Scott BowdenandClaude Opus 5.5
3159fc0dd0
When sample points say two bodies are apart or one is inside the other, the facetings are now checked for surfaces passing through each other; if they do, the boolean is computed instead of shortcut. If it still can't be intersected, the sampled answer is kept as a flagged, unverified result, and Interference lists such pairs as "could not be checked" with the reason. Fixes #442 and #443. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
547 lines
22 KiB
Rust
547 lines
22 KiB
Rust
use serde::{Deserialize, Serialize};
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use crate::Vec3;
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/// Axis-aligned bounding box.
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#[derive(Clone, Copy, Debug, PartialEq, Serialize, Deserialize)]
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pub struct Aabb3 {
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pub min: Vec3,
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pub max: Vec3,
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}
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impl Default for Aabb3 {
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fn default() -> Self {
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Aabb3::EMPTY
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}
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}
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impl Aabb3 {
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pub const EMPTY: Aabb3 = Aabb3 {
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min: Vec3::new(f64::INFINITY, f64::INFINITY, f64::INFINITY),
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max: Vec3::new(f64::NEG_INFINITY, f64::NEG_INFINITY, f64::NEG_INFINITY),
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};
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pub fn is_empty(&self) -> bool {
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!(self.min.x <= self.max.x && self.min.y <= self.max.y && self.min.z <= self.max.z)
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}
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pub fn add(&mut self, p: Vec3) {
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if p.is_finite() {
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self.min = self.min.min(p);
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self.max = self.max.max(p);
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}
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}
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pub fn union(&self, o: &Aabb3) -> Aabb3 {
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if self.is_empty() {
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return *o;
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}
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if o.is_empty() {
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return *self;
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}
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Aabb3 { min: self.min.min(o.min), max: self.max.max(o.max) }
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}
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pub fn center(&self) -> Vec3 {
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if self.is_empty() { Vec3::ZERO } else { (self.min + self.max) * 0.5 }
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}
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pub fn size(&self) -> Vec3 {
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if self.is_empty() { Vec3::ZERO } else { self.max - self.min }
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}
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pub fn diagonal(&self) -> f64 {
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self.size().len()
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}
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}
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/// An indexed triangle mesh with per-vertex normals, a face id per triangle (the B-rep face it
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/// came from) and edge polylines (the B-rep edges, for display and picking).
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#[derive(Clone, Debug, Default, Serialize, Deserialize)]
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pub struct Mesh {
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pub positions: Vec<Vec3>,
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pub normals: Vec<Vec3>,
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/// Triangles as vertex index triples (counter-clockwise seen from outside).
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pub triangles: Vec<[u32; 3]>,
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/// B-rep face index per triangle.
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pub tri_face: Vec<u32>,
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/// B-rep edges as polylines.
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pub edges: Vec<Vec<Vec3>>,
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/// Per edge: a seam between two pieces of the same smooth surface (not drawn).
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#[serde(default)]
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pub seams: Vec<bool>,
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/// Display-only tangent joins. Edge identities, picking and face groups stay intact.
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#[serde(skip)]
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pub smooth_edges: Vec<bool>,
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/// Display-protected boundaries: certified current creases or authored splits.
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/// Overrides coarse seam fits; not a geometric/topological authority.
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#[serde(skip)]
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pub sharp_edges: Vec<bool>,
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/// Per edge: the B-rep faces it bounds (one or two).
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#[serde(default)]
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pub edge_faces: Vec<Vec<u32>>,
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}
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fn boxes_meet(a: &Aabb3, b: &Aabb3) -> bool {
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a.min.x <= b.max.x && b.min.x <= a.max.x && a.min.y <= b.max.y && b.min.y <= a.max.y && a.min.z <= b.max.z && b.min.z <= a.max.z
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}
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/// Two triangles that pass through each other (see [`Mesh::crosses`]).
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fn triangles_cross(t: &[Vec3; 3], u: &[Vec3; 3], tol: f64) -> bool {
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// Signed distances of one triangle's corners from the other's plane, when they lie more
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// than `tol` to both sides of it.
