Display tessellation plans (1/4): planner with shared edge nodes (#802)
Adds TessPlan and the kernel planner (shared edge nodes, structured and Coons grids, constrained Delaunay for trimmed faces) behind Body::display_plan. Nothing drawn changes yet. Refs #303 Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
Irakli KourtisandClaude Opus 5.5 authored and GitHub committed
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//! Faces the structured grid cannot take (trimmed faces, holes): a constrained Delaunay
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//! triangulation of the boundary loops in (u, v) scaled by the surface's mean metric, with
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//! interior seed points, refinement wherever a triangle sags more than the tolerance from the
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//! surface, then Ruppert refinement for shape. Constraint edges are never split, so the
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//! boundary stays exactly the shared edge nodes.
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use std::collections::HashMap;
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use solidcraft_geom::Vec3;
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use spade::handles::FixedVertexHandle;
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use spade::{AngleLimit, ConstrainedDelaunayTriangulation, Point2, RefinementParameters, Triangulation};
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type Cdt = ConstrainedDelaunayTriangulation<Point2<f64>>;
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/// Smallest angle Ruppert refinement aims for.
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const MIN_ANGLE_DEG: f64 = 20.0;
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/// Rounds of sag refinement.
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const SAG_ROUNDS: usize = 16;
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/// The surface, for refining where the triangles leave it.
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pub(crate) struct Sag<'a> {
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pub eval: &'a dyn Fn(f64, f64) -> Option<Vec3>,
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pub tol: f64,
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/// Scale of u and v in the triangulation (the surface's mean |S_u|, |S_v|).
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pub scale: [f64; 2],
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}
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/// How to fill the inside of the loops.
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pub(crate) struct Fill<'a> {
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/// Interior points (already inside the loops).
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pub seeds: &'a [[f64; 2]],
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/// Refinement, adding at most this many points in all.
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pub refine: Option<(Sag<'a>, usize)>,
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}
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/// Triangulate the region bounded by `loops` (ranges of `boundary`, each closed). Boundary
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/// vertices keep their indices; added points follow. Triangles are counter-clockwise in
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/// (u, v). `None` when a loop cannot be kept as constraints (it crosses itself or another).
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pub(crate) fn triangulate(boundary: &[[f64; 2]], loops: &[std::ops::Range<usize>], fill: Fill) -> Option<(Vec<[f64; 2]>, Vec<[u32; 3]>)> {
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if boundary.iter().flatten().any(|x| !x.is_finite()) {
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return None;
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}
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let scale = match &fill.refine {
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Some((sag, _)) if sag.scale.iter().all(|k| k.is_finite() && *k > 0.0) => sag.scale,
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_ => [1.0, 1.0],
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};
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let to = |p: &[f64; 2]| Point2::new(p[0] * scale[0], p[1] * scale[1]);
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let from = |p: Point2<f64>| [p.x / scale[0], p.y / scale[1]];
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let mut cdt = Cdt::new();
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let mut index: HashMap<FixedVertexHandle, u32> = HashMap::new();
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let mut handles: Vec<FixedVertexHandle> = Vec::with_capacity(boundary.len());
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for (i, p) in boundary.iter().enumerate() {
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let h = cdt.insert(to(p)).ok()?;
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index.entry(h).or_insert(u32::try_from(i).ok()?);
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handles.push(h);
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}
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for r in loops {
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let n = r.len();
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for k in 0..n {
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let (a, b) = (*handles.get(r.start + k)?, *handles.get(r.start + (k + 1) % n)?);
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if a == b || cdt.exists_constraint(a, b) {
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continue;
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}
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if !cdt.can_add_constraint(a, b) {
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return None;
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}
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cdt.add_constraint(a, b);
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}
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}
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for s in fill.seeds {
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if s.iter().all(|x| x.is_finite()) {
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let _ = cdt.insert(to(s));
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}
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}
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if let Some((sag, budget)) = &fill.refine {
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let constraints = cdt.num_constraints();
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let added = refine_sag(&mut cdt, sag, *budget, &from);
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let params = RefinementParameters::<f64>::new()
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.keep_constraint_edges()
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.exclude_outer_faces(true)
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.with_angle_limit(AngleLimit::from_deg(MIN_ANGLE_DEG))
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.with_max_additional_vertices(budget.saturating_sub(added));
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cdt.refine(params);
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// A split constraint would put a point on the boundary the neighbour does not have.
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if cdt.num_constraints() != constraints {
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return None;
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}
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}
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let mut uv: Vec<[f64; 2]> = boundary.to_vec();
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let mut tris = Vec::new();
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let region = region(&cdt);
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for face in cdt.inner_faces() {
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if !region.get(face.index()).copied().unwrap_or(false) {
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continue;
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}
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let vs = face.vertices();
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let mut t = [0u32; 3];
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for (slot, v) in t.iter_mut().zip(vs) {
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*slot = match index.get(&v.fix()) {
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Some(&i) => i,
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None => {
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let i = u32::try_from(uv.len()).ok()?;
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uv.push(from(v.position()));
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index.insert(v.fix(), i);
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i
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}
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};
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}
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tris.push(t);
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}
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let extra = uv.split_off(boundary.len());
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Some((extra, tris))
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}
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/// Insert the parameters of the surface point under every triangle centre and every
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/// non-constraint edge middle that lies more than the tolerance from the triangle, until none
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/// does or `budget` points were added. Returns the points added.
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fn refine_sag(cdt: &mut Cdt, sag: &Sag, budget: usize, from: &dyn Fn(Point2<f64>) -> [f64; 2]) -> usize {
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let mut added = 0;
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let mut cache: HashMap<FixedVertexHandle, Option<Vec3>> = HashMap::new();
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for _ in 0..SAG_ROUNDS {
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let mut todo: Vec<Point2<f64>> = Vec::new();
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let mut at = |h: FixedVertexHandle, p: Point2<f64>| {
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*cache.entry(h).or_insert_with(|| {
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let q = from(p);
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(sag.eval)(q[0], q[1])
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})
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};
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let region = region(cdt);
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for face in cdt.inner_faces() {
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if !region.get(face.index()).copied().unwrap_or(false) {
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continue;
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}
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let vs = face.vertices();
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let ps = vs.map(|v| v.position());
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let c = Point2::new((ps[0].x + ps[1].x + ps[2].x) / 3.0, (ps[0].y + ps[1].y + ps[2].y) / 3.0);
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let (Some(a), Some(b), Some(d)) = (at(vs[0].fix(), ps[0]), at(vs[1].fix(), ps[1]), at(vs[2].fix(), ps[2])) else { continue };
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let off = |q: Point2<f64>, chord: Vec3| {
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let uv = from(q);
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(sag.eval)(uv[0], uv[1]).is_some_and(|s| s.dist(chord) > sag.tol)
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};
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if off(c, (a + b + d) * (1.0 / 3.0)) {
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todo.push(c);
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continue;
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}
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for (e, (pa, pb)) in face.adjacent_edges().into_iter().zip([(a, b), (b, d), (d, a)]) {
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if e.is_constraint_edge() {
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continue;
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}
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let [p, q] = e.positions();
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let m = Point2::new(0.5 * (p.x + q.x), 0.5 * (p.y + q.y));
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if off(m, (pa + pb) * 0.5) {
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todo.push(m);
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}
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}
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}
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if todo.is_empty() {
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break;
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}
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todo.sort_by(|a, b| a.x.total_cmp(&b.x).then(a.y.total_cmp(&b.y)));
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todo.dedup();
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for p in todo {
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if added >= budget {
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return added;
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}
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if cdt.insert(p).is_ok() {
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added += 1;
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}
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}
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}
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added
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}
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/// Per face (by index): inside the region the constraint loops bound. A flood fill from the
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/// outer face that flips parity each time it crosses a constraint edge (holes are out), linear
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/// in the number of triangles.
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fn region(cdt: &Cdt) -> Vec<bool> {
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use spade::handles::{FixedFaceHandle, InnerTag};
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let mut parity: Vec<Option<bool>> = vec![None; cdt.num_all_faces()];
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let mut todo: Vec<(FixedFaceHandle<InnerTag>, bool)> = Vec::new();
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for e in cdt.convex_hull() {
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// Hull edges have the outer face on one side; the other side is an inner face.
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for side in [e, e.rev()] {
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if let Some(inner) = side.face().as_inner() {
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todo.push((inner.fix(), e.is_constraint_edge()));
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}
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}
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}
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while let Some((h, odd)) = todo.pop() {
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match parity.get_mut(h.index()) {
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Some(slot @ None) => *slot = Some(odd),
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_ => continue,
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}
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for e in cdt.face(h).adjacent_edges() {
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if let Some(next) = e.rev().face().as_inner() {
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todo.push((next.fix(), odd ^ e.is_constraint_edge()));
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}
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}
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}
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parity.into_iter().map(|p| p.unwrap_or(false)).collect()
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}
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/// The grid points `us` × `vs` inside the region bounded by the loops (even–odd, so holes are
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/// out): per grid line, the loops' crossings sorted once, then each point by binary search.
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pub(crate) fn inside_grid(us: &[f64], vs: &[f64], polys: &[&[[f64; 2]]]) -> Vec<[f64; 2]> {
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let mut out = Vec::new();
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let mut xs: Vec<f64> = Vec::new();
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for &v in vs {
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xs.clear();
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for poly in polys {
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let n = poly.len();
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for k in 0..n {
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let (Some(a), Some(b)) = (poly.get(k), poly.get((k + 1) % n)) else { continue };
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if (a[1] > v) != (b[1] > v) {
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xs.push(a[0] + (v - a[1]) * (b[0] - a[0]) / (b[1] - a[1]));
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}
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}
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}
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xs.sort_by(f64::total_cmp);
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for &u in us {
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if xs.partition_point(|x| *x < u) % 2 == 1 {
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out.push([u, v]);
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}
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}
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}
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out
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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fn area(uv: &[[f64; 2]], tris: &[[u32; 3]]) -> f64 {
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tris.iter()
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.map(|t| {
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let (a, b, c) = (uv[t[0] as usize], uv[t[1] as usize], uv[t[2] as usize]);
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0.5 * ((b[0] - a[0]) * (c[1] - a[1]) - (c[0] - a[0]) * (b[1] - a[1]))
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})
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.sum()
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}
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#[test]
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fn square_with_a_hole_keeps_its_boundary() {
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let mut b = vec![[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]];
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b.extend([[0.4, 0.4], [0.4, 0.6], [0.6, 0.6], [0.6, 0.4]]);
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let loops = [0..4, 4..8];
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let flat = |u: f64, v: f64| Some(Vec3::new(u, v, 0.0));
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for refine in [false, true] {
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let refine = refine.then_some((Sag { eval: &flat, tol: 1e-3, scale: [2.0, 1.0] }, 200));
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let label = refine.is_some();
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let Some((extra, tris)) = triangulate(&b, &loops, Fill { seeds: &[[0.2, 0.2], [0.5, 0.5]], refine }) else { panic!("meshes") };
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let mut uv = b.clone();
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uv.extend(extra);
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assert!((area(&uv, &tris) - 0.96).abs() < 1e-12, "refined: {label}");
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// No added point on the boundary: boundary segments stay whole.
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for r in &loops {
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for k in r.clone() {
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let next = if k + 1 == r.end { r.start } else { k + 1 };
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let (p, q) = (k as u32, next as u32);
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let uses =
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tris.iter().filter(|t| (0..3).any(|e| (t[e] == p && t[(e + 1) % 3] == q) || (t[e] == q && t[(e + 1) % 3] == p))).count();
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assert_eq!(uses, 1, "segment {p}-{q}");
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}
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}
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}
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}
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#[test]
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fn crossing_loops_are_refused() {
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let b = [[0.0, 0.0], [1.0, 1.0], [1.0, 0.0], [0.0, 1.0]];
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let whole = std::slice::from_ref(&(0..4));
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assert!(triangulate(&b, whole, Fill { seeds: &[], refine: None }).is_none());
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}
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}
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@@ -0,0 +1,235 @@
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//! Structured meshing of a four-cornered face whose sides are not parameter lines (a fillet
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//! strip with mitred ends, the wall of a cross hole): a transfinite (Coons) blend of the four
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//! sides gives an interior grid in (u, v), joined to the shared edge nodes by zipped strips.
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//! A blend that folds (a strongly non-convex boundary) is refused, and the face goes to the
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//! constrained Delaunay path.
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use solidcraft_geom::Vec3;
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/// Smallest turn (radians) of the boundary at a corner, in the tolerance metric.
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const CORNER_TURN: f64 = 0.6;
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/// One side: boundary vertex indices from one corner to the next, with each node's position
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/// along the side (0 to 1, by length in 3D).
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struct Side {
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nodes: Vec<u32>,
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at: Vec<f64>,
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}
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/// The four corners of a single boundary loop, by how sharply the loop turns there in (u, v)
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/// scaled by `scale` (one unit per tolerance cell); `None` unless there are exactly four.
