Variable-radius and chord-length fillets

New kernel file blend_variable.rs. The hooks into blend.rs are visibility
only: plane_normal, vtx, rebuild_face and unsupported are now pub(crate).
- fillet_variable(body, edge, start, r0, r1) works on the same edge
  configuration as the constant fillet (straight edge, planar faces, end
  faces square to it). The radius runs linearly from the end nearest
  `start`, and every section square to the edge is a circular arc. The
  blend is an exact degree (2, 1) rational B-spline: arc control points
  move linearly.
- fillet_chord(body, edges, chord): the radius per edge comes from its
  face angle (chord = 2 r cos(phi/2)).

Fillet feature: style constant | chord | variable {radius2, start};
FusionFilletEdgesCommand takes type, radius2 and start.

Tests:
- Variable 2 -> 5 on a box edge removes (1 - pi/4) L (r0^2 + r0 r1 + r1^2)/3.
  Starting from the other end gives the same solid; equal radii give the
  constant fillet; too large is refused.
- Chord 4 on a right angle equals radius 4/sqrt(2).
- Engine: both types by command.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01AS5Tn3xieewUSg3uxrMVdL

crates/kernel/src/blend_variable.rs

@@ -0,0 +1,271 @@
+//! Fillets beyond a constant radius: a radius that varies along the edge (from one end to the
+//! other) and chord-length fillets (the width across the blend given instead of the radius).
+//!
+//! Variable radius: a straight, convex or concave edge between two planar faces whose ends each
+//! touch one more planar face square to the edge (the configuration of `blend`). Every section
+//! square to the edge is a circular arc tangent to both faces, its radius running linearly from
+//! one end to the other; the arcs' control points move linearly, so the blend is exactly a
+//! rational B-spline of degree 2 across and 1 along.
+
+use std::collections::HashMap;
+
+use solvecraft_geom::Vec3;
+use truck_modeling::{self as mt, builder};
+
+use crate::blend::{plane_normal, rebuild_face, unsupported, vtx};
+use crate::body::{Body, Solid, p3};
+use crate::{KernelError, Result, guard};
+
+/// The radius of a chord-length fillet between faces whose in-face directions (away from the
+/// edge) make the angle `phi`: the arc spans π − φ, so the chord is 2 r cos(φ/2).
+fn chord_radius(chord: f64, phi: f64) -> f64 {
+    chord / (2.0 * (phi / 2.0).cos())
+}
+
+/// The two planar faces at an edge, the in-face directions away from it (`t1`, `t2`), the
+/// first face's normal, the angle between the directions and the side of the material.
+struct EdgeFrame {
+    i1: usize,
+    i2: usize,
+    n1: Vec3,
+    t1: Vec3,
+    t2: Vec3,
+    phi: f64,
+    side: f64,
+}
+
+fn edge_frame(faces: &[&mt::Face], edge: &mt::Edge) -> Result<EdgeFrame> {
+    let on_edge: Vec<usize> = (0..faces.len()).filter(|i| faces.get(*i).is_some_and(|f| f.edge_iter().any(|e| e.id() == edge.id()))).collect();
+    let [i1, i2] = on_edge[..] else { return Err(unsupported("the edge is not between two faces")) };
+    let (Some(f1), Some(f2)) = (faces.get(i1), faces.get(i2)) else { return Err(KernelError::Failed("faces".into())) };
+    let (Some(n1), Some(n2)) = (plane_normal(f1), plane_normal(f2)) else { return Err(unsupported("both faces next to the edge must be planar")) };
+    let into = |f: &mt::Face, n: Vec3| -> Option<Vec3> {
+        let e = f.boundary_iters().into_iter().flatten().find(|e| e.id() == edge.id())?;
+        let dir = (vtx(e.back()) - vtx(e.front())).normalized()?;
+        n.cross(dir).normalized()
+    };
+    let (Some(t1), Some(t2)) = (into(f1, n1), into(f2, n2)) else { return Err(KernelError::Failed("blend: edge direction".into())) };
+    let phi = t1.dot(t2).clamp(-1.0, 1.0).acos();
+    let convex = n1.dot(t2) < -1e-9 && n2.dot(t1) < -1e-9;
+    let concave = n1.dot(t2) > 1e-9 && n2.dot(t1) > 1e-9;
+    if !(phi > 1e-3 && phi < std::f64::consts::PI - 1e-3) || !(convex || concave) {
+        return Err(unsupported("the faces at the edge are tangent or the edge is ambiguous"));
+    }
+    Ok(EdgeFrame { i1, i2, n1, t1, t2, phi, side: if convex { -1.0 } else { 1.0 } })
+}
+
+/// Fillet one straight edge with radius `r0` at its end nearest `start` and `r1` at the other.