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let sides = |tri: &[Vec3; 3], plane: &[Vec3; 3]| -> Option<(Vec3, [f64; 3])> {
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let n = (plane[1] - plane[0]).cross(plane[2] - plane[0]).normalized()?;
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let d = [n.dot(tri[0] - plane[0]), n.dot(tri[1] - plane[0]), n.dot(tri[2] - plane[0])];
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let (lo, hi) = d.iter().fold((f64::INFINITY, f64::NEG_INFINITY), |(lo, hi), v| (lo.min(*v), hi.max(*v)));
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(lo < -tol && hi > tol).then_some((n, d))
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};
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let (Some((nu, dt)), Some((nt, du))) = (sides(t, u), sides(u, t)) else { return false };
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let Some(line) = nt.cross(nu).normalized() else { return false };
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// Where a triangle's edges pass through the other's plane, measured along the line the
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// two planes share.
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let reach = |tri: &[Vec3; 3], d: &[f64; 3]| -> (f64, f64) {
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let (mut lo, mut hi) = (f64::INFINITY, f64::NEG_INFINITY);
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for (i, j) in [(0, 1), (1, 2), (2, 0)] {
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let (p, q, dp, dq) = (tri[i], tri[j], d[i], d[j]);
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if (dp < 0.0) != (dq < 0.0) && dp != dq {
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let at = line.dot(p + (q - p) * (dp / (dp - dq)));
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lo = lo.min(at);
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hi = hi.max(at);
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}
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}
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(lo, hi)
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};
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let ((t0, t1), (u0, u1)) = (reach(t, &dt), reach(u, &du));
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t1.min(u1) - t0.max(u0) > tol
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}
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/// Mass properties of a closed mesh.
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#[derive(Clone, Copy, Debug, Default, PartialEq, Serialize, Deserialize)]
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pub struct MeshMeasure {
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pub volume: f64,
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pub area: f64,
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pub centroid: Vec3,
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}
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impl Mesh {
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/// Visibility in shaded edge presentation, independent of selection/topology.
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pub fn shaded_edge_visible(&self, index: usize) -> bool {
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self.edge_pickable(index) && !self.smooth_edges.get(index).copied().unwrap_or(false)
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}
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pub fn edge_pickable(&self, index: usize) -> bool {
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!self.seams.get(index).copied().unwrap_or(false) || self.sharp_edges.get(index).copied().unwrap_or(false)
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}
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/// Edges bounding face `f`.
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pub fn face_edges(&self, f: u32) -> Vec<usize> {
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self.edge_faces.iter().enumerate().filter(|(_, fs)| fs.contains(&f)).map(|(i, _)| i).collect()
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}
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/// Pieces of one surface joined across hidden seams, including `face` itself.
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pub fn surface_patch(&self, face: usize) -> Vec<usize> {
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let mut patch = vec![face];
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let mut todo = vec![face];
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while let Some(f) = todo.pop() {
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for (ei, fs) in self.edge_faces.iter().enumerate() {
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if !self.seams.get(ei).copied().unwrap_or(false)
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|| self.sharp_edges.get(ei).copied().unwrap_or(false)
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|| !fs.iter().any(|x| *x as usize == f)
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{
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continue;
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}
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for &next in fs {
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let next = next as usize;
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if !patch.contains(&next) {
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patch.push(next);
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todo.push(next);
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}
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}
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}
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}
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patch.sort_unstable();
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patch
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}
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/// A complete circular rim may be split into several kernel edges. Keep its pieces
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/// together for picking, without joining other tangent curves or changing edge indices.
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pub fn circular_rim(&self, edge: usize) -> Vec<usize> {
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let single = vec![edge];
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let Some(p) = self.edges.get(edge).filter(|p| p.len() >= 3) else { return single };
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let (Some(&a), Some(&b), Some(&c)) = (p.first(), p.get(p.len() / 2), p.last()) else { return single };
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let (u, v) = (b - a, c - a);
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let n = u.cross(v);
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if !(n.len2() > u.len2() * v.len2() * 1e-12) {
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return single;
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}
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let center = a + (v.cross(n) * u.len2() + n.cross(u) * v.len2()) / (2.0 * n.len2());
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let radius = center.dist(a);
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let normal = n.normalized().unwrap_or(Vec3::ZERO);
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let tol = (radius * 1e-6).max(1e-9);
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let mut rim = self.tangent_chain(edge, 2f64.to_radians());
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if rim.len() < 2 || !radius.is_finite() {
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return single;
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}
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// All samples must lie on this circle, and every end must join exactly one other
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// piece. Open arcs, ellipses, and branching tangent chains stay separate.