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fn corners(uv: &[[f64; 2]], scale: [f64; 2]) -> Option<[usize; 4]> {
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let n = uv.len();
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if n < 4 {
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return None;
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}
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let p = |i: usize| uv.get(i % n).map(|q| [q[0] * scale[0], q[1] * scale[1]]);
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let mut found = Vec::new();
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for i in 0..n {
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let (a, b, c) = (p(i + n - 1)?, p(i)?, p(i + 1)?);
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let (d0, d1) = ([b[0] - a[0], b[1] - a[1]], [c[0] - b[0], c[1] - b[1]]);
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let (l0, l1) = (d0[0].hypot(d0[1]), d1[0].hypot(d1[1]));
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// Two copies of a pole meet with no length between them: that is a corner.
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if l0 == 0.0 || l1 == 0.0 {
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found.push(i);
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continue;
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}
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let turn = (d0[0] * d1[1] - d0[1] * d1[0]).atan2(d0[0] * d1[0] + d0[1] * d1[1]).abs();
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if turn > CORNER_TURN {
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found.push(i);
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}
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}
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let [a, b, c, d] = found[..] else { return None };
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Some([a, b, c, d])
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}
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fn side(fixed: &[Vec3], n: usize, from: usize, to: usize) -> Option<Side> {
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let len = (to + n - from) % n;
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if len == 0 {
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return None;
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}
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let nodes: Vec<u32> = (0..=len).map(|k| ((from + k) % n) as u32).collect();
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let mut at = vec![0.0];
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let mut total = 0.0;
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for w in nodes.windows(2) {
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total += fixed.get(w[0] as usize)?.dist(*fixed.get(w[1] as usize)?);
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at.push(total);
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}
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if !(total > 0.0) {
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// A pole side: evenly along it.
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let m = (nodes.len() - 1).max(1) as f64;
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return Some(Side { at: (0..nodes.len()).map(|k| k as f64 / m).collect(), nodes });
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}
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Some(Side { nodes, at: at.into_iter().map(|x| x / total).collect() })
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}
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/// The point of a side at position `s` (0 to 1), linear between its nodes.
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fn along(side: &Side, uv: &[[f64; 2]], s: f64) -> Option<[f64; 2]> {
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let k = side.at.partition_point(|x| *x < s).clamp(1, side.at.len().saturating_sub(1).max(1));
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let (a0, a1) = (*side.at.get(k - 1)?, *side.at.get(k)?);
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let (p, q) = (uv.get(*side.nodes.get(k - 1)? as usize)?, uv.get(*side.nodes.get(k)? as usize)?);
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let f = if a1 > a0 { ((s - a0) / (a1 - a0)).clamp(0.0, 1.0) } else { 0.0 };
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Some([p[0] + (q[0] - p[0]) * f, p[1] + (q[1] - p[1]) * f])
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}
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/// Interior line positions for a pair of opposite sides: the sides' own when they have the
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/// same nodes (so the grid meets both node for node), else evenly as many as the denser side.
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fn lines(a: &Side, b: &Side) -> Vec<f64> {
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let inner = |s: &Side| s.at.get(1..s.at.len().saturating_sub(1)).map(<[f64]>::to_vec).unwrap_or_default();
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if a.at.len() == b.at.len() {
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let l: Vec<f64> = inner(a).iter().zip(inner(b)).map(|(x, y)| 0.5 * (x + y)).collect();
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if !l.is_empty() {
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return l;
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}
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}
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let n = a.at.len().max(b.at.len()).saturating_sub(1).max(2);
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(1..n).map(|i| i as f64 / n as f64).collect()
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}
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/// Triangulate the loop `uv` (with its fixed 3D nodes) as a Coons patch: boundary vertices
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/// keep their indices, the interior grid follows. Triangles counter-clockwise in (u, v).
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pub(crate) fn coons(uv: &[[f64; 2]], fixed: &[Vec3], scale: [f64; 2], max_points: usize) -> Option<(Vec<[f64; 2]>, Vec<[u32; 3]>)> {
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let n = uv.len();
|
||||
let [c0, c1, c2, c3] = corners(uv, scale)?;
|
||||
// Sides in loop order; the bottom (0) and right (1) run with the loop, the top (2) and
|
||||
// left (3) against it, so s and t both run from corner c0.
|
||||
let bottom = side(fixed, n, c0, c1)?;
|
||||
let right = side(fixed, n, c1, c2)?;
|
||||
let top = reversed(side(fixed, n, c2, c3)?);
|
||||
let left = reversed(side(fixed, n, c3, c0)?);
|
||||
let (ss, ts) = (lines(&bottom, &top), lines(&left, &right));
|
||||
if ss.len().checked_mul(ts.len())? > max_points {
|
||||
return None;
|
||||
}
|
||||
let corner = |i: usize| uv.get(i).copied();
|
||||
let (p00, p10, p11, p01) = (corner(c0)?, corner(c1)?, corner(c2)?, corner(c3)?);
|
||||
let mut out: Vec<[f64; 2]> = uv.to_vec();
|
||||
let base = u32::try_from(n).ok()?;
|
||||
for &t in &ts {
|
||||
for &s in &ss {
|
||||
let (b, tp, l, r) = (along(&bottom, uv, s)?, along(&top, uv, s)?, along(&left, uv, t)?, along(&right, uv, t)?);
|
||||
let blend = |d: usize| {
|
||||
(1.0 - t) * b[d] + t * tp[d] + (1.0 - s) * l[d] + s * r[d]
|
||||
- ((1.0 - s) * (1.0 - t) * p00[d] + s * (1.0 - t) * p10[d] + (1.0 - s) * t * p01[d] + s * t * p11[d])
|
||||
};
|
||||
out.push([blend(0), blend(1)]);
|
||||
}
|
||||
}
|
||||
let (ns, nt) = (ss.len(), ts.len());
|
||||
let g = |i: usize, j: usize| base + (j * ns + i) as u32;
|
||||
let mut tris = Vec::new();
|
||||
for j in 0..nt.saturating_sub(1) {
|
||||
for i in 0..ns.saturating_sub(1) {
|
||||
tris.push([g(i, j), g(i + 1, j), g(i + 1, j + 1)]);
|
||||
tris.push([g(i, j), g(i + 1, j + 1), g(i, j + 1)]);
|
||||
}
|
||||
}
|
||||
// Strips: each side against its grid row or column, by position along the side. In (s, t)
|
||||
// the bottom and right strips come out counter-clockwise, the top and left clockwise.
|
||||
let row = |j: usize| (0..ns).map(|i| g(i, j)).collect::<Vec<u32>>();
|
||||
let col = |i: usize| (0..nt).map(|j| g(i, j)).collect::<Vec<u32>>();
|
||||
zip(&bottom, &row(0), &ss, false, &mut tris)?;
|
||||
zip(&right, &col(ns - 1), &ts, false, &mut tris)?;
|
||||
zip(&top, &row(nt - 1), &ss, true, &mut tris)?;
|
||||
zip(&left, &col(0), &ts, true, &mut tris)?;
|
||||
// The (s, t) square maps to (u, v) keeping or reversing orientation, with the loop: all
|
||||
// triangles must share one sign, which is then made counter-clockwise.
|
||||
let area = |t: &[u32; 3]| -> Option<f64> {
|
||||
let (a, b, c) = (out.get(t[0] as usize)?, out.get(t[1] as usize)?, out.get(t[2] as usize)?);
|
||||
Some((b[0] - a[0]) * (c[1] - a[1]) - (c[0] - a[0]) * (b[1] - a[1]))
|
||||
};
|
||||
let first = area(tris.first()?)?;
|
||||
let sign = if first > 0.0 { 1.0 } else { -1.0 };
|
||||
for t in &tris {
|
||||
if !(area(t)? * sign > 0.0) {
|
||||
return None;
|
||||
}
|
||||
}
|
||||
if sign < 0.0 {
|
||||
for t in &mut tris {
|
||||
t.swap(1, 2);
|
||||
}
|
||||
}
|
||||
let extra = out.split_off(n);
|
||||
Some((extra, tris))
|
||||
}
|
||||
|
||||
fn reversed(s: Side) -> Side {
|
||||
Side { nodes: s.nodes.into_iter().rev().collect(), at: s.at.into_iter().rev().map(|x| 1.0 - x).collect() }
|
||||
}
|
||||
|
||||
/// Join a side (its nodes at positions `side.at`) to a grid row at positions `inner_at`.
|
||||
fn zip(side: &Side, inner: &[u32], inner_at: &[f64], flip: bool, tris: &mut Vec<[u32; 3]>) -> Option<()> {
|
||||
let mut push = |a: u32, b: u32, c: u32| tris.push(if flip { [a, c, b] } else { [a, b, c] });
|
||||
let (outer, oat) = (&side.nodes, &side.at);
|
||||
let (mut a, mut b) = (0usize, 0usize);
|
||||
while a + 1 < outer.len() || b + 1 < inner.len() {
|
||||
let advance_outer = if a + 1 >= outer.len() {
|
||||
false
|
||||
} else if b + 1 >= inner.len() {
|
||||
true
|
||||
} else {
|
||||
oat.get(a + 1)? <= inner_at.get(b + 1)?
|
||||
};
|
||||
if advance_outer {
|
||||
push(*outer.get(a)?, *outer.get(a + 1)?, *inner.get(b)?);
|
||||
a += 1;
|
||||
} else {
|
||||
push(*outer.get(a)?, *inner.get(b + 1)?, *inner.get(b)?);
|
||||
b += 1;
|
||||
}
|
||||
}
|
||||
Some(())
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
|
||||
fn area(uv: &[[f64; 2]], tris: &[[u32; 3]]) -> f64 {
|
||||
tris.iter()
|
||||
.map(|t| {
|
||||
let (a, b, c) = (uv[t[0] as usize], uv[t[1] as usize], uv[t[2] as usize]);
|
||||
0.5 * ((b[0] - a[0]) * (c[1] - a[1]) - (c[0] - a[0]) * (b[1] - a[1]))
|
||||
})
|
||||
.sum()
|
||||
}
|
||||
|
||||
/// A trapezoid (a strip with mitred ends), counter-clockwise, `k` nodes per side.
|
||||
fn trapezoid(k: usize) -> Vec<[f64; 2]> {
|
||||
let corners = [[0.0, 0.0], [10.0, 0.0], [8.0, 2.0], [2.0, 2.0]];
|
||||
let mut b = Vec::new();
|
||||
for w in 0..4 {
|
||||
let (p, q) = (corners[w], corners[(w + 1) % 4]);
|
||||
for i in 0..k {
|
||||
let f = i as f64 / k as f64;
|
||||
b.push([p[0] + (q[0] - p[0]) * f, p[1] + (q[1] - p[1]) * f]);
|
||||
}
|
||||
}
|
||||
b
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn trapezoid_is_tiled_exactly() {
|
||||
for k in [2, 5] {
|
||||
for reverse in [false, true] {
|
||||
let mut b = trapezoid(k);
|
||||
if reverse {
|
||||
b.reverse();
|
||||
}
|
||||
let fixed: Vec<Vec3> = b.iter().map(|p| Vec3::new(p[0], p[1], 0.0)).collect();
|
||||
let Some((extra, tris)) = coons(&b, &fixed, [1.0, 1.0], 10_000) else { panic!("meshes (k {k})") };
|
||||
let mut uv = b.clone();
|
||||
uv.extend(extra);
|
||||
assert!((area(&uv, &tris) - 16.0).abs() < 1e-9, "k {k} reverse {reverse}: {}", area(&uv, &tris));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn five_corners_is_not_a_coons_patch() {
|
||||
let b = [[0.0, 0.0], [1.0, 0.0], [1.0, 0.5], [0.5, 1.0], [0.0, 1.0]];
|
||||
let fixed: Vec<Vec3> = b.iter().map(|p| Vec3::new(p[0], p[1], 0.0)).collect();
|
||||
assert!(coons(&b, &fixed, [1.0, 1.0], 100).is_none());
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,97 @@
|
||||
//! Edge nodes: every edge of a body sampled once, so the faces on either side share the very
|
||||
//! same boundary points (watertight by construction).
|
||||
|
||||
use solidcraft_geom::Vec3;
|
||||
use truck_meshalgo::prelude::*;
|
||||
use truck_modeling as mt;
|
||||
|
||||
use crate::body::from_p3;
|
||||
|
||||
/// Most nodes on one edge.
|
||||
pub(crate) const MAX_EDGE_NODES: usize = 20_000;
|
||||
/// Deepest bisection of one edge segment.
|
||||
const MAX_DEPTH: u32 = 24;
|
||||
|
||||
/// Nodes of `edge` from its absolute front to its absolute back, every chord within `tol` of
|
||||
/// the curve (checked at the quarter points, so an S-bend in one segment is not missed). The
|
||||
/// end nodes are the vertices' own points, so edges meeting at a vertex meet exactly.
|
||||
pub(crate) fn sample_edge(edge: &mt::Edge, tol: f64) -> Vec<Vec3> {
|
||||
let front = from_p3(edge.absolute_front().point());
|
||||
let back = from_p3(edge.absolute_back().point());
|
||||
let curve = edge.curve();
|
||||
if matches!(curve, mt::Curve::Line(_)) {
|
||||
return vec![front, back];
|
||||
}
|
||||
let (t0, t1) = curve.range_tuple();
|
||||
if !(t0.is_finite() && t1.is_finite() && t1 > t0) {
|
||||
return vec![front, back];
|
||||
}
|
||||
// Our evaluator where the curve has a form it knows (no allocation per point); truck's
|
||||
// for intersection curves.
