::new();
+    let mut points: Vec<Vec3> = Vec::new();
+    let ids: Vec<usize> = m
+        .positions
+        .iter()
+        .map(|p| {
+            let (cx, cy, cz) = cell(p);
+            for (dx, dy, dz) in (-1..=1).flat_map(|x| (-1..=1).flat_map(move |y| (-1..=1).map(move |z| (x, y, z)))) {
+                if let Some(i) = grid.get(&(cx + dx, cy + dy, cz + dz)).and_then(|v| v.iter().find(|i| points[**i].dist(*p) < eps)) {
+                    return *i;
+                }
+            }
+            points.push(*p);
+            grid.entry((cx, cy, cz)).or_default().push(points.len() - 1);
+            points.len() - 1
+        })
+        .collect();
+    let mut sides: HashMap<(usize, usize), i32> = HashMap::new();
+    for t in &m.triangles {
+        let [a, b, c] = t.map(|k| ids[k as usize]);
+        // A triangle at a pole has two corners in one point: no area, no sides.
+        if a == b || b == c || c == a {
+            continue;
+        }
+        for (p, q) in [(a, b), (b, c), (c, a)] {
+            *sides.entry((p.min(q), p.max(q))).or_default() += 1;
+        }
+    }
+    sides.values().filter(|n| **n != 2).count()
+}
+
+/// The polyline segments around a circle of `radius` about `centre` in the plane z = `z`,
+/// and the widest angle one of them spans.
+fn rim(m: &Mesh, centre: Vec2, radius: f64, z: f64) -> (usize, f64) {
+    let on = |p: &Vec3| (p.z - z).abs() < 1e-6 && (Vec2::new(p.x, p.y).dist(centre) - radius).abs() < 1e-6;
+    let (mut segments, mut widest) = (0, 0.0f64);
+    for e in m.edges.iter().filter(|e| e.len() >= 2 && e.iter().all(on)) {
+        for w in e.windows(2) {
+            segments += 1;
+            widest = widest.max(2.0 * (w[0].dist(w[1]) / (2.0 * radius)).clamp(0.0, 1.0).asin());
+        }
+    }
+    (segments, widest)
+}
+
+#[test]
+fn a_small_bend_on_a_large_sheet_is_meshed_round() {
+    let b = bent_sheet(3000.0);
+    let tol = display_tol(&b);
+    // The tolerance is larger than either side's sagitta: 1 - cos 45° of the radius.
+    assert!(tol > 3.0 * (1.0 - (PI / 4.0).cos()));
+    let coarse = b.display_mesh(tol).unwrap();
+    let round = b.display_mesh_angular(tol, DISPLAY_ANGLE).unwrap();
+    // A quarter turn in facets of at most DISPLAY_ANGLE.
+    let facets = (FRAC_PI_2 / DISPLAY_ANGLE).ceil() as usize;
+    assert_eq!(facets, 5);
+    for radius in [1.0, 3.0] {
+        let faces = cylinder_faces(&b, radius);
+        assert_eq!(faces.len(), 1, "one bend face of radius {radius}");
+        let (face, origin, axis) = faces[0];
+        // The chord tolerance alone: one flat strip from tangent line to tangent line.
+        assert_eq!(angles_around(&coarse, face, origin, axis).len(), 2, "radius {radius}");
+        assert!(sag(&coarse, face, origin, axis, radius) > 0.29 * radius);
+        let a = angles_around(&round, face, origin, axis);
+        assert!(a.len() > facets, "radius {radius}: {} facets across the bend", a.len() - 1);
+        assert!((a[a.len() - 1] - FRAC_PI_2).abs() < 1e-6, "the bend is a quarter turn: {a:?}");
+        let widest = a.windows(2).map(|w| w[1] - w[0]).fold(0.0, f64::max);
+        assert!(widest <= DISPLAY_ANGLE * 1.001, "radius {radius}: a facet spans {} degrees", widest.to_degrees());
+        // Within the chord tolerance of the cylinder, and by much: a facet that turns no more
+        // than the angle sags no more than 1 - cos(angle / 2) of the radius.
+        let s = sag(&round, face, origin, axis, radius);
+        assert!(s <= radius * (1.0 - (DISPLAY_ANGLE / 2.0).cos()) * 1.001 && s < tol, "radius {radius}: sag {s}");
+    }
+    // The flat faces along the sheet meet the bends in straight lines and need nothing more:
+    // only the bends, and the two ends where their arcs now have more points, gain triangles.
+    let count = |m: &Mesh, face: usize| m.tri_face.iter().filter(|f| **f as usize == face).count();
+    let mut along = 0;
+    for face in 0..b.face_count() {
+        if let Some(FaceSurface::Plane { normal, .. }) = face_surface(&b, face)
+            && normal.dot(Vec3::Z).abs() < 0.5
+        {
+            along += 1;
+            assert_eq!(count(&round, face), count(&coarse, face), "face {face}");
+        }
+    }
+    assert_eq!(along, 6);
+}
+
+#[test]