+pub fn fillet_variable(body: &Body, edge_at: Vec3, start: Vec3, r0: f64, r1: f64) -> Result<Body> {
+    body.require_brep("fillet")?;
+    for r in [r0, r1] {
+        if !(r.is_finite() && r > 1e-6 && r < 1e6) {
+            return Err(KernelError::Invalid("fillet radii must be positive".into()));
+        }
+    }
+    let edge = crate::surfaces::edge_near(body, edge_at).ok_or_else(|| KernelError::Invalid(format!("no edge at {edge_at:?}")))?;
+    let size = body.size();
+    guard("variable fillet", || {
+        let solid: &Solid = &body.solid;
+        if !matches!(edge.curve(), mt::Curve::Line(_)) {
+            return Err(unsupported("only straight edges take a variable radius"));
+        }
+        let shells = solid.boundaries();
+        let (si, shell) = shells
+            .iter()
+            .enumerate()
+            .find(|(_, sh)| sh.edge_iter().any(|e| e.id() == edge.id()))
+            .ok_or_else(|| KernelError::Failed("edge not found".into()))?;
+        let faces: Vec<&mt::Face> = shell.face_iter().collect();
+        let fr = edge_frame(&faces, &edge)?;
+        let (v0, v1) = (edge.absolute_front().clone(), edge.absolute_back().clone());
+        // r0 at the end nearest `start` (the edge keeps its own direction).
+        let (ra, rb) = if vtx(&v1).dist(start) < vtx(&v0).dist(start) { (r1, r0) } else { (r0, r1) };
+        let (p0, p1) = (vtx(&v0), vtx(&v1));
+        let d = (p1 - p0).normalized().ok_or_else(|| KernelError::Failed("zero-length edge".into()))?;
+        let tol = (size * 1e-7).max(1e-9);
+        let back = |r: f64| r / (fr.phi / 2.0).tan();
+        // Each end: the end face and its edges along the two faces.
+        struct End {
+            v: mt::Vertex,
+            g: usize,
+            e1: mt::Edge,
+            e2: mt::Edge,
+        }
+        let mut ends = Vec::new();
+        for (v, p, r) in [(&v0, p0, ra), (&v1, p1, rb)] {
+            let at_v: Vec<usize> = (0..faces.len()).filter(|i| faces.get(*i).is_some_and(|f| f.vertex_iter().any(|x| &x == v))).collect();
+            let others: Vec<usize> = at_v.iter().copied().filter(|i| *i != fr.i1 && *i != fr.i2).collect();
+            let [g] = others[..] else { return Err(unsupported("each end of the edge must touch exactly one more face")) };
+            let gf = faces.get(g).ok_or_else(|| KernelError::Failed("face".into()))?;
+            let ng = plane_normal(gf).ok_or_else(|| unsupported("the faces at the edge ends must be planar"))?;
+            if ng.dot(d).abs() < 1.0 - 1e-9 {
+                return Err(unsupported("the faces at the edge ends must be perpendicular to the edge"));
+            }
+            let shared = |fi: usize| -> Result<mt::Edge> {
+                let f = faces.get(fi).ok_or_else(|| KernelError::Failed("face".into()))?;
+                f.edge_iter()
+                    .find(|e| e.id() != edge.id() && (e.front() == v || e.back() == v) && gf.edge_iter().any(|x| x.id() == e.id()))
+                    .ok_or_else(|| unsupported("unexpected corner topology"))
+            };
+            let (e1, e2) = (shared(fr.i1)?, shared(fr.i2)?);
+            for (e, t) in [(&e1, fr.t1), (&e2, fr.t2)] {
+                if !matches!(e.curve(), mt::Curve::Line(_)) {
+                    return Err(unsupported("the edges at the corners must be straight"));
+                }
+                let other = if e.front() == v { vtx(e.back()) } else { vtx(e.front()) };
+                let along = (other - p).dot(t);
+                if (other - p - t * along).len() > tol * 100.0 + 1e-7 || along <= back(r) + tol {
+                    return Err(unsupported("the blend is larger than the neighbouring faces"));
+                }
+            }
+            ends.push(End { v: v.clone(), g, e1, e2 });
+        }
+        let [end0, end1] = &ends[..] else { return Err(KernelError::Failed("ends".into())) };
+        if end0.g == end1.g {
+            return Err(unsupported("both ends touch the same face"));
+        }