|
||||
let fast = super::surface::eval_curve(&curve);
|
||||
let at = |t: f64| {
|
||||
match &fast {
|
||||
Some(c) => c.eval(t).map(|(p, _)| p),
|
||||
None => Some(from_p3(curve.subs(t))),
|
||||
}
|
||||
.filter(|p| p.is_finite())
|
||||
};
|
||||
// A closed curve's chord between its ends is empty: start from a few segments.
|
||||
let initial: u32 = 4;
|
||||
let t_at = |i: u32| t0 + (t1 - t0) * f64::from(i) / f64::from(initial);
|
||||
let mut out_t = vec![t0];
|
||||
// Depth-first bisection, segment by segment, keeping the output ordered.
|
||||
let mut stack: Vec<(f64, f64, u32)> = (0..initial).rev().map(|i| (t_at(i), t_at(i + 1), 0)).collect();
|
||||
while let Some((a, b, depth)) = stack.pop() {
|
||||
let flat = depth >= MAX_DEPTH || out_t.len() + stack.len() >= MAX_EDGE_NODES || {
|
||||
let (Some(pa), Some(pb)) = (at(a), at(b)) else { return vec![front, back] };
|
||||
[0.25, 0.5, 0.75].iter().all(|f| at(a + (b - a) * f).is_none_or(|q| q.dist_to_segment(pa, pb) <= tol))
|
||||
};
|
||||
if flat {
|
||||
out_t.push(b);
|
||||
} else {
|
||||
let m = 0.5 * (a + b);
|
||||
stack.push((m, b, depth + 1));
|
||||
stack.push((a, m, depth + 1));
|
||||
}
|
||||
}
|
||||
let mut pts: Vec<Vec3> = out_t.iter().filter_map(|&t| at(t)).collect();
|
||||
if pts.len() < 2 {
|
||||
return vec![front, back];
|
||||
}
|
||||
if let Some(p) = pts.first_mut() {
|
||||
*p = front;
|
||||
}
|
||||
if let Some(p) = pts.last_mut() {
|
||||
*p = back;
|
||||
}
|
||||
pts
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
|
||||
#[test]
|
||||
fn circle_edges_are_within_tolerance_and_end_on_vertices() {
|
||||
let Ok(cyl) = crate::cylinder(Vec3::ZERO, Vec3::Z, 10.0, 5.0) else { panic!("cylinder") };
|
||||
for tol in [0.1, 0.01, 0.001] {
|
||||
for e in cyl.solid.edge_iter() {
|
||||
let pts = sample_edge(&e, tol);
|
||||
assert!(pts.len() >= 2);
|
||||
assert_eq!(pts.first().copied(), Some(from_p3(e.absolute_front().point())));
|
||||
assert_eq!(pts.last().copied(), Some(from_p3(e.absolute_back().point())));
|
||||
if matches!(e.curve(), mt::Curve::Line(_)) {
|
||||
assert_eq!(pts.len(), 2);
|
||||
continue;
|
||||
}
|
||||
// Circle of radius 10: every chord's middle sags at most `tol` (plus rounding).
|
||||
for w in pts.windows(2) {
|
||||
let m = (w[0] + w[1]) * 0.5;
|
||||
let r = (m.x * m.x + m.y * m.y).sqrt();
|
||||
assert!(10.0 - r <= tol * 1.0001, "sag {} at tol {tol}", 10.0 - r);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,322 @@
|
||||
//! Structured meshing of a face whose boundary runs along its parameter box: a grid of
|
||||
//! interior lines (spaced by the surface's own curvature), joined to the shared edge nodes on
|
||||
//! each side by a zipped strip (after Cadium's structured and zipped grids: the larger side
|
||||
//! fans into the smaller one, so the edge nodes are used exactly as they are).
|
||||
|
||||
/// Most grid points of one face.
|
||||
pub(crate) const MAX_FACE_GRID: usize = 150_000;
|
||||
|
||||
/// The four sides of a parameter box, in counter-clockwise order.
|
||||
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
|
||||
enum Side {
|
||||
VMin,
|
||||
UMax,
|
||||
VMax,
|
||||
UMin,
|
||||
}
|
||||
|
||||
const SIDES: [Side; 4] = [Side::VMin, Side::UMax, Side::VMax, Side::UMin];
|
||||
|
||||
impl Side {
|
||||
/// Bit in a node's side mask.
|
||||
fn bit(self) -> u8 {
|
||||
match self {
|
||||
Side::VMin => 1,
|
||||
Side::UMax => 2,
|
||||
Side::VMax => 4,
|
||||
Side::UMin => 8,
|
||||
}
|
||||
}
|
||||
/// The parameter that runs along this side.
|
||||
fn along(self) -> usize {
|
||||
match self {
|
||||
Side::VMin | Side::VMax => 0,
|
||||
Side::UMax | Side::UMin => 1,
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/// A face's boundary split into its four sides: for each side (in [`SIDES`] order) the
|
||||
/// boundary vertex indices along it, ordered by increasing `along` parameter, corners included.
|
||||
pub(crate) struct Quad {
|
||||
sides: [Vec<u32>; 4],
|
||||
bbox: [(f64, f64); 2],
|
||||
}
|
||||
|
||||
/// The boundary as four sides on its parameter box, when it is one: every node on the box,
|
||||
/// exactly four corner nodes, and the chains between consecutive corners each on one side.
|
||||
pub(crate) fn quad(boundary: &[[f64; 2]]) -> Option<Quad> {
|
||||
let n = boundary.len();
|
||||
if n < 4 {
|
||||
return None;
|
||||
}
|
||||
let mut bbox = [(f64::MAX, f64::MIN); 2];
|
||||
for p in boundary {
|
||||
for d in 0..2 {
|
||||
bbox[d] = (bbox[d].0.min(p[d]), bbox[d].1.max(p[d]));
|
||||
}
|
||||
}
|
||||
let ext = [bbox[0].1 - bbox[0].0, bbox[1].1 - bbox[1].0];
|
||||
if !(ext[0] > 0.0 && ext[1] > 0.0) || !(ext[0].is_finite() && ext[1].is_finite()) {
|
||||
return None;
|
||||
}
|
||||
let eps = [ext[0] * 1e-7, ext[1] * 1e-7];
|
||||
let mask = |p: &[f64; 2]| {
|
||||
let mut m = 0u8;
|
||||
if (p[1] - bbox[1].0).abs() <= eps[1] {
|
||||
m |= Side::VMin.bit();
|
||||
}
|
||||
if (p[0] - bbox[0].1).abs() <= eps[0] {
|
||||
m |= Side::UMax.bit();
|
||||
}
|
||||
if (p[1] - bbox[1].1).abs() <= eps[1] {
|
||||
m |= Side::VMax.bit();
|
||||
}
|
||||
if (p[0] - bbox[0].0).abs() <= eps[0] {
|
||||
m |= Side::UMin.bit();
|
||||
}
|
||||
m
|
||||
};
|
||||
let masks: Vec<u8> = boundary.iter().map(mask).collect();
|
||||
if masks.contains(&0) {
|
||||
return None;
|
||||
}
|
||||
let corners: Vec<usize> = (0..n).filter(|&i| masks.get(i).is_some_and(|m| m.count_ones() == 2)).collect();
|
||||
if corners.len() != 4 {
|
||||
return None;
|
||||
}
|
||||
let mut sides: [Vec<u32>; 4] = Default::default();
|
||||
let mut seen = 0u8;
|
||||
for (k, &c0) in corners.iter().enumerate() {
|
||||
let c1 = *corners.get((k + 1) % 4)?;
|
||||
let len = (c1 + n - c0) % n;
|
||||
let chain: Vec<usize> = (0..=len).map(|i| (c0 + i) % n).collect();
|
||||
let common = chain.iter().fold(0xFu8, |m, &i| m & masks.get(i).copied().unwrap_or(0));
|
||||
let side = SIDES.into_iter().find(|s| common & s.bit() != 0)?;
|
||||
if seen & side.bit() != 0 {
|
||||
return None;
|
||||
}
|
||||
seen |= side.bit();
|
||||
let d = side.along();
|
||||
let mut chain: Vec<u32> = chain.into_iter().map(|i| i as u32).collect();
|
||||
let coord = |i: &u32| boundary.get(*i as usize).map_or(0.0, |p| p[d]);
|
||||
if chain.first().map(coord) > chain.last().map(coord) {
|
||||
chain.reverse();
|
||||
}
|
||||
// The edge nodes must advance along the side.
|
||||
if chain.windows(2).any(|w| coord(&w[0]) >= coord(&w[1])) && chain.len() > 2 {
|
||||
return None;
|
||||
}
|
||||
let slot = SIDES.iter().position(|s| *s == side)?;
|
||||
*sides.get_mut(slot)? = chain;
|
||||
}
|
||||
Some(Quad { sides, bbox })
|
||||
}
|
||||
|
||||
/// Lines along direction `d` taken from the boundary, when the two sides running along `d`
|
||||
/// carry the same parameters (as opposite iso-lines of one surface sampled alike do): the grid
|
||||
/// then meets both sides node for node. Interior values only.
|
||||
pub(crate) fn aligned_lines(boundary: &[[f64; 2]], q: &Quad, d: usize) -> Option<Vec<f64>> {
|
||||
let (a, b) = if d == 0 { (q.sides.first()?, q.sides.get(2)?) } else { (q.sides.get(1)?, q.sides.get(3)?) };
|
||||
if a.len() != b.len() || a.len() < 3 {
|
||||
return None;
|
||||
}
|
||||
let (lo, hi) = q.bbox.get(d).copied()?;
|
||||
let eps = (hi - lo) * 1e-9;
|
||||
let mut lines = Vec::with_capacity(a.len());
|
||||
for (i, j) in a.iter().zip(b) {
|
||||
let (x, y) = (boundary.get(*i as usize)?[d], boundary.get(*j as usize)?[d]);
|
||||
if (x - y).abs() > eps {
|
||||
return None;
|
||||
}
|
||||
if x > lo + eps && x < hi - eps {
|
||||
lines.push(x);
|
||||
}
|
||||
}
|
||||
Some(lines)
|
||||
}
|
||||
|
||||
/// A face straight across direction `1 − d` (no interior lines there, as a cylinder wall along
|
||||
/// its axis): the two sides running along `d` zipped straight to each other, when the other two
|
||||
/// sides are single segments. Triangles counter-clockwise, or `None`.
|
||||
pub(crate) fn strip(boundary: &[[f64; 2]], q: &Quad, d: usize) -> Option<Vec<[u32; 3]>> {
|
||||
// Sides along u are VMin (low) and VMax (high); along v, UMax (high) and UMin (low).
|
||||
let (low, high, cross) = if d == 0 { (0, 2, [1, 3]) } else { (3, 1, [0, 2]) };
|
||||
if cross.iter().any(|&k| q.sides.get(k).is_none_or(|c| c.len() != 2)) {
|
||||
return None;
|
||||
}
|
||||
let mut tris = Vec::new();
|
||||
zip(boundary, q.sides.get(low)?, q.sides.get(high)?, d, d == 1, &mut tris)?;
|
||||
for t in &tris {
|
||||
if !(signed_area(boundary, *t)? > 0.0) {
|
||||
return None;
|
||||
}
|
||||
}
|
||||
Some(tris)
|
||||
}
|
||||
|
||||
/// The interior lines of a structured face: `us`, `vs` strictly inside the box. Each
|
||||
/// direction gets at least one line so every side has an inner chain to zip to.
|
||||
pub(crate) fn interior(lines: Vec<f64>, (a, b): (f64, f64)) -> Vec<f64> {
|
||||
let inner: Vec<f64> = lines.into_iter().filter(|x| *x > a && *x < b).collect();
|
||||
if inner.is_empty() { vec![0.5 * (a + b)] } else { inner }
|
||||
}
|
||||
|
||||
/// Triangulate a [`Quad`] face: boundary vertices are `0..boundary.len()`; the interior grid
|
||||
/// (`us` × `vs`, strictly inside the box) follows, row by row. Returns the interior
|
||||
/// parameters and the triangles (counter-clockwise in (u, v)), or `None` if a strip would
|
||||
/// fold over.