+fn the_round_display_mesh_stays_closed_and_keeps_its_edges_and_bounds() {
+    let b = bent_sheet(3000.0);
+    let tol = display_tol(&b);
+    let coarse = b.display_mesh(tol).unwrap();
+    let round = b.display_mesh_angular(tol, DISPLAY_ANGLE).unwrap();
+    // Neighbouring faces share the points of the edge between them.
+    assert_eq!(open_sides(&round, 1e-6), 0);
+    // The same edges in the same order, between the same faces, with the same ends and flags.
+    assert_eq!(round.edges.len(), coarse.edges.len());
+    assert_eq!(round.edge_faces, coarse.edge_faces);
+    assert_eq!((&round.seams, &round.smooth_edges, &round.sharp_edges), (&coarse.seams, &coarse.smooth_edges, &coarse.sharp_edges));
+    for (fine, rough) in round.edges.iter().zip(&coarse.edges) {
+        assert!(fine.len() >= rough.len());
+        assert!(fine[0].dist(rough[0]) < 1e-9 && fine[fine.len() - 1].dist(rough[rough.len() - 1]) < 1e-9);
+    }
+    // The body's box: flat faces and tangent lines bound it, so nothing moves.
+    let (r, c) = (round.bounds(), coarse.bounds());
+    assert!(r.min.dist(c.min) < 1e-9 && r.max.dist(c.max) < 1e-9);
+    // Closer to the solid: the flat strips cut the outer bend's corner off and fill the inner one.
+    let exact = crate::measure(&b).unwrap().volume;
+    assert!((round.measure().volume - exact).abs() < (coarse.measure().volume - exact).abs());
+}
+
+#[test]
+fn a_small_hole_on_a_large_plate_has_a_round_rim() {
+    let centre = Vec2::new(30.0, 20.0);
+    let b = plate_with_holes(&[centre], 2.0);
+    let tol = display_tol(&b);
+    assert!(tol > 2.0, "the hole's radius is below the chord tolerance");
+    let coarse = b.display_mesh(tol).unwrap();
+    let round = b.display_mesh_angular(tol, DISPLAY_ANGLE).unwrap();
+    let segments = (TAU / DISPLAY_ANGLE).ceil() as usize;
+    assert_eq!(segments, 18);
+    for z in [0.0, 2.0] {
+        // The chord tolerance alone: each half circle is one segment, the rim a line.
+        assert_eq!(rim(&coarse, centre, 2.0, z).0, 2);
+        let (n, widest) = rim(&round, centre, 2.0, z);
+        assert!(n >= segments, "{n} segments around the rim at z = {z}");
+        assert!(widest <= DISPLAY_ANGLE * 1.001, "a segment spans {} degrees", widest.to_degrees());
+    }
+    // The hole's wall follows its rims.
+    for (face, origin, axis) in cylinder_faces(&b, 2.0) {
+        let a = angles_around(&round, face, origin, axis);
+        assert!(a.windows(2).map(|w| w[1] - w[0]).fold(0.0, f64::max) <= DISPLAY_ANGLE * 1.001);
+        assert!(sag(&round, face, origin, axis, 2.0) <= 2.0 * (1.0 - (DISPLAY_ANGLE / 2.0).cos()) * 1.001);
+    }
+    assert_eq!(open_sides(&round, 1e-6), 0);
+}
+
+#[test]
+fn an_arc_the_chord_tolerance_already_divides_finely_is_left_alone() {
+    // A 40 mm cylinder at a tolerance of 0.01 mm: 64 facets around, far inside the angle.
+    let b = crate::cylinder(Vec3::ZERO, Vec3::Z, 20.0, 30.0).unwrap();
+    let coarse = b.display_mesh(0.01).unwrap();
+    let round = b.display_mesh_angular(0.01, DISPLAY_ANGLE).unwrap();
+    assert_eq!(round.positions, coarse.positions);
+    assert_eq!(round.triangles, coarse.triangles);
+    assert_eq!(round.edges, coarse.edges);
+    // And a body with nothing curved at any tolerance.
+    let b = crate::box_solid(Vec3::ZERO, Vec3::new(3000.0, 1000.0, 2.0)).unwrap();
+    let tol = display_tol(&b);
+    assert_eq!(b.display_mesh_angular(tol, DISPLAY_ANGLE).unwrap().positions, b.display_mesh(tol).unwrap().positions);
+}
+
+#[test]
+fn a_radius_far_below_the_tolerance_keeps_its_chord_facets() {
+    // A half circle of radius 0.002 in a 3 m plate sags less than a thousandth of the chord
+    // tolerance: below that floor nothing is divided for the angle, however far the body
+    // outgrows its smallest radius.
+    let centre = Vec2::new(30.0, 20.0);
+    let b = plate_with_holes(&[centre], 0.002);
+    let tol = display_tol(&b);
+    let coarse = b.display_mesh(tol).unwrap();
+    let round = b.display_mesh_angular(tol, DISPLAY_ANGLE).unwrap();
+    assert_eq!(round.triangles.len(), coarse.triangles.len());
+    assert_eq!(round.edges, coarse.edges);
+    // Just above the floor the rim is divided, but coarsely: the angle stops where the sag
+    // falls below the floor, not where the facets reach the angle.