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for &i in &rim {
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let Some(points) = self.edges.get(i) else { return single };
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if points.iter().any(|q| !q.is_finite() || (q.dist(center) - radius).abs() > tol || (*q - center).dot(normal).abs() > tol) {
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return single;
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}
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for end in [points.first(), points.last()].into_iter().flatten() {
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let joins = rim
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.iter()
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.filter(|&&j| j != i)
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.filter_map(|&j| self.edges.get(j))
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.flat_map(|q| [q.first(), q.last()])
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.flatten()
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.filter(|q| q.dist(*end) < tol)
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.count();
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if joins != 1 {
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return single;
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}
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}
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}
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rim.sort_unstable();
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rim
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}
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/// The edges reached from `e` through vertices where the next edge continues smoothly
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/// (angle between the end tangents below `max_angle`), including `e` itself.
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pub fn tangent_chain(&self, e: usize, max_angle: f64) -> Vec<usize> {
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// (end point, direction leaving the edge there). A polyline's end chord leans inward
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// on a curve by half the turn to the next chord; extrapolating the two end chords
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// recovers the curve's end tangent.
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let end_dir = |p0: Vec3, p1: Vec3, p2: Option<Vec3>| -> Option<Vec3> {
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let u1 = (p0 - p1).normalized()?;
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match p2.and_then(|p2| (p1 - p2).normalized()) {
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Some(u2) => (u1 * 1.5 - u2 * 0.5).normalized(),
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None => Some(u1),
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}
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};
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let ends = |i: usize| -> Option<[(Vec3, Vec3); 2]> {
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let p = self.edges.get(i)?;
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let n = p.len();
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let (a, a1, a2) = (*p.first()?, *p.get(1)?, p.get(2).copied().filter(|_| n > 2));
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let (b, b1) = (*p.last()?, *p.get(n.checked_sub(2)?)?);
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let b2 = n.checked_sub(3).and_then(|k| p.get(k)).copied();
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Some([(a, end_dir(a, a1, a2)?), (b, end_dir(b, b1, b2)?)])
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};
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let size = self.bounds().diagonal().max(1e-9);
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let tol = size * 1e-7;
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let cos = max_angle.cos();
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let mut chain = vec![e];
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let mut todo = vec![e];
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while let Some(cur) = todo.pop() {
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let Some(ce) = ends(cur) else { continue };
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for (i, _) in self.edges.iter().enumerate() {
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if chain.contains(&i) || !self.edge_pickable(i) {
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continue;
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}
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let Some(ne) = ends(i) else { continue };
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// Smooth: leaving `cur` at a shared end continues into `i` (opposite directions).
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let smooth = ce.iter().any(|(p, d)| ne.iter().any(|(q, dn)| p.dist(*q) < tol && d.dot(-*dn) > cos));
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if smooth && chain.len() < 10_000 {
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chain.push(i);
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todo.push(i);
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}
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}
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}
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chain
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}
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pub fn tri(&self, t: &[u32; 3]) -> Option<[Vec3; 3]> {
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Some([*self.positions.get(t[0] as usize)?, *self.positions.get(t[1] as usize)?, *self.positions.get(t[2] as usize)?])
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}
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pub fn bounds(&self) -> Aabb3 {
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let mut b = Aabb3::EMPTY;
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for p in &self.positions {
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b.add(*p);
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}
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b
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}
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/// Signed volume (divergence theorem), surface area and volume centroid.
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pub fn measure(&self) -> MeshMeasure {
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let (mut v6, mut area, mut c) = (0.0, 0.0, Vec3::ZERO);
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for t in &self.triangles {
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let Some([a, b, cc]) = self.tri(t) else { continue };
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let d = a.dot(b.cross(cc));
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v6 += d;
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c += (a + b + cc) * d;
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area += (b - a).cross(cc - a).len() * 0.5;
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}
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let volume = v6 / 6.0;
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let centroid = if v6.abs() > 1e-12 { c / (4.0 * v6) } else { self.bounds().center() };
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MeshMeasure { volume, area, centroid }
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}
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/// Append another mesh (face ids offset by `face_offset`).