|
||||
pub(crate) fn structured(boundary: &[[f64; 2]], q: &Quad, us: &[f64], vs: &[f64]) -> Option<(Vec<[f64; 2]>, Vec<[u32; 3]>)> {
|
||||
let (nu, nv) = (us.len(), vs.len());
|
||||
if nu == 0 || nv == 0 || nu.checked_mul(nv)? > MAX_FACE_GRID {
|
||||
return None;
|
||||
}
|
||||
let n = u32::try_from(boundary.len()).ok()?;
|
||||
let g = |i: usize, j: usize| n + (j * nu + i) as u32;
|
||||
let mut uv: Vec<[f64; 2]> = boundary.to_vec();
|
||||
for &v in vs {
|
||||
for &u in us {
|
||||
uv.push([u, v]);
|
||||
}
|
||||
}
|
||||
let mut tris: Vec<[u32; 3]> = Vec::with_capacity(2 * (nu + 1) * (nv + 1) + 2 * boundary.len());
|
||||
for j in 0..nv.saturating_sub(1) {
|
||||
for i in 0..nu.saturating_sub(1) {
|
||||
let (a, b, c, d) = (g(i, j), g(i + 1, j), g(i + 1, j + 1), g(i, j + 1));
|
||||
tris.push([a, b, c]);
|
||||
tris.push([a, c, d]);
|
||||
}
|
||||
}
|
||||
for (slot, side) in SIDES.iter().enumerate() {
|
||||
let outer = q.sides.get(slot)?;
|
||||
let inner: Vec<u32> = match side {
|
||||
Side::VMin => (0..nu).map(|i| g(i, 0)).collect(),
|
||||
Side::VMax => (0..nu).map(|i| g(i, nv - 1)).collect(),
|
||||
Side::UMin => (0..nv).map(|j| g(0, j)).collect(),
|
||||
Side::UMax => (0..nv).map(|j| g(nu - 1, j)).collect(),
|
||||
};
|
||||
// The strip lies inside the box from its side: below the top and left of the right
|
||||
// side its triangles come out clockwise.
|
||||
let flip = matches!(side, Side::VMax | Side::UMin);
|
||||
zip(&uv, outer, &inner, side.along(), flip, &mut tris)?;
|
||||
}
|
||||
// Every triangle counter-clockwise: one that is not has folded over.
|
||||
for t in &tris {
|
||||
if !(signed_area(&uv, *t)? > 0.0) {
|
||||
return None;
|
||||
}
|
||||
}
|
||||
let extra = uv.split_off(boundary.len());
|
||||
Some((extra, tris))
|
||||
}
|
||||
|
||||
fn signed_area(uv: &[[f64; 2]], t: [u32; 3]) -> Option<f64> {
|
||||
let (a, b, c) = (uv.get(t[0] as usize)?, uv.get(t[1] as usize)?, uv.get(t[2] as usize)?);
|
||||
Some((b[0] - a[0]) * (c[1] - a[1]) - (c[0] - a[0]) * (b[1] - a[1]))
|
||||
}
|
||||
|
||||
/// Join a side's outer chain (edge nodes) to the inner chain (grid line), both ordered along
|
||||
/// direction `d`: advance whichever chain's next node comes first along the side, so nodes at
|
||||
/// the same parameter on both chains are joined straight across.
|
||||
fn zip(uv: &[[f64; 2]], outer: &[u32], inner: &[u32], d: usize, flip: bool, tris: &mut Vec<[u32; 3]>) -> Option<()> {
|
||||
let mut push = |a: u32, b: u32, c: u32| tris.push(if flip { [a, c, b] } else { [a, b, c] });
|
||||
let coord = |chain: &[u32], k: usize| chain.get(k).and_then(|i| uv.get(*i as usize)).map(|p| p[d]);
|
||||
let (mut a, mut b) = (0usize, 0usize);
|
||||
while a + 1 < outer.len() || b + 1 < inner.len() {
|
||||
let advance_outer = if a + 1 >= outer.len() {
|
||||
false
|
||||
} else if b + 1 >= inner.len() {
|
||||
true
|
||||
} else {
|
||||
coord(outer, a + 1)? <= coord(inner, b + 1)?
|
||||
};
|
||||
if advance_outer {
|
||||
push(*outer.get(a)?, *outer.get(a + 1)?, *inner.get(b)?);
|
||||
a += 1;
|
||||
} else {
|
||||
push(*outer.get(a)?, *inner.get(b + 1)?, *inner.get(b)?);
|
||||
b += 1;
|
||||
}
|
||||
}
|
||||
Some(())
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
|
||||
/// A unit square boundary with `k` nodes per side, counter-clockwise from (0, 0).
|
||||
fn square(k: usize) -> Vec<[f64; 2]> {
|
||||
let mut b = Vec::new();
|
||||
for i in 0..k {
|
||||
b.push([i as f64 / k as f64, 0.0]);
|
||||
}
|
||||
for i in 0..k {
|
||||
b.push([1.0, i as f64 / k as f64]);
|
||||
}
|
||||
for i in 0..k {
|
||||
b.push([1.0 - i as f64 / k as f64, 1.0]);
|
||||
}
|
||||
for i in 0..k {
|
||||
b.push([0.0, 1.0 - i as f64 / k as f64]);
|
||||
}
|
||||
b
|
||||
}
|
||||
|
||||
fn area(uv: &[[f64; 2]], tris: &[[u32; 3]]) -> f64 {
|
||||
tris.iter().map(|t| signed_area(uv, *t).unwrap_or(f64::NAN) * 0.5).sum()
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn grid_and_strips_tile_the_box_exactly() {
|
||||
for (k, us, vs) in [(1, vec![0.5], vec![0.5]), (5, vec![0.3, 0.6], vec![0.2, 0.4, 0.8]), (13, vec![0.5], vec![0.1, 0.9])] {
|
||||
let b = square(k);
|
||||
let Some(q) = quad(&b) else { panic!("a quad") };
|
||||
let Some((extra, tris)) = structured(&b, &q, &us, &vs) else { panic!("meshes") };
|
||||
let mut uv = b.clone();
|
||||
uv.extend(extra);
|
||||
assert!((area(&uv, &tris) - 1.0).abs() < 1e-12, "k = {k}");
|
||||
assert!(tris.iter().all(|t| signed_area(&uv, *t).is_some_and(|a| a > 0.0)));
|
||||
// Every boundary segment is used by exactly one triangle (no node skipped).
|
||||
let n = b.len() as u32;
|
||||
for i in 0..n {
|
||||
let (p, q) = (i, (i + 1) % n);
|
||||
let uses = tris.iter().filter(|t| (0..3).any(|e| (t[e] == p && t[(e + 1) % 3] == q) || (t[e] == q && t[(e + 1) % 3] == p))).count();
|
||||
assert_eq!(uses, 1, "boundary segment {p}-{q}");
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn a_pole_side_is_a_two_node_chain() {
|
||||
// A triangle-like patch whose top side is a pole (two copies of one point in 3D).
|
||||
let b = vec![[0.0, 0.0], [0.5, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]];
|
||||
let Some(q) = quad(&b) else { panic!("a quad") };
|
||||
let Some((_, tris)) = structured(&b, &q, &[0.5], &[0.5]) else { panic!("meshes") };
|
||||
assert!(!tris.is_empty());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn straight_faces_are_one_strip() {
|
||||
// Five nodes along the bottom, three along the top, single-segment ends.
|
||||
let b = vec![[0.0, 0.0], [0.25, 0.0], [0.5, 0.0], [0.75, 0.0], [1.0, 0.0], [1.0, 1.0], [0.5, 1.0], [0.0, 1.0]];
|
||||
let Some(q) = quad(&b) else { panic!("a quad") };
|
||||
let Some(tris) = strip(&b, &q, 0) else { panic!("a strip") };
|
||||
assert_eq!(tris.len(), 6);
|
||||
assert!((area(&b, &tris) - 1.0).abs() < 1e-12);
|
||||
// Transposed: the long sides run along v.
|
||||
let t: Vec<[f64; 2]> = b.iter().map(|p| [p[1], p[0]]).rev().collect();
|
||||
let Some(q) = quad(&t) else { panic!("a quad") };
|
||||
let Some(tris) = strip(&t, &q, 1) else { panic!("a strip") };
|
||||
assert!((area(&t, &tris) - 1.0).abs() < 1e-12);
|
||||
assert!(strip(&b, &q, 0).is_none() || strip(&t, &q, 0).is_none());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn not_a_quad() {
|
||||
// A hole-like loop inside the box, and a five-cornered loop.
|
||||
assert!(quad(&[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0]]).is_none());
|
||||
let pentagon = [[0.0, 0.0], [1.0, 0.0], [1.0, 0.5], [0.5, 1.0], [0.0, 1.0]];
|
||||
assert!(quad(&pentagon).is_none());
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,307 @@
|
||||
//! Display tessellation: each face's triangulation in its own parameters, with every edge
|
||||
//! sampled once so neighbouring faces share their boundary points exactly, handed over as a
|
||||
//! [`TessPlan`] for the CPU or GPU evaluator.
|
||||
//!
|
||||
//! Per face, cheapest first:
|
||||
//! - planar faces: a constrained Delaunay triangulation of the edge nodes alone (a plane needs
|
||||
//! no interior points);
|
||||
//! - faces whose boundary runs along their parameter box (cylinder halves, sphere and torus
|
||||
//! patches, fillets): a structured grid zipped to the edge nodes;
|
||||
//! - four-cornered faces whose sides are not parameter lines (mitred fillet strips, cross
|
||||
//! hole walls): a Coons blend of the four sides, zipped the same way;
|
||||
//! - anything else (trimmed faces, holes): constrained Delaunay with interior seeds and
|
||||
//! Ruppert refinement.
|
||||
//!
|
||||
//! A face the planner cannot handle (its surface has no evaluable form, a boundary that does
|
||||
//! not project or crosses itself) fails the whole plan, and the caller meshes the body the
|
||||
//! old way.
|
||||
|
||||
pub(crate) mod cdt;
|
||||
pub(crate) mod coons;
|
||||
pub(crate) mod edges;
|
||||
pub(crate) mod grid;
|
||||
pub(crate) mod surface;
|
||||
pub(crate) mod uv;
|
||||
|
||||
use std::collections::HashMap;
|
||||
|
||||
use solidcraft_geom::Vec3;
|
||||
use solidcraft_geom::tess::{EvalSurface, FacePlan, TessPlan};
|
||||
use truck_modeling as mt;
|
||||
|
||||
use crate::body::{Solid, edge_order};
|
||||
use crate::{KernelError, Result};
|
||||
|
||||
/// How the faces of a plan were meshed.
|
||||
#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
|
||||
pub struct PlanStats {
|
||||
pub planar: usize,
|
||||
pub structured: usize,
|
||||
pub delaunay: usize,
|
||||
}
|
||||
|
||||
/// Most lines a curved face's grid gets in one direction.
|
||||
const MAX_LINES: usize = 1024;
|
||||
/// Most points Ruppert refinement may add to one face, beyond its seeds.
|
||||
const MAX_REFINE: usize = 20_000;
|
||||
|
||||
fn unsupported(what: impl std::fmt::Display) -> KernelError {
|
||||
KernelError::Failed(format!("not supported yet: tessellation: {what}"))
|
||||
}
|
||||
|
||||
/// Plan the display tessellation of `solid` with chord tolerance `tol`.
|
||||
pub(crate) fn plan(solid: &Solid, tol: f64) -> Result<(TessPlan, PlanStats)> {
|
||||
let faces: Vec<&mt::Face> = solid.face_iter().collect();
|
||||
let (edges, edge_faces) = edge_order(faces.iter().copied());
|
||||
// Every edge once, in parallel; faces then read their nodes.
|
||||
let sampled = crate::par::map("edge nodes", &edges, 64, |e| Ok(edges::sample_edge(e, tol)));
|
||||
let mut nodes: HashMap<_, Vec<Vec3>> = HashMap::with_capacity(edges.len());
|
||||
for (e, pts) in edges.iter().zip(sampled) {
|
||||
nodes.insert(e.id(), pts?);
|
||||
}
|
||||
let oriented = |e: &mt::Edge| -> Option<Vec<Vec3>> {
|
||||
let mut pts = nodes.get(&e.id())?.clone();
|
||||
if !e.orientation() {
|
||||
pts.reverse();
|
||||
}
|
||||
Some(pts)
|
||||
};
|
||||
let indexed: Vec<(usize, &mt::Face)> = faces.iter().copied().enumerate().collect();
|
||||
let planned = crate::par::map("face tessellation", &indexed, 8, |(fi, face)| {
|
||||
let fi = *fi;
|
||||
let surface = face.surface();
|
||||
let eval = surface::eval_surface(&surface).ok_or_else(|| unsupported(format!("face {fi}: surface not evaluable")))?;
|
||||
// Boundary nodes, loop by loop (each edge's last node is the next edge's first).
|
||||
let mut loops3: Vec<Vec<Vec3>> = Vec::new();
|
||||
for wire in face.absolute_boundaries() {
|
||||
let mut pts = Vec::new();
|
||||
for e in wire.edge_iter() {
|
||||
let mut ep = oriented(e).ok_or_else(|| unsupported("edge without nodes"))?;
|
||||
ep.pop();
|
||||
pts.extend(ep);
|
||||
}
|
||||
if pts.len() >= 2 {
|
||||
loops3.push(pts);
|
||||
}
|
||||
}
|
||||
let mut stats = PlanStats::default();
|
||||
let fp = plan_face(fi, &eval, &loops3, tol, &mut stats)?;
|
||||
let fp = FacePlan {
|
||||
flip: !face.orientation(),
|
||||
triangles: if face.orientation() { fp.triangles } else { fp.triangles.into_iter().map(|[a, b, c]| [a, c, b]).collect() },
|
||||
..fp
|
||||
};
|
||||
Ok((fp, eval, stats))
|
||||
});
|
||||
let mut plan = TessPlan::default();
|
||||
let mut stats = PlanStats::default();
|
||||
for r in planned {
|
||||
let (fp, eval, s) = r?;
|
||||
let surface = u32::try_from(plan.surfaces.len()).map_err(|_| unsupported("too many faces"))?;
|
||||
plan.surfaces.push(eval);
|
||||
plan.faces.push(FacePlan { surface: Some(surface), ..fp });
|
||||
stats.planar += s.planar;
|
||||
stats.structured += s.structured;
|
||||
stats.delaunay += s.delaunay;
|
||||
}
|
||||
plan.edges = edges.iter().filter_map(oriented).collect();
|
||||
plan.edge_faces = edge_faces.into_iter().map(|fs| fs.into_iter().map(|f| u32::try_from(f).unwrap_or(u32::MAX)).collect()).collect();
|
||||
Ok((plan, stats))
|
||||
}
|
||||
|
||||
/// One face: boundary loops in 3D (shared edge nodes) to parameters and triangles.