+    let b = plate_with_holes(&[centre], 0.01);
+    let round = b.display_mesh_angular(display_tol(&b), DISPLAY_ANGLE).unwrap();
+    let (n, _) = rim(&round, centre, 0.01, 2.0);
+    assert!((3..18).contains(&n), "{n} segments");
+}
+
+#[test]
+fn a_face_crowded_with_holes_gets_a_coarser_angle_and_bounded_work() {
+    // 1000 holes of diameter 4 in a 3 m plate. At the full angle the top and bottom faces
+    // would each be bounded by more than 20 000 segments, and the work of triangulating a
+    // face grows faster than its boundary.
+    let centres: Vec<Vec2> = (0..50).flat_map(|i| (0..20).map(move |j| Vec2::new(30.0 + 60.0 * i as f64, 25.0 + 50.0 * j as f64))).collect();
+    let b = plate_with_holes(&centres, 2.0);
+    let tol = display_tol(&b);
+    let coarse = b.display_mesh(tol).unwrap();
+    let round = b.display_mesh_angular(tol, DISPLAY_ANGLE).unwrap();
+    let boundary = |m: &Mesh, z: f64| m.edges.iter().filter(|e| e.iter().all(|p| (p.z - z).abs() < 1e-6)).map(|e| e.len() - 1).sum::<usize>();
+    let budget = truck_meshalgo::tessellation::Deflection::MAX_ANGLE_BOUNDARY;
+    for z in [0.0, 2.0] {
+        assert_eq!(boundary(&coarse, z), 4 + 2 * centres.len());
+        let n = boundary(&round, z);
+        assert!(n > boundary(&coarse, z), "the rims are still rounder than the chord tolerance leaves them: {n}");
+        assert!(n <= budget, "{n} segments bound the face at z = {z}");
+    }
+    // Every rim got the same share, and the walls follow their rims.
+    let per_rim: Vec<usize> = centres.iter().map(|c| rim(&round, *c, 2.0, 2.0).0).collect();
+    assert!(per_rim.iter().all(|n| *n == per_rim[0] && *n >= 3), "{:?}", &per_rim[..4]);
+    assert!(
+        round.triangles.len() < 4 * coarse.triangles.len(),
+        "{} triangles, {} at the chord tolerance",
+        round.triangles.len(),
+        coarse.triangles.len()
+    );
+    assert_eq!(open_sides(&round, 1e-6), 0);
+    // A plate with few holes keeps the full angle.
+    let few = plate_with_holes(&centres[..40], 2.0);
+    let round = few.display_mesh_angular(display_tol(&few), DISPLAY_ANGLE).unwrap();
+    assert!(rim(&round, centres[0], 2.0, 2.0).0 >= 18);
+}
+
+#[test]
+fn round_faces_of_every_kind_are_divided_by_the_angle() {
+    // A sphere, a torus and a cone a few millimetres across, drawn at the 3 mm tolerance of a
+    // body 3 m long: more than any of their sagittas.
+    let disc = Region2 { outer: Loop2::circle(Vec2::ZERO, 4.0), holes: vec![] };
+    let bodies = [
+        ("sphere", crate::sphere(Vec3::ZERO, 4.0).unwrap()),
+        ("torus", crate::torus(Vec3::ZERO, 6.0, 2.0).unwrap()),
+        ("cone", crate::extrude_tapered(&Plane::XY, &disc, 6.0, 1.0, -0.3).unwrap()),
+    ];
+    // The most the surface normal turns along one side of a triangle of a curved face.
+    let turn = |b: &Body, m: &Mesh| {
+        let flat: Vec<bool> = (0..b.face_count()).map(|i| matches!(face_surface(b, i), Some(FaceSurface::Plane { .. }))).collect();
+        m.triangles
+            .iter()
+            .zip(&m.tri_face)
+            .filter(|(_, f)| !flat[**f as usize])
+            .flat_map(|(t, _)| [(t[0], t[1]), (t[1], t[2]), (t[2], t[0])])
+            .filter(|(a, b)| m.positions[*a as usize].dist(m.positions[*b as usize]) > 1e-9)
+            .map(|(a, b)| m.normals[a as usize].dot(m.normals[b as usize]).clamp(-1.0, 1.0).acos())
+            .fold(0.0, f64::max)
+    };
+    let check = |name: &str, b: &Body| {
+        let coarse = b.display_mesh(3.0).unwrap();
+        let round = b.display_mesh_angular(3.0, DISPLAY_ANGLE).unwrap();
+        assert!(turn(b, &coarse) > 2.0 * DISPLAY_ANGLE, "{name}: the chord tolerance leaves facets of {} degrees", turn(b, &coarse).to_degrees());
+        // A side crosses at most one facet in each direction.
+        assert!(turn(b, &round) <= 1.5 * DISPLAY_ANGLE, "{name}: a side turns {} degrees", turn(b, &round).to_degrees());
+        assert_eq!(open_sides(&round, 1e-6), 0, "{name}");
+        // Bounded: no more than a full turn of facets each way on every face.
+        assert!(round.triangles.len() <= b.face_count() * 2 * 36 * 36, "{name}: {} triangles", round.triangles.len());
+    };
+    for (name, b) in &bodies {
+        check(name, b);
+    }
+}