+        let (s0, s1) = (back(ra), back(rb));
+        let (pa0, pb0, pa1, pb1) = (p0 + fr.t1 * s0, p0 + fr.t2 * s0, p1 + fr.t1 * s1, p1 + fr.t2 * s1);
+        let (a0, b0, a1, b1) = (builder::vertex(p3(pa0)), builder::vertex(p3(pb0)), builder::vertex(p3(pa1)), builder::vertex(p3(pb1)));
+        let arc_mid = |p: Vec3, s: f64, r: f64| {
+            let c = p + fr.t1 * s + fr.n1 * (r * fr.side);
+            c + (p - c).normalized().unwrap_or(-fr.n1) * r
+        };
+        let c0 = builder::circle_arc(&a0, &b0, p3(arc_mid(p0, s0, ra)));
+        let c1 = builder::circle_arc(&a1, &b1, p3(arc_mid(p1, s1, rb)));
+        let la = builder::line(&a0, &a1);
+        let lb = builder::line(&b0, &b1);
+        let mut subst: HashMap<mt::EdgeID, mt::Edge> = HashMap::new();
+        for (end, a, b) in [(end0, &a0, &b0), (end1, &a1, &b1)] {
+            for (e, nv) in [(&end.e1, a), (&end.e2, b)] {
+                let (f, bk) = (e.absolute_front(), e.absolute_back());
+                let ne = if f == &end.v { builder::line(nv, bk) } else { builder::line(f, nv) };
+                subst.insert(e.id(), ne);
+            }
+        }
+        let mut new_faces: Vec<mt::Face> = Vec::with_capacity(faces.len() + 1);
+        for (i, f) in faces.iter().enumerate() {
+            let nf = if i == fr.i1 {
+                let mut m = subst.clone();
+                m.insert(edge.id(), la.clone());
+                rebuild_face(f, &m, &[])?
+            } else if i == fr.i2 {
+                let mut m = subst.clone();
+                m.insert(edge.id(), lb.clone());
+                rebuild_face(f, &m, &[])?
+            } else if i == end0.g {
+                rebuild_face(f, &subst, std::slice::from_ref(&c0))?
+            } else if i == end1.g {
+                rebuild_face(f, &subst, std::slice::from_ref(&c1))?
+            } else {
+                (*f).clone()
+            };
+            new_faces.push(nf);
+        }
+        // The blend surface: rational quadratic arcs (tangent points and the edge point, middle
+        // weight sin(φ/2)) at each end, joined linearly.
+        let w = (fr.phi / 2.0).sin();
+        let h = |p: Vec3, wt: f64| mt::Vector4::new(p.x * wt, p.y * wt, p.z * wt, wt);
+        let ctrl = vec![vec![h(pa0, 1.0), h(pa1, 1.0)], vec![h(p0, w), h(p1, w)], vec![h(pb0, 1.0), h(pb1, 1.0)]];
+        let bsp = mt::BSplineSurface::new((mt::KnotVec::bezier_knot(2), mt::KnotVec::bezier_knot(1)), ctrl);
+        let mut surf = mt::Surface::NurbsSurface(mt::NurbsSurface::new(bsp));
+        // Outward: away from the arc centre on a convex edge, toward it on a concave one.
+        let (c, mid) = (p0 + fr.t1 * s0 + fr.n1 * (ra * fr.side), arc_mid(p0, s0, ra));
+        let outward = (mid - c) * (-fr.side);
+        {
+            use mt::{ParametricSurface3D, SearchParameter};
+            if let Some((u, v)) = surf.search_parameter(p3(mid), None, 100) {
+                let nn = surf.normal(u, v);
+                if Vec3::new(nn.x, nn.y, nn.z).dot(outward) < 0.0 {
+                    surf = mt::Invertible::inverse(&surf);
+                }
+            }
+        }
+        // The blend face uses each new edge opposite to its neighbour.
+        let f1_forward =
+            faces.get(fr.i1).is_some_and(|f| f.boundaries().iter().any(|w| w.edge_iter().any(|e| e.id() == edge.id() && e.front() == &v0)));
+        let wire: mt::Wire = if f1_forward {
+            vec![c0.clone(), lb.clone(), c1.inverse(), la.inverse()].into()
+        } else {
+            vec![la.clone(), c1.clone(), lb.inverse(), c0.inverse()].into()
+        };
+        let blend = mt::Face::try_new(vec![wire], surf).map_err(|e| KernelError::Failed(format!("fillet face: {e}")))?;
+        new_faces.push(blend);
+        let mut shells = solid.boundaries().clone();
+        if let Some(sh) = shells.get_mut(si) {
+            *sh = new_faces.into();
+        }
+        Body::new(Solid::try_new(shells).map_err(|e| KernelError::Failed(format!("variable fillet produced an invalid solid: {e}")))?)