|
||||
fn plan_face(fi: usize, s: &EvalSurface, loops3: &[Vec<Vec3>], tol: f64, stats: &mut PlanStats) -> Result<FacePlan> {
|
||||
let dom = uv::domain(s);
|
||||
let accept = (tol * 10.0).max(1e-6);
|
||||
let fail = |why: &str| unsupported(format!("face {fi}: {why}"));
|
||||
// Project every loop, unwrapping periodic parameters along it and splitting poles.
|
||||
let mut fixed: Vec<Vec3> = Vec::new();
|
||||
let mut uvs: Vec<[f64; 2]> = Vec::new();
|
||||
let mut ranges: Vec<std::ops::Range<usize>> = Vec::new();
|
||||
for pts in loops3 {
|
||||
let mut luv: Vec<[f64; 2]> = Vec::with_capacity(pts.len());
|
||||
let mut prev: Option<[f64; 2]> = None;
|
||||
for p in pts {
|
||||
let mut q = uv::project(s, &dom, *p, prev, accept).ok_or_else(|| fail("boundary does not lie on the surface"))?;
|
||||
if let Some(pr) = prev {
|
||||
for d in 0..2 {
|
||||
q[d] = uv::unwrap(q[d], pr[d], dom.period[d]);
|
||||
}
|
||||
}
|
||||
luv.push(q);
|
||||
prev = Some(q);
|
||||
}
|
||||
// A loop that winds once around a periodic direction does not close in (u, v).
|
||||
if let (Some(first), Some(last)) = (luv.first(), luv.last()) {
|
||||
for d in 0..2 {
|
||||
if let Some(per) = dom.period[d]
|
||||
&& (uv::unwrap(first[d], last[d], Some(per)) - first[d]).abs() > per * 0.25
|
||||
{
|
||||
return Err(fail("boundary winds around the surface"));
|
||||
}
|
||||
}
|
||||
}
|
||||
let start = uvs.len();
|
||||
let n = luv.len();
|
||||
for (k, (q, p)) in luv.iter().zip(pts).enumerate() {
|
||||
// At a pole the parameter along the degenerate direction is free: one copy with
|
||||
// the previous node's value, one with the next node's.
|
||||
let (prev, next) = (luv.get((k + n - 1) % n).copied(), luv.get((k + 1) % n).copied());
|
||||
let pole = (0..2).find(|&d| uv::degenerate(s, *q, d));
|
||||
match (pole, prev, next) {
|
||||
(Some(d), Some(a), Some(b)) => {
|
||||
let mut qa = *q;
|
||||
let mut qb = *q;
|
||||
qa[d] = a[d];
|
||||
qb[d] = b[d];
|
||||
uvs.push(qa);
|
||||
fixed.push(*p);
|
||||
if (qa[d] - qb[d]).abs() > 1e-12 {
|
||||
uvs.push(qb);
|
||||
fixed.push(*p);
|
||||
}
|
||||
}
|
||||
_ => {
|
||||
uvs.push(*q);
|
||||
fixed.push(*p);
|
||||
}
|
||||
}
|
||||
}
|
||||
ranges.push(start..uvs.len());
|
||||
}
|
||||
if uvs.len() < 3 {
|
||||
return Err(fail("degenerate boundary"));
|
||||
}
|
||||
let planar = matches!(s, EvalSurface::Plane { .. });
|
||||
let (extra, triangles) = if planar {
|
||||
stats.planar += 1;
|
||||
cdt::triangulate(&uvs, &ranges, cdt::Fill { seeds: &[], refine: None }).ok_or_else(|| fail("boundary crosses itself"))?
|
||||
} else {
|
||||
let mut bbox = [(f64::MAX, f64::MIN); 2];
|
||||
for p in &uvs {
|
||||
for d in 0..2 {
|
||||
bbox[d] = (bbox[d].0.min(p[d]), bbox[d].1.max(p[d]));
|
||||
}
|
||||
}
|
||||
let mut us = uv::divide(s, 0, bbox[0], bbox[1], tol, MAX_LINES);
|
||||
let mut vs = uv::divide(s, 1, bbox[1], bbox[0], tol, MAX_LINES);
|
||||
thin(&mut us, &mut vs, grid::MAX_FACE_GRID);
|
||||
let structured = match (ranges.len(), grid::quad(&uvs)) {
|
||||
(1, Some(q)) => {
|
||||
// Interior lines: the boundary's own where opposite sides agree, else the
|
||||
// tolerance division.
|
||||
let lines = |d: usize, div: &Vec<f64>| {
|
||||
grid::aligned_lines(&uvs, &q, d).unwrap_or_else(|| div.iter().copied().filter(|x| *x > bbox[d].0 && *x < bbox[d].1).collect())
|
||||
};
|
||||
let (lu, lv) = (lines(0, &us), lines(1, &vs));
|
||||
let strip = match (lu.is_empty(), lv.is_empty()) {
|
||||
(false, true) => grid::strip(&uvs, &q, 0),
|
||||
(true, false) => grid::strip(&uvs, &q, 1),
|
||||
_ => None,
|
||||
};
|
||||
strip.map(|t| (Vec::new(), t)).or_else(|| grid::structured(&uvs, &q, &grid::interior(lu, bbox[0]), &grid::interior(lv, bbox[1])))
|
||||
}
|
||||
_ => None,
|
||||
};
|
||||
let cells = |lines: &Vec<f64>, (a, b): (f64, f64)| (lines.len().saturating_sub(1).max(1) as f64) / (b - a).max(f64::MIN_POSITIVE);
|
||||
let scale = [cells(&us, bbox[0]), cells(&vs, bbox[1])];
|
||||
let structured = match structured {
|
||||
None if ranges.len() == 1 => coons::coons(&uvs, &fixed, scale, grid::MAX_FACE_GRID),
|
||||
other => other,
|
||||
};
|
||||
match structured {
|
||||
Some(r) => {
|
||||
stats.structured += 1;
|
||||
r
|
||||
}
|
||||
None => {
|
||||
stats.delaunay += 1;
|
||||
let polys: Vec<&[[f64; 2]]> = ranges.iter().filter_map(|r| uvs.get(r.clone())).collect();
|
||||
let inner = |lines: &Vec<f64>, (a, b): (f64, f64)| lines.iter().copied().filter(|x| *x > a && *x < b).collect::<Vec<f64>>();
|
||||
let seeds = cdt::inside_grid(&inner(&us, bbox[0]), &inner(&vs, bbox[1]), &polys);
|
||||
let eval = |u: f64, v: f64| s.derivs(u, v).map(|(p, _, _)| p);
|
||||
// One unit per tolerance cell in each direction: a straight direction (one
|
||||
// cell) keeps long triangles, Ruppert shapes them in that metric.
|
||||
let sag = cdt::Sag { eval: &eval, tol, scale };
|
||||
let fill = cdt::Fill { seeds: &seeds, refine: Some((sag, MAX_REFINE)) };
|
||||
cdt::triangulate(&uvs, &ranges, fill).ok_or_else(|| fail("boundary crosses itself"))?
|
||||
}
|
||||
}
|
||||
};
|
||||
// At a pole the boundary has two copies of one node: a triangle on both copies has two
|
||||
// corners at one point and no area (its other two sides are one segment both ways).
|
||||
let pole_pair = |i: u32, j: u32| i != j && fixed.get(i as usize).zip(fixed.get(j as usize)).is_some_and(|(p, q)| p == q);
|
||||
let mut triangles = triangles;
|
||||
triangles.retain(|t| !(pole_pair(t[0], t[1]) || pole_pair(t[1], t[2]) || pole_pair(t[2], t[0])));
|
||||
if !closed_boundary(&ranges, &fixed, &triangles) {
|
||||
return Err(fail("triangulation does not follow the boundary"));
|
||||
}
|
||||
let mut all = uvs;
|
||||
all.extend(extra);
|
||||
Ok(FacePlan { face: u32::try_from(fi).unwrap_or(u32::MAX), surface: None, uv: all, fixed, normals: Vec::new(), flip: false, triangles })
|
||||
}
|
||||
|
||||
/// Every boundary segment (consecutive nodes of a loop) is the side of exactly one triangle:
|
||||
/// the face covers its boundary with nothing missing or doubled, so it meets its neighbours
|
||||
/// exactly. Pole copies of one node (consecutive in a loop, at one point) are one vertex: the
|
||||
/// segment between them has no length, and a side ending on either copy is the same side.
|
||||
fn closed_boundary(ranges: &[std::ops::Range<usize>], fixed: &[Vec3], triangles: &[[u32; 3]]) -> bool {
|
||||
let mut one: Vec<u32> = (0..fixed.len() as u32).collect();
|
||||
let root = |one: &[u32], mut i: u32| {
|
||||
while let Some(&j) = one.get(i as usize).filter(|j| **j != i) {
|
||||
i = j;
|
||||
}
|
||||
i
|
||||
};
|
||||
let segment = |r: &std::ops::Range<usize>, k: usize| ((r.start + k) as u32, (r.start + (k + 1) % r.len()) as u32);
|
||||
for r in ranges {
|
||||
for k in 0..r.len() {
|
||||
let (a, b) = segment(r, k);
|
||||
if fixed.get(a as usize).zip(fixed.get(b as usize)).is_some_and(|(p, q)| p == q) {
|
||||
let (ra, rb) = (root(&one, a), root(&one, b));
|
||||
if let Some(x) = one.get_mut(rb.max(ra) as usize) {
|
||||
*x = ra.min(rb);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
let side = |a: u32, b: u32| {
|
||||
let (a, b) = (root(&one, a), root(&one, b));
|
||||
(a != b).then_some((a.min(b), a.max(b)))
|
||||
};
|
||||
let mut sides: HashMap<(u32, u32), u32> = HashMap::with_capacity(triangles.len() * 3);
|
||||
for t in triangles {
|
||||
for e in 0..3 {
|
||||
if let Some(k) = side(t[e], t[(e + 1) % 3]) {
|
||||
*sides.entry(k).or_default() += 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
ranges.iter().all(|r| {
|
||||
(0..r.len()).all(|k| {
|
||||
let (a, b) = segment(r, k);
|
||||
side(a, b).is_none_or(|k| sides.get(&k).copied() == Some(1))
|
||||
})
|
||||
})
|
||||
}
|
||||
|
||||
/// Keep at most `cap` grid points by taking every k-th line in both directions (ends kept).
|
||||
fn thin(us: &mut Vec<f64>, vs: &mut Vec<f64>, cap: usize) {
|
||||
let total = us.len().saturating_mul(vs.len());
|
||||
if total <= cap {
|
||||
return;
|
||||
}
|
||||
let f = (total as f64 / cap.max(4) as f64).sqrt();
|
||||
let pick = |d: &mut Vec<f64>| {
|
||||
let n = ((d.len() as f64 / f).ceil() as usize).max(2);
|
||||
if d.len() > n {
|
||||
let len = d.len();
|
||||
*d = (0..n).filter_map(|i| d.get(i * (len - 1) / (n - 1)).copied()).collect();
|
||||
}
|
||||
};
|
||||
pick(us);
|
||||
pick(vs);
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests;
|
||||
@@ -0,0 +1,156 @@
|
||||
//! Truck surfaces in the evaluator's form ([`EvalSurface`]), which the CPU and GPU evaluators
|
||||
//! share. Surfaces the evaluators cannot express (a revolved intersection curve) or that are
|
||||
//! too large for them give `None`; their faces are evaluated here instead.
|
||||
|
||||
use solidcraft_geom::Vec3;
|
||||
use solidcraft_geom::bspline::MAX_SPLINE_DEGREE;
|
||||
use solidcraft_geom::tess::{EvalCurve, EvalSurface, MAX_EVAL_KNOTS, MAX_EVAL_POINTS};
|
||||
use truck_meshalgo::prelude::*;
|
||||
use truck_modeling as mt;
|
||||
|
||||
use crate::body::from_p3;
|
||||
|
||||
/// `surface` in the evaluator's form, parameterised exactly as truck parameterises it.