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pub fn append(&mut self, o: &Mesh, face_offset: u32) {
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let base = u32::try_from(self.positions.len()).unwrap_or(u32::MAX);
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self.positions.extend_from_slice(&o.positions);
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self.normals.extend_from_slice(&o.normals);
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self.triangles.extend(o.triangles.iter().map(|t| [t[0].saturating_add(base), t[1].saturating_add(base), t[2].saturating_add(base)]));
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self.tri_face.extend(o.tri_face.iter().map(|f| f.saturating_add(face_offset)));
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self.edges.extend(o.edges.iter().cloned());
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}
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/// Number of triangles a ray crosses (for inside/outside tests on closed meshes).
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pub fn ray_crossings(&self, o: Vec3, dir: Vec3) -> usize {
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let mut n = 0;
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for t in &self.triangles {
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let Some([a, b, c]) = self.tri(t) else { continue };
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let (e1, e2) = (b - a, c - a);
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let p = dir.cross(e2);
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let det = e1.dot(p);
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if det.abs() < 1e-14 {
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continue;
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}
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let inv = 1.0 / det;
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let s = o - a;
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let u = s.dot(p) * inv;
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if !(0.0..1.0).contains(&u) {
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continue;
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}
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let q = s.cross(e1);
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let v = dir.dot(q) * inv;
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if v < 0.0 || u + v >= 1.0 {
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continue;
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}
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if e2.dot(q) * inv > 0.0 {
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n += 1;
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}
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}
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n
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}
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/// Point inside a closed mesh (majority vote of three skewed rays).
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pub fn contains(&self, p: Vec3) -> bool {
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let dirs = [Vec3::new(0.5773, 0.5774, 0.5776), Vec3::new(-0.6123, 0.3141, 0.7254), Vec3::new(0.2718, -0.8414, 0.4673)];
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dirs.iter().filter(|d| self.ray_crossings(p, **d) % 2 == 1).count() >= 2
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}
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/// Whether the surfaces of two meshes pass through each other by more than `tol`: some
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/// triangle of one has corners more than `tol` to both sides of a triangle of the other,
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/// and the reverse, and they share a stretch of the line where their planes meet longer
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/// than `tol`. Faces that only touch, lie on each other or stop on the other surface don't
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/// count, nor do two facetings of one curved surface that are within `tol` of it. Bodies
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/// can still overlap without crossing: one inside the other, or sharing a slab between
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/// faces that are parallel or in one plane.
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pub fn crosses(&self, o: &Mesh, tol: f64) -> bool {
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if !tol.is_finite() {
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return false;
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}
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let tol = tol.max(0.0);
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let (ba, bb) = (self.bounds(), o.bounds());
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let region = Aabb3 { min: ba.min.max(bb.min), max: ba.max.min(bb.max) };
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if region.is_empty() {
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return false;
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}
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let near = |m: &Mesh| -> Vec<([Vec3; 3], Aabb3)> {
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m.triangles
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.iter()
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.filter_map(|t| {
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let t = m.tri(t)?;
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let mut bx = Aabb3::EMPTY;
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t.iter().for_each(|p| bx.add(*p));
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(!bx.is_empty() && boxes_meet(&bx, ®ion)).then_some((t, bx))
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})
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.collect()
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};
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let (ta, tb) = (near(self), near(o));
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if ta.is_empty() || tb.is_empty() {
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return false;
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}
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// A grid over the shared box holds the other mesh's triangles.
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let n = ((tb.len() as f64).cbrt().ceil() as usize).clamp(1, 24);
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let size = region.size();
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let cell = |v: f64, lo: f64, s: f64| -> usize { if s > 0.0 { (((v - lo) / s * n as f64).floor().max(0.0) as usize).min(n - 1) } else { 0 } };
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let span = |bx: &Aabb3| -> [(usize, usize); 3] {
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[
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(cell(bx.min.x, region.min.x, size.x), cell(bx.max.x, region.min.x, size.x)),
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(cell(bx.min.y, region.min.y, size.y), cell(bx.max.y, region.min.y, size.y)),
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(cell(bx.min.z, region.min.z, size.z), cell(bx.max.z, region.min.z, size.z)),
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]
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};
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let mut cells: Vec<Vec<u32>> = vec![Vec::new(); n * n * n];
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for (i, (_, bx)) in tb.iter().enumerate() {
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let [x, y, z] = span(bx);
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for ix in x.0..=x.1 {
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for iy in y.0..=y.1 {
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for iz in z.0..=z.1 {
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if let Some(c) = cells.get_mut((ix * n + iy) * n + iz) {
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c.push(i as u32);
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}
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}
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}
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}
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}
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// Per triangle of `o`: the last triangle of `self` tested against it, plus one.