crates/kernel/src/lib.rs

@@ -73,7 +73,7 @@ mod tspline;
 pub use blend::{ChamferSide, chamfer, chamfer_sides, fillet, fillet_max};
 pub use blend_corner::fillet_radii;
 pub use blend_variable::{fillet_chord, fillet_variable, fillet_variable_points};
-pub use body::{Body, CapSignature, EdgeInfo, FaceInfo, FacePaint, FaceSource, Paint};
+pub use body::{Body, CapSignature, DISPLAY_ANGLE, EdgeInfo, FaceInfo, FacePaint, FaceSource, Paint};
 pub use boolean_diagnostics::{BooleanDiagnostics, BooleanFallback, BooleanStrategy, capture_boolean_diagnostics};
 pub use build::{PathSeg, box_solid, canonical_revolve_axis, cylinder, extrude, extrude_tapered, loft, revolve, sphere, sweep, torus};
 pub use delete_face::delete_faces;

vendor/README.md

@@ -62,6 +62,16 @@ Changes:
   point that does not evaluate counts as flat instead of recursing). Surface grids refine only
   the direction that bends, and a ruling left undivided gets cells comparable to the other
   direction (long triangles from a trim loop to the grid's far ends cut through cylinders).
+- `tessellation/mod.rs`, `tessellation/triangulation.rs`, for display: a `Deflection` is the
+  chord tolerance plus an optional bound on the angle one facet spans, and
+  `RoundMeshableShape::robust_triangulation_within` divides by it: an edge or a grid direction
+  within the chord tolerance is still halved while a piece turns more than the angle, until its
+  sag is under a floor (a radius that is small beside the tolerance was one flat facet).
+  Bounded work: a face that would be bounded by more than 4096 segments has its curved edges
+  divided at twice the angle, and again, down to the chord tolerance alone, and the angle
+  stops refining a face's grid at 16 384 points. Each edge is still divided once for both its
+  faces. `triangulation` and `robust_triangulation` divide by the chord tolerance alone, as
+  before.
 - `lib.rs`: compiler warnings no longer fail the build. Example, test and bench targets are
   dropped (their sources are not vendored).
 

vendor/truck-meshalgo/src/tessellation/mod.rs

@@ -44,6 +44,71 @@ impl<S: MeshableSurface + SearchNearestParameter<D2, Point = Point3>> RobustMesh
 
 type PolylineCurve = truck_polymesh::PolylineCurve<Point3>;
 
+/// SolidCraft: how finely curves and surfaces are divided into facets. `chord` is the usual
+/// tolerance: the most a facet may sag from the true shape. `angle`, when finite, also bounds
+/// what one facet spans: a facet that turns more than `angle` is split whatever its size (a
+/// radius that is small beside the tolerance would otherwise stay one flat facet), until its
+/// sag is below `floor`.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct Deflection {
+    /// Most a facet may sag from the curve or surface.
+    pub chord: f64,
+    /// Most a facet may turn (radians: the arc it spans on a circle); infinite for no bound.
+    pub angle: f64,
+    /// Sag below which `angle` no longer splits a facet.
+    pub floor: f64,
+}
+
+impl Deflection {
+    /// Most boundary segments a face may get from the angle bound. Triangulating a face tests
+    /// each triangle against the boundary loops around it, so the work grows faster than the
+    /// boundary (with its square for one long loop): the curved edges of a face that would
+    /// get more are divided at twice the angle, and again, down to the chord tolerance alone.
+    pub const MAX_ANGLE_BOUNDARY: usize = 4096;
+    /// Most grid points a face may get from the angle bound (beyond them only `chord` refines).
+    pub const MAX_ANGLE_GRID: usize = 16_384;
+    /// How often the angle is doubled for a crowded face before only `chord` is left.
+    pub const MAX_RELAX: u8 = 4;
+
+    /// The chord tolerance alone: what `triangulation(tol)` divides by.
+    pub const fn chord(tol: f64) -> Self {
+        Self {
+            chord: tol,
+            angle: f64::INFINITY,
+            floor: 0.0,
+        }
+    }
+
+    /// Whether `angle` bounds anything.
+    pub fn angular(&self) -> bool { self.angle.is_finite() && self.angle > 0.0 }
+
+    /// The same with the angle doubled `level` times; from [`Deflection::MAX_RELAX`] times, or
+    /// past half a turn, the chord tolerance alone.
+    pub fn relaxed(&self, level: u8) -> Self {
+        let angle = self.angle * f64::from(1u32 << level.min(Self::MAX_RELAX));
+        match level == 0 || (level < Self::MAX_RELAX && angle < std::f64::consts::PI) {
+            true => Self { angle, ..*self },
+            false => Self::chord(self.chord),
+        }
+    }
+
+    /// The squared sag over squared length above which a facet turns more than `angle`: a
+    /// chord spanning `a` of a circle sags `tan(a / 4) / 2` of its length. Infinite without
+    /// an angle bound.
+    pub(super) fn turn2(&self) -> f64 {
+        match self.angular() && self.angle < std::f64::consts::PI {
+            true => (f64::tan(self.angle / 4.0) / 2.0).powi(2),
+            false => f64::INFINITY,
+        }
+    }
+
+    /// Whether the angle bound splits a facet of squared sag `sag2` and squared length `len2`
+    /// (`turn2` from [`Deflection::turn2`]).
+    pub(super) fn turns(&self, turn2: f64, sag2: f64, len2: f64) -> bool {
+        turn2.is_finite() && sag2 > self.floor * self.floor && sag2 > turn2 * len2
+    }
+}
+
 /// Trait for converting tessellated shape into polygon.
 pub trait MeshedShape {
     /// Converts tessellated shape into polygon.
@@ -258,11 +323,15 @@ impl<C: PolylineableCurve, S: MeshableSurface> MeshableShape for Shell<Point3, C
     fn triangulation(&self, tol: f64) -> Self::MeshedShape {
         nonpositive_tolerance!(tol);
         #[cfg(not(target_arch = "wasm32"))]
-        let res = triangulation::shell_tessellation(self, tol, triangulation::by_search_parameter);
+        let res = triangulation::shell_tessellation(
+            self,
+            Deflection::chord(tol),
+            triangulation::by_search_parameter,
+        );
         #[cfg(target_arch = "wasm32")]
         let res = triangulation::shell_tessellation_single_thread(
             self,
-            tol,
+            Deflection::chord(tol),
             triangulation::by_search_parameter,
         );
         res
@@ -272,17 +341,39 @@ impl<C: PolylineableCurve, S: MeshableSurface> MeshableShape for Shell<Point3, C
 impl<C: PolylineableCurve, S: RobustMeshableSurface> RobustMeshableShape for Shell<Point3, C, S> {
     type MeshedShape = Shell<Point3, PolylineCurve, Option<PolygonMesh>>;
     fn robust_triangulation(&self, tol: f64) -> Self::MeshedShape {
-        nonpositive_tolerance!(tol);
+        self.robust_triangulation_within(Deflection::chord(tol))
+    }
+}
+
+/// SolidCraft: tessellation with a bound on the angle one facet spans as well as on its sag.
+pub trait RoundMeshableShape {
+    /// Shape whose edges are made polylines and faces polygon surface.
+    type MeshedShape: MeshedShape;
+    /// [`RobustMeshableShape::robust_triangulation`] divided by `deflection`: with
+    /// [`Deflection::chord`] the very same shape; with an angle, curved edges and faces whose
+    /// radius is small beside the chord tolerance are divided as well. Every edge is still
+    /// divided once, for both faces it bounds, so neighbouring faces keep sharing its points.
+    ///
+    /// # Panics
+    ///
+    /// `deflection.chord` must be more than `TOLERANCE`.
+    fn robust_triangulation_within(&self, deflection: Deflection) -> Self::MeshedShape;
+}
+
+impl<C: PolylineableCurve, S: RobustMeshableSurface> RoundMeshableShape for Shell<Point3, C, S> {
+    type MeshedShape = Shell<Point3, PolylineCurve, Option<PolygonMesh>>;
+    fn robust_triangulation_within(&self, deflection: Deflection) -> Self::MeshedShape {
+        nonpositive_tolerance!(deflection.chord);
         #[cfg(not(target_arch = "wasm32"))]
         let res = triangulation::shell_tessellation(
             self,
-            tol,
+            deflection,
             triangulation::by_search_nearest_parameter,
         );
         #[cfg(target_arch = "wasm32")]
         let res = triangulation::shell_tessellation_single_thread(
             self,
-            tol,
+            deflection,
             triangulation::by_search_nearest_parameter,
         );
         res