|
||||
pub(crate) fn eval_surface(surface: &mt::Surface) -> Option<EvalSurface> {
|
||||
let s = match surface {
|
||||
mt::Surface::Plane(p) => {
|
||||
EvalSurface::Plane { origin: from_p3(p.subs(0.0, 0.0)), du: from_v3(p.uder(0.0, 0.0)), dv: from_v3(p.vder(0.0, 0.0)) }
|
||||
}
|
||||
mt::Surface::BSplineSurface(b) => {
|
||||
let ctrl = b.control_points().iter().map(|row| row.iter().map(|p| [p.x, p.y, p.z, 1.0]).collect()).collect();
|
||||
nurbs(b.degrees(), b.knot_vecs(), ctrl)?
|
||||
}
|
||||
mt::Surface::NurbsSurface(n) => {
|
||||
let ctrl = n.control_points().iter().map(|row| row.iter().map(|h| [h.x, h.y, h.z, h.w]).collect()).collect();
|
||||
nurbs((n.udegree(), n.vdegree()), n.knot_vecs(), ctrl)?
|
||||
}
|
||||
mt::Surface::RevolutedCurve(proc) => {
|
||||
let rev = proc.entity();
|
||||
let profile = eval_curve(rev.entity_curve())?;
|
||||
let axis = from_v3(rev.axis()).normalized()?;
|
||||
let m = proc.transform();
|
||||
// cgmath is column-major: m[column][row].
|
||||
let transform = [0, 1, 2].map(|r| [m[0][r], m[1][r], m[2][r], m[3][r]]);
|
||||
if transform.iter().flatten().any(|x| !x.is_finite()) {
|
||||
return None;
|
||||
}
|
||||
EvalSurface::Revolved { profile, origin: from_p3(rev.origin()), axis, transform, swap: !proc.orientation() }
|
||||
}
|
||||
};
|
||||
Some(s)
|
||||
}
|
||||
|
||||
fn from_v3(v: mt::Vector3) -> Vec3 {
|
||||
Vec3::new(v.x, v.y, v.z)
|
||||
}
|
||||
|
||||
fn knots(k: &mt::KnotVec) -> Option<Vec<f64>> {
|
||||
let v: Vec<f64> = k.iter().copied().collect();
|
||||
(v.len() <= MAX_EVAL_KNOTS && v.iter().all(|x| x.is_finite())).then_some(v)
|
||||
}
|
||||
|
||||
/// Truck's `control_points[i][j]` (i along u) as the evaluator's u-fastest array.
|
||||
fn nurbs((pu, pv): (usize, usize), kv: &(mt::KnotVec, mt::KnotVec), rows: Vec<Vec<[f64; 4]>>) -> Option<EvalSurface> {
|
||||
let nu = rows.len();
|
||||
let nv = rows.first()?.len();
|
||||
if pu == 0 || pv == 0 || pu > MAX_SPLINE_DEGREE || pv > MAX_SPLINE_DEGREE || nu.checked_mul(nv)? > MAX_EVAL_POINTS {
|
||||
return None;
|
||||
}
|
||||
let mut ctrl = Vec::with_capacity(nu * nv);
|
||||
for j in 0..nv {
|
||||
for row in &rows {
|
||||
ctrl.push(<[[f64; 4]]>::get(row, j).copied()?);
|
||||
}
|
||||
}
|
||||
if ctrl.iter().flatten().any(|x| !x.is_finite()) {
|
||||
return None;
|
||||
}
|
||||
let knots = [knots(&kv.0)?, knots(&kv.1)?];
|
||||
(knots[0].len() == nu + pu + 1 && knots[1].len() == nv + pv + 1).then_some(EvalSurface::Nurbs { degree: [pu, pv], knots, count: [nu, nv], ctrl })
|
||||
}
|
||||
|
||||
/// A profile curve in the evaluator's form (a line extends for ever, as truck's does).
|
||||
pub(crate) fn eval_curve(c: &mt::Curve) -> Option<EvalCurve> {
|
||||
let (degree, kv, ctrl): (usize, Vec<f64>, Vec<[f64; 4]>) = match c {
|
||||
mt::Curve::Line(l) => (1, vec![0.0, 0.0, 1.0, 1.0], vec![[l.0.x, l.0.y, l.0.z, 1.0], [l.1.x, l.1.y, l.1.z, 1.0]]),
|
||||
mt::Curve::BSplineCurve(b) => (b.degree(), knots(b.knot_vec())?, b.control_points().iter().map(|p| [p.x, p.y, p.z, 1.0]).collect()),
|
||||
mt::Curve::NurbsCurve(n) => (n.degree(), knots(n.knot_vec())?, n.control_points().iter().map(|h| [h.x, h.y, h.z, h.w]).collect()),
|
||||
mt::Curve::IntersectionCurve(_) => return None,
|
||||
};
|
||||
let ok = (1..=MAX_SPLINE_DEGREE).contains(°ree)
|
||||
&& ctrl.len() <= MAX_EVAL_POINTS
|
||||
&& kv.len() == ctrl.len() + degree + 1
|
||||
&& ctrl.iter().flatten().all(|x| x.is_finite());
|
||||
ok.then_some(EvalCurve { degree, knots: kv, ctrl })
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
use crate::body::Solid;
|
||||
|
||||
/// Every face of `solid` evaluates as truck evaluates it, over its own parameter box.
|
||||
fn assert_matches_truck(solid: &Solid) -> [usize; 4] {
|
||||
let mut kinds = [0; 4];
|
||||
for face in solid.face_iter() {
|
||||
let surface = face.surface();
|
||||
let kind = match surface {
|
||||
mt::Surface::Plane(_) => 0,
|
||||
mt::Surface::BSplineSurface(_) => 1,
|
||||
mt::Surface::NurbsSurface(_) => 2,
|
||||
mt::Surface::RevolutedCurve(_) => 3,
|
||||
};
|
||||
let Some(eval) = eval_surface(&surface) else { panic!("not evaluable: {surface:?}") };
|
||||
// Sample the face's parameter box from its boundary vertices.
|
||||
let pts: Vec<(f64, f64)> = face.vertex_iter().filter_map(|v| surface.search_parameter(v.point(), None, 100)).collect();
|
||||
if pts.is_empty() {
|
||||
continue;
|
||||
}
|
||||
let (u0, u1) = pts.iter().fold((f64::MAX, f64::MIN), |(a, b), p| (a.min(p.0), b.max(p.0)));
|
||||
let (v0, v1) = pts.iter().fold((f64::MAX, f64::MIN), |(a, b), p| (a.min(p.1), b.max(p.1)));
|
||||
for i in 0..=6 {
|
||||
for j in 0..=6 {
|
||||
let (u, v) = (u0 + (u1 - u0) * i as f64 / 6.0, v0 + (v1 - v0) * j as f64 / 6.0);
|
||||
let (p, n) = eval.eval(u, v);
|
||||
let want = from_p3(surface.subs(u, v));
|
||||
assert!(p.dist(want) < 1e-9 * (1.0 + want.len()), "point at ({u}, {v}): {p:?} vs {want:?}");
|
||||
let wn = from_v3(surface.normal(u, v));
|
||||
if wn.len() > 0.5 {
|
||||
assert!(n.dist(wn) < 1e-6, "normal at ({u}, {v}): {n:?} vs {wn:?} ({surface:?})");
|
||||
}
|
||||
kinds[kind] += 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
kinds
|
||||
}
|
||||
|
||||
fn solid(b: crate::Body) -> Solid {
|
||||
(*b.solid).clone()
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn primitives_evaluate_like_truck() {
|
||||
let Ok(bx) = crate::box_solid(Vec3::new(-1.0, -2.0, 0.0), Vec3::new(3.0, 4.0, 5.0)) else { panic!("box") };
|
||||
let Ok(cyl) = crate::cylinder(Vec3::new(1.0, 2.0, 3.0), Vec3::new(0.0, 1.0, 1.0), 2.5, 7.0) else { panic!("cylinder") };
|
||||
let Ok(sph) = crate::sphere(Vec3::new(0.0, 0.0, 1.0), 4.0) else { panic!("sphere") };
|
||||
let Ok(tor) = crate::torus(Vec3::ZERO, 6.0, 1.5) else { panic!("torus") };
|
||||
let mut kinds = [0; 4];
|
||||
for b in [bx, cyl, sph, tor] {
|
||||
for (k, n) in kinds.iter_mut().zip(assert_matches_truck(&solid(b))) {
|
||||
*k += n;
|
||||
}
|
||||
}
|
||||
// Planes, rational patches (sphere) and revolved profiles (cylinder, torus) all covered.
|
||||
assert!(kinds[0] > 0 && kinds[3] > 0 && kinds[1] + kinds[2] > 0, "{kinds:?}");
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn transformed_and_mirrored_bodies_evaluate_like_truck() {
|
||||
let Ok(cyl) = crate::cylinder(Vec3::ZERO, Vec3::Z, 2.0, 5.0) else { panic!("cylinder") };
|
||||
// Column-major: x → 3 − x, z → z + 1.
|
||||
let mirror = [[-1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [3.0, 0.0, 1.0, 1.0]];
|
||||
let Ok(m) = crate::transform_matrix(&cyl, mirror) else { panic!("transform") };
|
||||
assert!(assert_matches_truck(&solid(m)).iter().sum::<usize>() > 0);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,245 @@
|
||||
use std::collections::HashMap;
|
||||
|
||||
use solidcraft_geom::{Mesh, Vec3};
|
||||
|
||||
use super::*;
|
||||
use crate::{Body, BoolOp};
|
||||
|
||||
/// Every triangle edge, with vertices merged by exact position, is shared by exactly two
|
||||
/// triangles: the mesh is closed and its faces meet exactly (no cracks, no T-junctions).
|
||||
fn assert_watertight(m: &Mesh, name: &str) {
|
||||
// By value: −0.0 and 0.0 are one position (adding 0.0 makes −0.0 into 0.0).
|
||||
let key = |i: u32| m.positions.get(i as usize).map(|p| [(p.x + 0.0).to_bits(), (p.y + 0.0).to_bits(), (p.z + 0.0).to_bits()]);
|
||||
let mut uses: HashMap<([u64; 3], [u64; 3]), i32> = HashMap::new();
|
||||
for t in &m.triangles {
|
||||
for e in 0..3 {
|
||||
let (Some(a), Some(b)) = (key(t[e]), key(t[(e + 1) % 3])) else { panic!("{name}: bad index") };
|
||||
if a == b {
|
||||
continue;
|
||||
}
|
||||
// Directed: a closed, consistently oriented mesh uses each edge once each way.
|
||||
*uses.entry((a, b)).or_default() += 1;
|
||||
*uses.entry((b, a)).or_default() -= 1;
|
||||
}
|
||||
}
|
||||
let open: Vec<_> = uses.iter().filter(|(_, n)| **n != 0).collect();
|
||||
assert!(open.is_empty(), "{name}: {} unmatched directed edges, e.g. {:?}", open.len(), open.first());
|
||||
}
|
||||
|
||||
fn plan_body(b: &Body, tol: f64) -> (Mesh, PlanStats) {
|
||||
match plan(&b.solid, tol) {
|
||||
Ok((p, stats)) => (p.evaluate(), stats),
|
||||
Err(e) => panic!("plan: {e}"),
|
||||
}
|
||||
}
|
||||
|
||||
fn check(name: &str, b: &Body, tol: f64, volume: f64) -> PlanStats {
|
||||
let (m, stats) = plan_body(b, tol);
|
||||
assert_watertight(&m, name);
|
||||
let got = m.measure().volume;
|
||||
// Chord error tol over the surface: the volume is short by at most about area · tol.
|
||||
let area = m.measure().area;
|
||||
assert!((got - volume).abs() <= area * tol * 1.5 + 1e-9, "{name}: volume {got} vs {volume} (area {area}, tol {tol})");
|
||||
// Outward normals: the divergence theorem gives a positive volume only if they are.
|
||||
assert!(got > 0.0, "{name}: inside out");
|
||||
let faces = b.solid.face_iter().count();
|
||||
assert_eq!(stats.planar + stats.structured + stats.delaunay, faces, "{name}: every face planned");
|
||||
stats
|
||||
}
|
||||
|
||||
fn ok<T>(r: crate::Result<T>) -> T {
|
||||
match r {
|
||||
Ok(v) => v,
|
||||
Err(e) => panic!("{e}"),
|
||||
}
|
||||
}
|
||||
|
||||
fn cut(a: &Body, b: &Body) -> Body {
|
||||
match crate::boolean(a, b, BoolOp::Cut) {
|
||||
Ok(Some(r)) => r,
|
||||
other => panic!("cut: {other:?}"),
|
||||
}
|
||||
}
|
||||
|
||||
const PI: f64 = std::f64::consts::PI;
|
||||
|
||||
#[test]
|
||||
fn primitives_are_watertight_with_the_right_volume() {
|
||||
for tol in [0.05, 0.005] {
|
||||
let s = check("box", &ok(crate::box_solid(Vec3::ZERO, Vec3::new(10.0, 6.0, 4.0))), tol, 240.0);
|
||||
assert_eq!(s, PlanStats { planar: 6, structured: 0, delaunay: 0 });
|
||||
let s = check("cylinder", &ok(crate::cylinder(Vec3::new(1.0, 2.0, 3.0), Vec3::new(0.0, 1.0, 1.0), 2.5, 7.0)), tol, PI * 2.5 * 2.5 * 7.0);
|
||||
assert_eq!(s.delaunay, 0, "cylinder walls are structured");
|
||||
let s = check("torus", &ok(crate::torus(Vec3::ZERO, 6.0, 1.5)), tol, 2.0 * PI * PI * 6.0 * 1.5 * 1.5);
|
||||
assert_eq!(s.delaunay, 0, "torus patches are structured");
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn holes_and_trimmed_faces_are_watertight() {
|
||||
let tol = 0.01;
|
||||
let bx = ok(crate::box_solid(Vec3::ZERO, Vec3::new(10.0, 10.0, 4.0)));
|
||||
let pin = ok(crate::cylinder(Vec3::new(5.0, 5.0, -1.0), Vec3::Z, 2.0, 6.0));
|
||||
check("box with a hole", &cut(&bx, &pin), tol, 400.0 - PI * 4.0 * 4.0);
|
||||
// A cylinder with a cross hole: trimmed cylinder halves (Delaunay) and intersection-curve walls.