+    })
+}
+
+/// Chord-length fillet: each edge (straight, between planar faces) rounded so that the blend
+/// is `chord` wide across; edges with the same face angle share a radius.
+pub fn fillet_chord(body: &Body, edges: &[Vec3], chord: f64) -> Result<Body> {
+    body.require_brep("fillet")?;
+    if !(chord.is_finite() && chord > 1e-6 && chord < 1e6) {
+        return Err(KernelError::Invalid("the chord length must be positive".into()));
+    }
+    if edges.is_empty() || edges.len() > 1000 {
+        return Err(KernelError::Invalid("select 1…1000 edges".into()));
+    }
+    // Radius per edge from its face angle.
+    let mut groups: Vec<(f64, Vec<Vec3>)> = Vec::new();
+    for p in edges {
+        let e = crate::surfaces::edge_near(body, *p).ok_or_else(|| KernelError::Invalid(format!("no edge at {p:?}")))?;
+        let shell =
+            body.solid.boundaries().iter().find(|sh| sh.edge_iter().any(|x| x.id() == e.id())).ok_or_else(|| KernelError::Failed("edge".into()))?;
+        let faces: Vec<&mt::Face> = shell.face_iter().collect();
+        let fr = edge_frame(&faces, &e)?;
+        let r = chord_radius(chord, fr.phi);
+        match groups.iter_mut().find(|(gr, _)| (gr - r).abs() <= 1e-9 * r) {
+            Some((_, v)) => v.push(*p),
+            None => groups.push((r, vec![*p])),
+        }
+    }
+    let mut cur = body.clone();
+    for (r, pts) in groups {
+        cur = crate::fillet(&cur, &pts, r)?;
+    }
+    Ok(cur)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::{box_solid, measure};
+
+    fn rel(a: f64, b: f64) -> f64 {
+        (a - b).abs() / b.abs().max(1e-9)
+    }
+
+    /// The material a variable fillet removes from a right-angled edge of length L, radius
+    /// running r0 → r1: ∫ (1 − π/4) r(t)² dt = (1 − π/4) L (r0² + r0 r1 + r1²) / 3.
+    #[test]
+    fn variable_radius_on_a_box_edge() {
+        let b = box_solid(Vec3::ZERO, Vec3::new(10.0, 20.0, 30.0)).unwrap();
+        // The edge along y at x = 10, z = 30; radius 2 at y = 0, 5 at y = 20.
+        let f = fillet_variable(&b, Vec3::new(10.0, 10.0, 30.0), Vec3::new(10.0, 0.0, 30.0), 2.0, 5.0).unwrap();
+        let removed = (1.0 - std::f64::consts::FRAC_PI_4) * 20.0 * (4.0 + 10.0 + 25.0) / 3.0;
+        let v = measure(&f).unwrap().volume;
+        assert!(rel(v, 6000.0 - removed) < 1e-4, "{v} vs {}", 6000.0 - removed);
+        // Started from the other end: the same solid.
+        let h = fillet_variable(&b, Vec3::new(10.0, 10.0, 30.0), Vec3::new(10.0, 20.0, 30.0), 5.0, 2.0).unwrap();
+        assert!(rel(measure(&h).unwrap().volume, v) < 1e-9);
+        // Equal radii give the constant fillet.
+        let g = fillet_variable(&b, Vec3::new(10.0, 10.0, 30.0), Vec3::new(10.0, 0.0, 30.0), 3.0, 3.0).unwrap();
+        let k = crate::fillet(&b, &[Vec3::new(10.0, 10.0, 30.0)], 3.0).unwrap();
+        assert!(rel(measure(&g).unwrap().volume, measure(&k).unwrap().volume) < 1e-6);
+        // Too big for the faces: refused.
+        assert!(fillet_variable(&b, Vec3::new(10.0, 10.0, 30.0), Vec3::new(10.0, 0.0, 30.0), 2.0, 50.0).is_err());
+    }
+
+    #[test]
+    fn chord_length_on_a_right_angle() {
+        let b = box_solid(Vec3::ZERO, Vec3::new(10.0, 20.0, 30.0)).unwrap();
+        // A right angle: chord c gives radius c / √2.
+        let f = fillet_chord(&b, &[Vec3::new(10.0, 10.0, 30.0)], 4.0).unwrap();
+        let k = crate::fillet(&b, &[Vec3::new(10.0, 10.0, 30.0)], 4.0 / 2f64.sqrt()).unwrap();
+        assert!(rel(measure(&f).unwrap().volume, measure(&k).unwrap().volume) < 1e-9);
+    }
+}