vendor/truck-meshalgo/src/tessellation/triangulation.rs

@@ -91,7 +91,7 @@ where
 #[cfg(not(target_arch = "wasm32"))]
 pub(super) fn shell_tessellation<'a, C, S>(
     shell: &Shell<Point3, C, S>,
-    tol: f64,
+    tol: Deflection,
     sp: impl SP<S>,
 ) -> MeshedShell
 where
@@ -104,18 +104,28 @@ where
         .map(|v| (v.id(), v.mapped(Point3::clone)))
         .collect();
     let eset: HashMap<_, _> = shell.edge_par_iter().map(move |e| (e.id(), e)).collect();
+    // SolidCraft: the polylines first, so that the edges of a face crowded by the angle bound
+    // can be divided again before any face is meshed.
+    let mut polys: HashMap<_, _> = eset
+        .par_iter()
+        .map(|(id, edge)| {
+            let curve = edge.curve();
+            (*id, (bounded_polyline(&curve, curve.range_tuple(), tol), 0))
+        })
+        .collect();
+    relax_crowded_faces(shell, &mut polys, tol);
     let edge_map: HashMap<_, _> = eset
         .into_par_iter()
         .map(move |(id, edge)| {
             let v0 = vmap.get(&edge.absolute_front().id()).unwrap();
             let v1 = vmap.get(&edge.absolute_back().id()).unwrap();
-            let curve = edge.curve();
-            let poly = bounded_polyline(&curve, curve.range_tuple(), tol);
-            (id, Edge::new_unchecked(v0, v1, poly))
+            let (poly, level) = polys.get(&id).unwrap().clone();
+            (id, (Edge::new_unchecked(v0, v1, poly), level))
         })
         .collect();
+    let edge_map = &edge_map;
     let create_edge = |edge: &Edge<Point3, C>| -> Edge<_, _> {
-        let new_edge = edge_map.get(&edge.id()).unwrap();
+        let (new_edge, _) = edge_map.get(&edge.id()).unwrap();
         match edge.orientation() {
             true => new_edge.clone(),
             false => new_edge.inverse(),
@@ -129,16 +139,83 @@ where
             .iter()
             .map(create_boundary)
             .collect();
-        shell_create_polygon(&face.surface(), wires, face.orientation(), tol, &sp, cap)
+        // SolidCraft: a face is divided like the coarsest of its edges.
+        let level = face
+            .absolute_boundaries()
+            .iter()
+            .flat_map(Wire::edge_iter)
+            .filter_map(|edge| edge_map.get(&edge.id()).map(|(_, level)| *level))
+            .max()
+            .unwrap_or(0);
+        shell_create_polygon(
+            &face.surface(),
+            wires,
+            face.orientation(),
+            tol.relaxed(level),
+            &sp,
+            cap,
+        )
     };
     shell.face_par_iter().map(create_face).collect()
 }
 