|
||||
let cyl = ok(crate::cylinder(Vec3::new(5.0, 5.0, -1.0), Vec3::Z, 2.0, 6.0));
|
||||
let cross = ok(crate::cylinder(Vec3::new(5.0, -1.0, 2.0), Vec3::Y, 1.0, 12.0));
|
||||
let body = cut(&cyl, &cross);
|
||||
let (m, stats) = plan_body(&body, tol);
|
||||
assert_watertight(&m, "cross hole");
|
||||
assert!(stats.delaunay > 0, "{stats:?}");
|
||||
// Against the reference mesher's volume (no closed form for the two-cylinder intersection).
|
||||
let Ok(reference) = body.tessellate(tol * 0.2) else { panic!("reference mesh") };
|
||||
let (a, b) = (m.measure().volume, reference.measure().volume);
|
||||
assert!((a - b).abs() < 0.01 * b, "cross hole volume {a} vs {b}");
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn faces_and_edges_keep_the_body_order() {
|
||||
let body = ok(crate::cylinder(Vec3::ZERO, Vec3::Z, 2.0, 5.0));
|
||||
let (m, _) = plan_body(&body, 0.01);
|
||||
let Ok(reference) = body.tessellate(0.01) else { panic!("reference mesh") };
|
||||
assert_eq!(m.edges.len(), reference.edges.len());
|
||||
assert_eq!(m.edge_faces, reference.edge_faces);
|
||||
// Same faces in the same order: each face's area agrees with the reference mesher's.
|
||||
let face_area = |m: &Mesh, f: u32| -> f64 {
|
||||
m.triangles
|
||||
.iter()
|
||||
.zip(&m.tri_face)
|
||||
.filter(|(_, tf)| **tf == f)
|
||||
.map(|(t, _)| {
|
||||
let p = |i: u32| m.positions.get(i as usize).copied().unwrap_or_default();
|
||||
(p(t[1]) - p(t[0])).cross(p(t[2]) - p(t[0])).len() * 0.5
|
||||
})
|
||||
.sum()
|
||||
};
|
||||
for f in 0..body.solid.face_iter().count() as u32 {
|
||||
let (a, b) = (face_area(&m, f), face_area(&reference, f));
|
||||
assert!((a - b).abs() < 0.01 * b.max(1e-9), "face {f}: {a} vs {b}");
|
||||
}
|
||||
// Each edge polyline ends on the same points as the reference's.
|
||||
for (a, b) in m.edges.iter().zip(&reference.edges) {
|
||||
assert!(a.first().zip(b.first()).is_some_and(|(p, q)| p.dist(*q) < 1e-9));
|
||||
assert!(a.last().zip(b.last()).is_some_and(|(p, q)| p.dist(*q) < 1e-9));
|
||||
}
|
||||
}
|
||||
|
||||
/// Side-by-side wireframes, reference mesher (left) and plan (right):
|
||||
/// `SOLIDCRAFT_TESS_SVG=<dir> cargo test -p solidcraft-kernel render_wireframes -- --ignored`.
|
||||
#[test]
|
||||
#[ignore]
|
||||
fn render_wireframes() {
|
||||
let Ok(dir) = std::env::var("SOLIDCRAFT_TESS_SVG") else { return };
|
||||
let tol = 0.02;
|
||||
let bx = ok(crate::box_solid(Vec3::ZERO, Vec3::new(10.0, 10.0, 4.0)));
|
||||
let pin = ok(crate::cylinder(Vec3::new(5.0, 5.0, -1.0), Vec3::Z, 2.0, 6.0));
|
||||
let cross = ok(crate::cylinder(Vec3::new(5.0, -1.0, 2.0), Vec3::Y, 1.0, 12.0));
|
||||
let filleted =
|
||||
ok(crate::fillet(&bx, &[Vec3::new(5.0, 0.0, 4.0), Vec3::new(10.0, 5.0, 4.0), Vec3::new(5.0, 10.0, 4.0), Vec3::new(0.0, 5.0, 4.0)], 1.5));
|
||||
let shapes = [
|
||||
("box_hole", cut(&bx, &pin)),
|
||||
("cylinder", pin.clone()),
|
||||
("cross_hole", cut(&pin, &cross)),
|
||||
("torus", ok(crate::torus(Vec3::ZERO, 6.0, 1.5))),
|
||||
("fillet", filleted),
|
||||
];
|
||||
for (name, body) in shapes {
|
||||
let t0 = std::time::Instant::now();
|
||||
let Ok(old) = body.tessellate(tol) else { panic!("reference") };
|
||||
let t_old = t0.elapsed().as_secs_f64() * 1e3;
|
||||
let t0 = std::time::Instant::now();
|
||||
let new = match plan(&body.solid, tol) {
|
||||
Ok((p, st)) => Some((p.evaluate(), st)),
|
||||
Err(e) => {
|
||||
println!("{name}: no plan ({e})");
|
||||
None
|
||||
}
|
||||
};
|
||||
let t_new = t0.elapsed().as_secs_f64() * 1e3;
|
||||
let mut svg = String::from("<svg xmlns='http://www.w3.org/2000/svg' width='1600' height='860' style='background:#fff'>");
|
||||
let label = |x: f64, text: String| format!("<text x='{x}' y='40' font-family='sans-serif' font-size='26'>{text}</text>");
|
||||
svg += &label(20.0, format!("meshalgo (Delaunay): {} tris, {t_old:.1} ms", old.triangles.len()));
|
||||
svg += &draw(&old, 0.0);
|
||||
if let Some((m, st)) = &new {
|
||||
svg += &label(
|
||||
820.0,
|
||||
format!("plan: {} tris, {t_new:.1} ms [{} planar, {} grid, {} cdt]", m.triangles.len(), st.planar, st.structured, st.delaunay),
|
||||
);
|
||||
svg += &draw(m, 800.0);
|
||||
}
|
||||
svg += "</svg>";
|
||||
let _ = std::fs::write(format!("{dir}/{name}.svg"), svg);
|
||||
}
|
||||
}
|
||||
|
||||
/// Isometric, painter-sorted, flat-shaded triangles with their edges, in an 800×800 panel.
|
||||
fn draw(m: &Mesh, x0: f64) -> String {
|
||||
let (c30, s30) = (30f64.to_radians().cos(), 30f64.to_radians().sin());
|
||||
let proj = |p: Vec3| -> (f64, f64, f64) {
|
||||
// Turn 45° about Z, tilt 30° about X; depth along the view.
|
||||
let (x, y) = ((p.x - p.y) * std::f64::consts::FRAC_1_SQRT_2, (p.x + p.y) * std::f64::consts::FRAC_1_SQRT_2);
|
||||
(x, p.z * c30 - y * s30, y * c30 + p.z * s30)
|
||||
};
|
||||
let pts: Vec<(f64, f64, f64)> = m.positions.iter().map(|p| proj(*p)).collect();
|
||||
let (mut lo, mut hi) = ((f64::MAX, f64::MAX), (f64::MIN, f64::MIN));
|
||||
for p in &pts {
|
||||
lo = (lo.0.min(p.0), lo.1.min(p.1));
|
||||
hi = (hi.0.max(p.0), hi.1.max(p.1));
|
||||
}
|
||||
let k = 700.0 / (hi.0 - lo.0).max(hi.1 - lo.1).max(1e-9);
|
||||
let sx = |p: (f64, f64, f64)| (x0 + 50.0 + (p.0 - lo.0) * k, 800.0 - (p.1 - lo.1) * k);
|
||||
let mut tris: Vec<(f64, [u32; 3], u32)> =
|
||||
m.triangles.iter().zip(&m.tri_face).map(|(t, f)| (t.iter().map(|&i| pts[i as usize].2).sum::<f64>(), *t, *f)).collect();
|
||||
tris.sort_by(|a, b| b.0.total_cmp(&a.0));
|
||||
let light = Vec3::new(0.3, -0.5, 0.8).normalized().unwrap_or(Vec3::new(0.0, 0.0, 1.0));
|
||||
let mut out = String::new();
|
||||
let tint = [(1.0, 1.0, 1.15), (1.15, 1.0, 1.0), (1.0, 1.15, 1.0), (1.1, 1.1, 0.9), (0.9, 1.1, 1.1), (1.1, 0.9, 1.1)];
|
||||
for (_, t, f) in tris {
|
||||
let (tr, tg, tb) = tint[f as usize % tint.len()];
|
||||
let [a, b, c] = t.map(|i| m.positions[i as usize]);
|
||||
let n = (b - a).cross(c - a).normalized().unwrap_or(Vec3::new(0.0, 0.0, 1.0));
|
||||
let shade = (90.0 + 150.0 * n.dot(light).max(0.0)) as u8;
|
||||
let q: Vec<(f64, f64)> = t.iter().map(|&i| sx(pts[i as usize])).collect();
|
||||
// Back faces away (screen y points down, so outward triangles wind clockwise here).
|
||||
if (q[1].0 - q[0].0) * (q[2].1 - q[0].1) - (q[2].0 - q[0].0) * (q[1].1 - q[0].1) > 0.0 {
|
||||
continue;
|
||||
}
|
||||
let pp: Vec<String> = q.iter().map(|(x, y)| format!("{x:.1},{y:.1}")).collect();
|
||||
out += &format!(
|
||||
"<polygon points='{}' fill='rgb({},{},{})' stroke='#1d3557' stroke-width='0.5'/>",
|
||||
pp.join(" "),
|
||||
(f64::from(shade) * tr).min(255.0) as u8,
|
||||
(f64::from(shade) * tg).min(255.0) as u8,
|
||||
(f64::from(shade) * tb).min(255.0) as u8,
|
||||
);
|
||||
}
|
||||
out
|
||||
}
|
||||
|
||||
/// Blind drilled holes (a box cut by a revolved drill with a 118° point, as the hole feature
|
||||
/// builds it): the point's apex is a pole of the cone faces, two copies of one boundary node.
|
||||
/// The plan is closed and has no triangle on both copies (no zero-area triangles), also where
|
||||
/// such a triangle carried a boundary side of the cone.
|
||||
#[test]
|
||||
fn a_drill_point_apex_leaves_no_zero_area_triangles() {
|
||||
use solidcraft_geom::{Loop2, Plane, Region2, Vec2};
|
||||
// (box size, hole position, radius, depth)
|
||||
let cases =
|
||||
[(Vec3::new(40.0, 30.0, 15.0), Vec3::new(20.0, 15.0, 15.0), 3.4, 8.0), (Vec3::new(60.0, 40.0, 15.0), Vec3::new(50.0, 20.0, 15.0), 3.0, 10.0)];
|
||||
for (size, at, r, depth) in cases {
|
||||
let bx = ok(crate::box_solid(Vec3::ZERO, size));
|
||||
let tip = r / (118f64 / 2.0).to_radians().tan();
|
||||
let Some(rp) = Plane::new(at, Vec3::X, Vec3::Z) else { panic!("plane") };
|
||||
let pts = [Vec2::new(0.0, 0.6), Vec2::new(r, 0.6), Vec2::new(r, -depth), Vec2::new(0.0, -depth - tip)];
|
||||
let region = Region2 { outer: Loop2::polygon(&pts), holes: vec![] };
|
||||
let Some(drill) = ok(crate::revolve(&rp, &[region], Vec2::ZERO, Vec2::Y, std::f64::consts::TAU)).pop() else { panic!("drill") };
|
||||
let body = cut(&bx, &drill);
|
||||
let name = format!("hole r {r} depth {depth}");
|
||||
let (m, _) = plan_body(&body, 0.02);
|
||||
assert_watertight(&m, &name);
|
||||
for t in &m.triangles {
|
||||
let [a, b, c] = t.map(|i| m.positions[i as usize]);
|
||||
assert!((b - a).cross(c - a).len() > 1e-12, "{name}: zero-area triangle {a:?} {b:?} {c:?}");
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,246 @@
|
||||
//! Parameters of points on a surface, on the evaluator's own surface form (so the parameters
|
||||
//! the plan stores are the ones the evaluators use), and the tolerance-driven divisions of a
|
||||
//! face's parameter box.
|
||||
|
||||
use solidcraft_geom::Vec3;
|
||||
use solidcraft_geom::tess::EvalSurface;
|
||||
|
||||
/// The parameter box of a surface and its periods.