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let mut seen = vec![0usize; tb.len()];
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for (i, (t, bx)) in ta.iter().enumerate() {
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let [x, y, z] = span(bx);
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for ix in x.0..=x.1 {
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for iy in y.0..=y.1 {
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for iz in z.0..=z.1 {
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for j in cells.get((ix * n + iy) * n + iz).into_iter().flatten() {
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let (Some(mark), Some((u, ub))) = (seen.get_mut(*j as usize), tb.get(*j as usize)) else { continue };
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if *mark == i + 1 {
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continue;
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}
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*mark = i + 1;
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if boxes_meet(bx, ub) && triangles_cross(t, u, tol) {
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return true;
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}
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}
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}
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}
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}
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}
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false
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}
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/// Closest intersection of a ray with the mesh: (distance along `dir`, triangle index).
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pub fn raycast(&self, o: Vec3, dir: Vec3) -> Option<(f64, usize)> {
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|
let mut best: Option<(f64, usize)> = None;
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for (i, t) in self.triangles.iter().enumerate() {
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let Some([a, b, c]) = self.tri(t) else { continue };
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let (e1, e2) = (b - a, c - a);
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let p = dir.cross(e2);
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let det = e1.dot(p);
|
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if det.abs() < 1e-14 {
|
|
continue;
|
|
}
|
|
let inv = 1.0 / det;
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|
let s = o - a;
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|
let u = s.dot(p) * inv;
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if !(0.0..=1.0).contains(&u) {
|
|
continue;
|
|
}
|
|
let q = s.cross(e1);
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|
let v = dir.dot(q) * inv;
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if v < 0.0 || u + v > 1.0 {
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|
continue;
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|
}
|
|
let t = e2.dot(q) * inv;
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if t > 1e-9 && best.is_none_or(|(bt, _)| t < bt) {
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|
best = Some((t, i));
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|
}
|
|
}
|
|
best
|
|
}
|
|
}
|
|
|
|
/// Point-in-mesh queries in bulk: for each of `Mesh::contains`'s three ray directions, the
|
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/// triangles binned on a grid in the plane square to it, so a ray tests only the triangles
|
|
/// whose shadow covers its cell. Answers exactly as `Mesh::contains` does.
|
|
pub struct InsideIndex<'a> {
|
|
mesh: &'a Mesh,
|
|
rays: Vec<RayGrid>,
|
|
}
|
|
|
|
struct RayGrid {
|
|
dir: Vec3,
|
|
u: Vec3,
|
|
v: Vec3,
|
|
min: (f64, f64),
|
|
cell: f64,
|
|
n: (usize, usize),
|
|
cells: Vec<Vec<u32>>,
|
|
}
|
|
|
|
const RAY_DIRS: [Vec3; 3] = [Vec3::new(0.5773, 0.5774, 0.5776), Vec3::new(-0.6123, 0.3141, 0.7254), Vec3::new(0.2718, -0.8414, 0.4673)];
|
|
|
|
impl Mesh {
|
|
/// An index for many `contains` queries on this mesh.