+/// SolidCraft: bounded work for the angle bound. A face bounded by more than
+/// `Deflection::MAX_ANGLE_BOUNDARY` segments has its curved edges divided again at twice the
+/// angle, as often as it takes, down to the chord tolerance alone (a plate with a thousand
+/// small holes is not worth a hundred times the work to draw each hole round). `polys` holds
+/// each edge's polyline and how often its angle was doubled. Every edge still has one
+/// polyline for both its faces, and the outcome does not depend on the order of the faces.
+fn relax_crowded_faces<C, S>(
+    shell: &Shell<Point3, C, S>,
+    polys: &mut HashMap<EdgeID<C>, (PolylineCurve, u8)>,
+    tol: Deflection,
+) where
+    C: PolylineableCurve,
+{
+    if !tol.angular() {
+        return;
+    }
+    let faces: Vec<Vec<Edge<Point3, C>>> = shell
+        .face_iter()
+        .map(|face| {
+            let wires = face.absolute_boundaries();
+            wires.iter().flat_map(Wire::edge_iter).cloned().collect()
+        })
+        .collect();
+    for level in 1..=Deflection::MAX_RELAX {
+        let segments = |edge: &Edge<Point3, C>| match polys.get(&edge.id()) {
+            // Straight at the full angle: nothing to relax, and no say in how its faces are divided.
+            Some((poly, 0)) if poly.len() <= 2 => (1, false),
+            Some((poly, done)) => (poly.len().saturating_sub(1), *done < level),
+            None => (0, false),
+        };
+        let crowded: Vec<&Edge<Point3, C>> = faces
+            .iter()
+            .filter(|edges| {
+                edges.iter().map(|edge| segments(edge).0).sum::<usize>()
+                    > Deflection::MAX_ANGLE_BOUNDARY
+            })
+            .flatten()
+            .filter(|edge| segments(edge).1)
+            .collect();
+        if crowded.is_empty() {
+            break;
+        }
+        let relaxed = tol.relaxed(level);
+        for edge in crowded {
+            if let Some(slot) = polys.get_mut(&edge.id()).filter(|(_, done)| *done < level) {
+                let curve = edge.curve();
+                *slot = (bounded_polyline(&curve, curve.range_tuple(), relaxed), level);
+            }
+        }
+    }
+}
+
 /// Tessellates faces
 #[cfg(any(target_arch = "wasm32", test))]
 pub(super) fn shell_tessellation_single_thread<'a, C, S>(
     shell: &'a Shell<Point3, C, S>,
-    tol: f64,
+    tol: Deflection,
     sp: impl SP<S>,
 ) -> MeshedShell
 where
@@ -148,6 +225,16 @@ where
     use truck_base::entry_map::FxEntryMap as EntryMap;
     use truck_topology::Vertex as TVertex;
     let cap = face_cap(shell.len());
+    // SolidCraft: the polylines first (see `shell_tessellation`).
+    let mut polys: HashMap<_, _> = shell
+        .edge_iter()
+        .map(|edge| {
+            let curve = edge.curve();
+            (edge.id(), (bounded_polyline(&curve, curve.range_tuple(), tol), 0))
+        })
+        .collect();
+    relax_crowded_faces(shell, &mut polys, tol);
+    let polys = &polys;
     let mut vmap = EntryMap::new(
         move |v: &TVertex<Point3>| v.id(),
         move |v| v.mapped(Point3::clone),
@@ -159,8 +246,7 @@ where
             let v0 = vmap.entry_or_insert(vf).clone();
             let vb = edge.absolute_back();
             let v1 = vmap.entry_or_insert(vb).clone();
-            let curve = edge.curve();
-            let poly = bounded_polyline(&curve, curve.range_tuple(), tol);
+            let (poly, _) = polys.get(&edge.id()).unwrap().clone();
             Edge::new_unchecked(&v0, &v1, poly)
         },
     );
@@ -180,7 +266,21 @@ where
             .iter()
             .map(&mut create_boundary)
             .collect();
-        shell_create_polygon(&face.surface(), wires, face.orientation(), tol, &sp, cap)
+        let level = face
+            .absolute_boundaries()
+            .iter()
+            .flat_map(Wire::edge_iter)
+            .filter_map(|edge| polys.get(&edge.id()).map(|(_, level)| *level))
+            .max()
+            .unwrap_or(0);
+        shell_create_polygon(
+            &face.surface(),
+            wires,
+            face.orientation(),
+            tol.relaxed(level),
+            &sp,
+            cap,
+        )
     };
     shell.face_iter().map(create_face).collect()
 }
@@ -197,6 +297,7 @@ where
 {
     let vertices = shell.vertices.clone();
     let cap = face_cap(shell.faces.len());
+    let tol = Deflection::chord(tol);
     let tessellate_edge = |edge: &CompressedEdge<C>| {
         let curve = &edge.curve;
         CompressedEdge {
@@ -245,7 +346,7 @@ fn shell_create_polygon<S: PreMeshableSurface>(
     surface: &S,
     wires: Vec<Wire<Point3, PolylineCurve>>,
     orientation: bool,
-    tol: f64,
+    tol: Deflection,
     sp: impl SP<S>,
     cap: usize,
 ) -> Face<Point3, PolylineCurve, Option<PolygonMesh>> {
@@ -382,7 +483,11 @@ fn loop_orientation(curve: &[Point2]) -> bool {
 }
 