|
||||
#[derive(Clone, Copy, Debug)]
|
||||
pub(crate) struct Domain {
|
||||
/// Bounded ranges (`None`: unbounded, as a plane's).
|
||||
pub range: [Option<(f64, f64)>; 2],
|
||||
pub period: [Option<f64>; 2],
|
||||
}
|
||||
|
||||
pub(crate) fn domain(s: &EvalSurface) -> Domain {
|
||||
let tau = std::f64::consts::TAU;
|
||||
match s {
|
||||
EvalSurface::Plane { .. } => Domain { range: [None, None], period: [None, None] },
|
||||
EvalSurface::Nurbs { degree, knots, count, .. } => {
|
||||
let r = |d: usize| Some((*knots[d].get(degree[d])?, *knots[d].get(count[d])?));
|
||||
Domain { range: [r(0), r(1)], period: [None, None] }
|
||||
}
|
||||
EvalSurface::Revolved { profile, swap, .. } => {
|
||||
let r = (|| Some((*profile.knots.get(profile.degree)?, *profile.knots.get(profile.ctrl.len())?)))();
|
||||
let (a, b) = ((r, None), (Some((0.0, tau)), Some(tau)));
|
||||
let (u, v) = if *swap { (b, a) } else { (a, b) };
|
||||
Domain { range: [u.0, v.0], period: [u.1, v.1] }
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
impl Domain {
|
||||
fn clamp(&self, uv: [f64; 2]) -> [f64; 2] {
|
||||
let mut out = uv;
|
||||
for (d, x) in out.iter_mut().enumerate() {
|
||||
if let (Some((a, b)), None) = (self.range[d], self.period[d]) {
|
||||
*x = x.clamp(a.min(b), a.max(b));
|
||||
}
|
||||
}
|
||||
out
|
||||
}
|
||||
}
|
||||
|
||||
/// Damped Gauss–Newton (Levenberg–Marquardt) for the parameters nearest to `p`, from `start`.
|
||||
/// Returns the parameters and their distance to `p`.
|
||||
fn newton(s: &EvalSurface, dom: &Domain, p: Vec3, start: [f64; 2]) -> Option<([f64; 2], f64)> {
|
||||
let mut uv = dom.clamp(start);
|
||||
let (mut q, mut su, mut sv) = s.derivs(uv[0], uv[1])?;
|
||||
let mut dist = q.dist(p);
|
||||
let mut lambda = 1e-6;
|
||||
for _ in 0..60 {
|
||||
let r = p - q;
|
||||
let (a, b, c) = (su.len2(), su.dot(sv), sv.len2());
|
||||
let (g0, g1) = (su.dot(r), sv.dot(r));
|
||||
let scale = a + c;
|
||||
if !(scale > 0.0) || !scale.is_finite() {
|
||||
break;
|
||||
}
|
||||
let (a2, c2) = (a + lambda * scale, c + lambda * scale);
|
||||
let det = a2 * c2 - b * b;
|
||||
if !(det.abs() > 0.0) {
|
||||
break;
|
||||
}
|
||||
let step = [(c2 * g0 - b * g1) / det, (a2 * g1 - b * g0) / det];
|
||||
let next = dom.clamp([uv[0] + step[0], uv[1] + step[1]]);
|
||||
let Some((nq, nsu, nsv)) = s.derivs(next[0], next[1]) else { break };
|
||||
let nd = nq.dist(p);
|
||||
if nd <= dist {
|
||||
let moved = (next[0] - uv[0]).abs() + (next[1] - uv[1]).abs();
|
||||
(uv, q, su, sv, dist) = (next, nq, nsu, nsv, nd);
|
||||
lambda = (lambda * 0.1).max(1e-12);
|
||||
if moved <= 1e-15 * (1.0 + uv[0].abs() + uv[1].abs()) {
|
||||
break;
|
||||
}
|
||||
} else {
|
||||
lambda *= 10.0;
|
||||
if lambda > 1e8 {
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
Some((uv, dist))
|
||||
}
|
||||
|
||||
/// Parameters of `p` (a point on the surface within `accept`), from `hint` when that
|
||||
/// converges, else from the best starts of a grid over the surface's domain.
|
||||
pub(crate) fn project(s: &EvalSurface, dom: &Domain, p: Vec3, hint: Option<[f64; 2]>, accept: f64) -> Option<[f64; 2]> {
|
||||
if let EvalSurface::Plane { origin, du, dv } = s {
|
||||
let r = p - *origin;
|
||||
let (a, b, c) = (du.len2(), du.dot(*dv), dv.len2());
|
||||
let det = a * c - b * b;
|
||||
if !(det.abs() > 0.0) {
|
||||
return None;
|
||||
}
|
||||
let (g0, g1) = (du.dot(r), dv.dot(r));
|
||||
let uv = [(c * g0 - b * g1) / det, (a * g1 - b * g0) / det];
|
||||
return (uv[0].is_finite() && uv[1].is_finite()).then_some(uv);
|
||||
}
|
||||
let mut best: Option<([f64; 2], f64)> = None;
|
||||
if let Some(h) = hint
|
||||
&& let Some((uv, d)) = newton(s, dom, p, h)
|
||||
{
|
||||
if d <= accept {
|
||||
return Some(uv);
|
||||
}
|
||||
best = Some((uv, d));
|
||||
}
|
||||
let (ur, vr) = (dom.range[0]?, dom.range[1]?);
|
||||
const N: usize = 16;
|
||||
let mut starts: Vec<(f64, [f64; 2])> = Vec::with_capacity((N + 1) * (N + 1));
|
||||
for i in 0..=N {
|
||||
for j in 0..=N {
|
||||
let uv = [ur.0 + (ur.1 - ur.0) * i as f64 / N as f64, vr.0 + (vr.1 - vr.0) * j as f64 / N as f64];
|
||||
if let Some((q, _, _)) = s.derivs(uv[0], uv[1]) {
|
||||
starts.push(((q - p).len2(), uv));
|
||||
}
|
||||
}
|
||||
}
|
||||
starts.sort_by(|a, b| a.0.total_cmp(&b.0));
|
||||
for (_, start) in starts.iter().take(4) {
|
||||
if let Some((uv, d)) = newton(s, dom, p, *start)
|
||||
&& best.is_none_or(|(_, bd)| d < bd)
|
||||
{
|
||||
best = Some((uv, d));
|
||||
}
|
||||
}
|
||||
best.filter(|(_, d)| *d <= accept).map(|(uv, _)| uv)
|
||||
}
|
||||
|
||||
/// `x` moved by whole periods to lie within half a period of `near`.
|
||||
pub(crate) fn unwrap(x: f64, near: f64, period: Option<f64>) -> f64 {
|
||||
match period {
|
||||
Some(p) if p > 0.0 => x - ((x - near) / p).round() * p,
|
||||
_ => x,
|
||||
}
|
||||
}
|
||||
|
||||
/// Is the surface degenerate along direction `d` at `uv` (a pole: moving along `d` does not
|
||||
/// move the point)?
|
||||
pub(crate) fn degenerate(s: &EvalSurface, uv: [f64; 2], d: usize) -> bool {
|
||||
let Some((_, su, sv)) = s.derivs(uv[0], uv[1]) else { return false };
|
||||
let (this, other) = if d == 0 { (su, sv) } else { (sv, su) };
|
||||
this.len() <= 1e-9 * other.len().max(1e-12)
|
||||
}
|
||||
|
||||
/// Division of `range` along direction `d` so that the surface between neighbouring lines
|
||||
/// sags at most `tol` from its chord, checked along iso-lines across `across`; at most
|
||||
/// `max_lines` lines, ends included.
|
||||
pub(crate) fn divide(s: &EvalSurface, d: usize, range: (f64, f64), across: (f64, f64), tol: f64, max_lines: usize) -> Vec<f64> {
|
||||
let (a0, a1) = range;
|
||||
if matches!(s, EvalSurface::Plane { .. }) || !(a1 > a0) {
|
||||
return vec![a0, a1];
|
||||
}
|
||||
let at = |x: f64, y: f64| {
|
||||
let (u, v) = if d == 0 { (x, y) } else { (y, x) };
|
||||
s.derivs(u, v).map(|(p, _, _)| p)
|
||||
};
|
||||
const ACROSS: usize = 5;
|
||||
let ys: Vec<f64> = (0..ACROSS).map(|k| across.0 + (across.1 - across.0) * k as f64 / (ACROSS - 1) as f64).collect();
|
||||
let flat = |a: f64, b: f64| {
|
||||
ys.iter().all(|&y| {
|
||||
let (Some(pa), Some(pb)) = (at(a, y), at(b, y)) else { return true };
|
||||
[0.25, 0.5, 0.75].iter().all(|f| at(a + (b - a) * f, y).is_none_or(|q| q.dist_to_segment(pa, pb) <= tol))
|
||||
})
|
||||
};
|
||||
// Start from quarter turns at most, so a closed iso-line is not taken for a flat one.
|
||||
let initial = ((a1 - a0) / std::f64::consts::FRAC_PI_2).ceil().clamp(1.0, 64.0) as u32;
|
||||
// Both ends exactly (a0 + (a1 − a0) · 1 may round away from a1): the end lines are the
|
||||
// face's own parameter box, which the boundary nodes sit on.
|
||||
let x_at = |i: u32| {
|
||||
let t = f64::from(i) / f64::from(initial);
|
||||
a0 * (1.0 - t) + a1 * t
|
||||
};
|
||||
let mut out = vec![a0];
|
||||
let mut stack: Vec<(f64, f64, u32)> = (0..initial).rev().map(|i| (x_at(i), x_at(i + 1), 0)).collect();
|
||||
while let Some((a, b, depth)) = stack.pop() {
|
||||
if depth >= 20 || out.len() + stack.len() >= max_lines.max(2) || flat(a, b) {
|
||||
out.push(b);
|
||||
} else {
|
||||
let m = 0.5 * (a + b);
|
||||
stack.push((m, b, depth + 1));
|
||||
stack.push((a, m, depth + 1));
|
||||
}
|
||||
}
|
||||
out
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use super::*;
|
||||
use solidcraft_geom::tess::EvalCurve;
|
||||
|
||||
fn cylinder() -> EvalSurface {
|
||||
EvalSurface::Revolved {
|
||||
profile: EvalCurve { degree: 1, knots: vec![0.0, 0.0, 1.0, 1.0], ctrl: vec![[3.0, 0.0, 0.0, 1.0], [3.0, 0.0, 4.0, 1.0]] },
|
||||
origin: Vec3::ZERO,
|
||||
axis: Vec3::Z,
|
||||
transform: [[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0]],
|
||||
swap: false,
|
||||
}
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn projects_points_back_to_their_parameters() {
|
||||
let s = cylinder();
|
||||
let dom = domain(&s);
|
||||
for &(u, v) in &[(0.1, 0.2), (0.5, 3.0), (0.9, 6.0), (0.0, 1.0)] {
|
||||
let (p, _) = s.eval(u, v);
|
||||
let Some(uv) = project(&s, &dom, p, None, 1e-9) else { panic!("projects") };
|
||||
let (q, _) = s.eval(uv[0], uv[1]);
|
||||
assert!(q.dist(p) < 1e-9);
|
||||
assert!((uv[0] - u).abs() < 1e-9);
|
||||
}
|
||||
// Off the surface by more than `accept`: no parameters.
|
||||
assert!(project(&s, &dom, Vec3::new(5.0, 0.0, 1.0), None, 1e-3).is_none());
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn divides_the_turn_but_not_the_straight_direction() {
|
||||
let s = cylinder();
|
||||
let turn = divide(&s, 1, (0.0, std::f64::consts::TAU), (0.0, 1.0), 0.01, 10_000);
|
||||
let along = divide(&s, 0, (0.0, 1.0), (0.0, std::f64::consts::TAU), 0.01, 10_000);
|
||||
assert_eq!(along, vec![0.0, 1.0]);
|
||||
// Chord sag r(1 − cos(θ/2)) ≤ 0.01 with r = 3 needs θ ≤ 0.163: at least 39 segments.
|
||||
assert!(turn.len() >= 40 && turn.len() < 80, "{}", turn.len());
|
||||
}
|
||||
|
||||
/// The first and last lines are the range's ends to the last bit: the boundary nodes sit on
|
||||
/// them, and a line a rounding inside would be taken for an interior one (a drill point's
|
||||
/// cone, where a0 + (a1 − a0) is not a1).
|
||||
#[test]
|
||||
fn divides_with_the_ends_exactly() {
|
||||
let (a0, a1) = (-1.010485317689877, 1.083909784703316);
|
||||
let lines = divide(&cylinder(), 1, (a0, a1), (0.0, 1.0), 0.01, 10_000);
|
||||
assert_eq!(lines.first().copied(), Some(a0));
|
||||
assert_eq!(lines.last().copied(), Some(a1));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn unwraps_across_the_period() {
|
||||
let tau = std::f64::consts::TAU;
|
||||
assert!((unwrap(0.1, tau - 0.1, Some(tau)) - (tau + 0.1)).abs() < 1e-12);
|
||||
assert_eq!(unwrap(0.1, 6.0, None), 0.1);
|
||||
}
|
||||
}
|
||||
Reference in new issue
Block a user