|
|
pub fn inside_index(&self) -> InsideIndex<'_> {
|
|
let rays = RAY_DIRS
|
|
.iter()
|
|
.map(|d| {
|
|
let u = d.any_perp();
|
|
let v = d.cross(u);
|
|
let tris: Vec<[(f64, f64); 3]> = self
|
|
.triangles
|
|
.iter()
|
|
.map(|t| match self.tri(t) {
|
|
Some([a, b, c]) => [(a.dot(u), a.dot(v)), (b.dot(u), b.dot(v)), (c.dot(u), c.dot(v))],
|
|
None => [(0.0, 0.0); 3],
|
|
})
|
|
.collect();
|
|
let (mut lo, mut hi) = ((f64::INFINITY, f64::INFINITY), (f64::NEG_INFINITY, f64::NEG_INFINITY));
|
|
for t in &tris {
|
|
for p in t {
|
|
lo = (lo.0.min(p.0), lo.1.min(p.1));
|
|
hi = (hi.0.max(p.0), hi.1.max(p.1));
|
|
}
|
|
}
|
|
let span = (hi.0 - lo.0).max(hi.1 - lo.1).max(1e-9);
|
|
let side = ((tris.len() as f64).sqrt().ceil() as usize).clamp(1, 256);
|
|
let cell = span / side as f64 * (1.0 + 1e-9);
|
|
let n = (side + 1, side + 1);
|
|
let mut cells = vec![Vec::new(); n.0 * n.1];
|
|
if lo.0.is_finite() {
|
|
for (i, t) in tris.iter().enumerate() {
|
|
let (x0, x1) = (t.iter().map(|p| p.0).fold(f64::INFINITY, f64::min), t.iter().map(|p| p.0).fold(f64::NEG_INFINITY, f64::max));
|
|
let (y0, y1) = (t.iter().map(|p| p.1).fold(f64::INFINITY, f64::min), t.iter().map(|p| p.1).fold(f64::NEG_INFINITY, f64::max));
|
|
let c = |x: f64, o: f64, m: usize| (((x - o) / cell).floor().max(0.0) as usize).min(m - 1);
|
|
for gx in c(x0, lo.0, n.0)..=c(x1, lo.0, n.0) {
|
|
for gy in c(y0, lo.1, n.1)..=c(y1, lo.1, n.1) {
|
|
if let Some(slot) = cells.get_mut(gx * n.1 + gy) {
|
|
slot.push(i as u32);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
RayGrid { dir: *d, u, v, min: lo, cell, n, cells }
|
|
})
|
|
.collect();
|
|
InsideIndex { mesh: self, rays }
|
|
}
|
|
}
|
|
|
|
impl InsideIndex<'_> {
|
|
fn crossings(&self, g: &RayGrid, o: Vec3) -> usize {
|
|
let (x, y) = (o.dot(g.u), o.dot(g.v));
|
|
if !(g.min.0.is_finite()) {
|
|
return 0;
|
|
}
|
|
let (fx, fy) = ((x - g.min.0) / g.cell, (y - g.min.1) / g.cell);
|
|
if fx < 0.0 || fy < 0.0 {
|
|
return 0;
|
|
}
|
|
let (gx, gy) = (fx.floor() as usize, fy.floor() as usize);
|
|
if gx >= g.n.0 || gy >= g.n.1 {
|
|
return 0;
|
|
}
|
|
let Some(list) = g.cells.get(gx * g.n.1 + gy) else { return 0 };
|
|
let dir = g.dir;
|
|
let mut n = 0;
|
|
for &i in list {
|
|
let Some(t) = self.mesh.triangles.get(i as usize) else { continue };
|
|
let Some([a, b, c]) = self.mesh.tri(t) else { continue };
|
|
let (e1, e2) = (b - a, c - a);
|
|
let p = dir.cross(e2);
|
|
let det = e1.dot(p);
|
|
if det.abs() < 1e-14 {
|
|
continue;
|
|
}
|
|
let inv = 1.0 / det;
|
|
let s = o - a;
|
|
let u = s.dot(p) * inv;
|
|
if !(0.0..1.0).contains(&u) {
|
|
continue;
|
|
}
|
|
let q = s.cross(e1);
|
|
let v = dir.dot(q) * inv;
|
|
if v < 0.0 || u + v >= 1.0 {
|
|
continue;
|
|
}
|
|
if e2.dot(q) * inv > 0.0 {
|
|
n += 1;
|
|
}
|
|
}
|
|
n
|
|
}
|
|
|
|
/// Same answer as `Mesh::contains`.
|
|
pub fn contains(&self, p: Vec3) -> bool {
|
|
self.rays.iter().filter(|g| self.crossings(g, p) % 2 == 1).count() >= 2
|
|
}
|
|
}
|