 impl PolyBoundary {
-    fn new(pieces: Vec<PolyBoundaryPiece>, surface: &impl PreMeshableSurface, tol: f64) -> Self {
+    fn new(
+        pieces: Vec<PolyBoundaryPiece>,
+        surface: &impl PreMeshableSurface,
+        tol: Deflection,
+    ) -> Self {
         let (mut closed, mut open) = (Vec::new(), Vec::new());
         pieces.into_iter().for_each(|PolyBoundaryPiece(mut vec)| {
             match vec[0].distance(vec[vec.len() - 1]) < 1.0e-3 {
@@ -577,8 +682,15 @@ fn spade_round(x: f64) -> f64 {
 }
 
 /// Tessellates one surface trimmed by polyline.
-fn trimming_tessellation<S>(surface: &S, polyboundary: &PolyBoundary, tol: f64, cap: usize) -> PolygonMesh
-where S: PreMeshableSurface {
+fn trimming_tessellation<S>(
+    surface: &S,
+    polyboundary: &PolyBoundary,
+    tol: Deflection,
+    cap: usize,
+) -> PolygonMesh
+where
+    S: PreMeshableSurface,
+{
     let mut triangulation = Cdt::new();
     polyboundary.insert_to(&mut triangulation);
     insert_surface(&mut triangulation, surface, polyboundary, tol, cap);
@@ -597,7 +709,7 @@ fn insert_surface(
     triangulation: &mut Cdt,
     surface: impl PreMeshableSurface,
     polyline: &PolyBoundary,
-    tol: f64,
+    tol: Deflection,
     cap: usize,
 ) {
     let bdb: BoundingBox<Point2> = polyline.0.iter().flatten().collect();
@@ -656,8 +768,10 @@ pub(super) fn face_cap(faces: usize) -> usize {
 
 /// SolidCraft: truck's curve division, bounded: at most `MAX_EDGE_POINTS` points and a
 /// bisection depth of 24; a midpoint that does not evaluate (NaN) counts as flat (truck's
-/// version recursed on it 100 levels deep, which never finishes).
-fn bounded_polyline<C: PolylineableCurve>(curve: &C, range: (f64, f64), tol: f64) -> PolylineCurve {
+/// version recursed on it 100 levels deep, which never finishes). A piece within the chord
+/// tolerance is still halved while it turns more than the deflection's angle.
+fn bounded_polyline<C: PolylineableCurve>(curve: &C, range: (f64, f64), d: Deflection) -> PolylineCurve {
+    let (tol, turn2) = (d.chord, d.turn2());
     let mut out = vec![curve.subs(range.0)];
     let mut stack: Vec<(f64, f64, usize)> = vec![(range.0, range.1, 0)];
     while let Some((a, b, depth)) = stack.pop() {
@@ -668,6 +782,7 @@ fn bounded_polyline<C: PolylineableCurve>(curve: &C, range: (f64, f64), tol: f64
         let tm = 0.5 * (a + b);
         let dm = curve.subs(tm).distance2(pa.midpoint(pb));
         let flat = !(d2 >= tol * tol || dm >= tol * tol);
+        let flat = flat && !d.turns(turn2, d2.max(dm), pa.distance2(pb));
         if flat || depth >= 24 || out.len() + stack.len() >= MAX_EDGE_POINTS {
             out.push(pb);
         } else {
@@ -680,12 +795,17 @@ fn bounded_polyline<C: PolylineableCurve>(curve: &C, range: (f64, f64), tol: f64
 }
 
 /// SolidCraft: truck's surface division, bounded: stops refining when the grid would exceed
-/// `cap` points or after 24 rounds; cells that do not evaluate (NaN) are not refined.
-fn bounded_surface_division<S: PreMeshableSurface>(surface: &S, (ur, vr): ((f64, f64), (f64, f64)), tol: f64, cap: usize) -> (Vec<f64>, Vec<f64>) {
+/// `cap` points or after 24 rounds; cells that do not evaluate (NaN) are not refined. A
+/// direction within the chord tolerance is still halved where a cell turns more than the
+/// deflection's angle along it, while the grid stays within `Deflection::MAX_ANGLE_GRID`.
+fn bounded_surface_division<S: PreMeshableSurface>(surface: &S, (ur, vr): ((f64, f64), (f64, f64)), d: Deflection, cap: usize) -> (Vec<f64>, Vec<f64>) {
+    let (tol, turn2) = (d.chord, d.turn2());
     let (mut udiv, mut vdiv) = (vec![ur.0, ur.1], vec![vr.0, vr.1]);
     for _ in 0..24 {
         let mut fu = vec![false; udiv.len() - 1];
         let mut fv = vec![false; vdiv.len() - 1];
+        // What the angle alone asks for.
+        let (mut au, mut av) = (fu.clone(), fv.clone());
         for (i, u) in udiv.windows(2).enumerate() {
             for (j, v) in vdiv.windows(2).enumerate() {
                 if fu[i] && fv[j] {
@@ -702,10 +822,12 @@ fn bounded_surface_division<S: PreMeshableSurface>(surface: &S, (ur, vr): ((f64,
                 let far = p0.distance2(pt) > tol * tol;
                 // Which direction bends: refine only that one (a cylinder needs no division
                 // along its rulings).
-                let alu = surface.subs(u[0], v0).to_vec() * (1.0 - p) + surface.subs(u[1], v0).to_vec() * p;
-                let alv = surface.subs(u0, v[0]).to_vec() * (1.0 - q) + surface.subs(u0, v[1]).to_vec() * q;
-                let bend_u = p0.distance2(Point3::from_vec(alu)) > tol * tol;
-                let bend_v = p0.distance2(Point3::from_vec(alv)) > tol * tol;
+                let (su, sv) = ([surface.subs(u[0], v0), surface.subs(u[1], v0)], [surface.subs(u0, v[0]), surface.subs(u0, v[1])]);
+                let alu = su[0].to_vec() * (1.0 - p) + su[1].to_vec() * p;
+                let alv = sv[0].to_vec() * (1.0 - q) + sv[1].to_vec() * q;
+                let (du, dv) = (p0.distance2(Point3::from_vec(alu)), p0.distance2(Point3::from_vec(alv)));
+                let bend_u = du > tol * tol;
+                let bend_v = dv > tol * tol;
                 if bend_u || bend_v {
                     fu[i] |= bend_u;
                     fv[j] |= bend_v;
@@ -713,8 +835,20 @@ fn bounded_surface_division<S: PreMeshableSurface>(surface: &S, (ur, vr): ((f64,
                     fu[i] = true;
                     fv[j] = true;
                 }
+                au[i] |= d.turns(turn2, du, su[0].distance2(su[1]));
+                av[j] |= d.turns(turn2, dv, sv[0].distance2(sv[1]));
             }
         }
+        let count = |f: &[bool], a: &[bool]| f.iter().zip(a).filter(|(f, a)| **f || **a).count();
+        let (nu, nv) = (udiv.len() + count(&fu, &au), vdiv.len() + count(&fv, &av));
+        // The angle refines only while the grid stays small: past that the chord tolerance alone.
+        let turning = turn2.is_finite() && nu.saturating_mul(nv) <= cap.min(Deflection::MAX_ANGLE_GRID);
+        if !turning {
+            au.fill(false);
+            av.fill(false);
+        }
+        fu.iter_mut().zip(&au).for_each(|(f, a)| *f |= *a);
+        fv.iter_mut().zip(&av).for_each(|(f, a)| *f |= *a);
         let nu = udiv.len() + fu.iter().filter(|x| **x).count();
         let nv = vdiv.len() + fv.iter().filter(|x| **x).count();
         if nu == udiv.len() && nv == vdiv.len() {
@@ -848,15 +982,42 @@ fn polyline_on_surface(
     surface: impl PreMeshableSurface,
     p: Point2,
     q: Point2,
-    tol: f64,
+    tol: Deflection,
 ) -> Vec<Point2> {
     use truck_geometry::prelude::*;
     let line = Line(p, q);
     let pcurve = PCurve::new(line, surface);
-    let (vec, _) = pcurve.parameter_division(pcurve.range_tuple(), tol);
+    let (vec, _) = pcurve.parameter_division(pcurve.range_tuple(), tol.chord);
+    let vec = halved_while_turning(|t| pcurve.subs(t), vec, tol);
     vec.into_iter().map(|t| line.subs(t)).collect()
 }
 
+/// SolidCraft: `params` with every interval halved while the curve turns more over it than the
+/// deflection's angle (at most 12 times each, and `MAX_EDGE_POINTS` in all). Unchanged without
+/// an angle.
+fn halved_while_turning(curve: impl Fn(f64) -> Point3, params: Vec<f64>, d: Deflection) -> Vec<f64> {
+    let turn2 = d.turn2();
+    if !turn2.is_finite() || params.len() < 2 {
+        return params;
+    }
+    let mut out = vec![params[0]];
+    for w in params.windows(2) {
+        let mut stack: Vec<(f64, f64, usize)> = vec![(w[0], w[1], 0)];
+        while let Some((a, b, depth)) = stack.pop() {
+            let (pa, pb, tm) = (curve(a), curve(b), 0.5 * (a + b));
+            let sag2 = curve(tm).distance2(pa.midpoint(pb));
+            let split = d.turns(turn2, sag2, pa.distance2(pb));
+            if split && depth < 12 && out.len() + stack.len() < MAX_EDGE_POINTS {
+                stack.push((tm, b, depth + 1));
+                stack.push((a, tm, depth + 1));
+            } else {
+                out.push(b);
+            }
+        }
+    }
+    out
+}
+
 #[test]
 #[ignore]
 #[cfg(not(target_arch = "wasm32"))]
@@ -872,13 +1033,13 @@ fn par_bench() {
 
     let instant = Instant::now();
     (0..100).for_each(|_| {
-        let _shell = shell_tessellation(&shell, 0.01, by_search_parameter);
+        let _shell = shell_tessellation(&shell, Deflection::chord(0.01), by_search_parameter);
     });
     println!("{}ms", instant.elapsed().as_millis());
 
     let instant = Instant::now();
     (0..100).for_each(|_| {
-        let _shell = shell_tessellation_single_thread(&shell, 0.01, by_search_parameter);
+        let _shell = shell_tessellation_single_thread(&shell, Deflection::chord(0.01), by_search_parameter);
     });
     println!("{}ms", instant.elapsed().as_millis());
 }