forked from 1b-agent/fieldcraft-upstream
Planar all-quad meshing: size fields, TFI mapped meshes, free quad mesher (M5 base) (#18)
* Planar all-quad meshing: size fields, TFI mapped meshes, free quad mesher, planar quad validity - modelcraft_mesh::size: SizeField trait, division counts, graded polyline division, per-loop parity - modelcraft_mesh::quad: transfinite (Gordon-Hall) mapped meshes of four-sided regions; free all-quad meshes of polygons with holes on prescribed boundary nodes (half-resolution CDT with Ruppert refinement, Lee-Lo recombination, uniform split, smart Laplacian plus Freitag-Plassmann untangling), exact validity gate on every element - modelcraft_mesh::quality: Robinson aspect ratio and skew for quads, exact planar quad validity Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm * quad mesher: true-boundary guard for Steiner points, untangling by corner area, parity retry, recombination quality floor; I-beam and perforated plate tests Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm * docs: quad meshing papers (B7), roadmap M5 and M2, architecture pipeline step Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm * quad mesher: simplify (shared corner and validity helpers, vertex rotation helper, guard decoupled from the CDT, verify inside the CDT, non-allocating final gate) Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm --------- Co-authored-by: jyviko <2501648+jyviko@users.noreply.github.com> Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
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//! Planar constrained Delaunay triangulation with Delaunay refinement to a size field.
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//!
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//! - Insertion: Bowyer–Watson (Bowyer, Comput. J. 24(2), 1981; Watson, Comput. J. 24(2), 1981)
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//! inside a super-triangle, with exact `orient2d`/`incircle` (Shewchuk 1997). The cavity grows
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//! from the triangle containing the point and never crosses a constrained edge, which is the
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//! constrained Delaunay insertion of Shewchuk, *Delaunay refinement algorithms for triangular
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//! mesh generation*, CGTA 22:21–74, 2002, §2.
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//! - Constraint recovery: Sloan, *A fast algorithm for generating constrained Delaunay
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//! triangulations*, Computers & Structures 47(3):441–450, 1993: flip the edges crossing a
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//! segment until it appears, then restore the Delaunay property with Lawson flips.
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//! - Refinement: Ruppert, *A Delaunay refinement algorithm for quality 2-dimensional mesh
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//! generation*, J. Algorithms 18(3):548–585, 1995 (circumcentres of triangles that are too
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//! large for the size field or have a circumradius-to-shortest-edge ratio above √2), with one
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//! change: boundary segments carry prescribed nodes and are never split, so a circumcentre that
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//! falls outside the region, comes closer than a fraction of the local size to a vertex, or is
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//! refused by the caller's guard (clearance from the true boundary) is not inserted (a
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//! too-large triangle gets its centroid instead). Ruppert's encroachment rule (diametral
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//! circles) would forbid any refinement next to a boundary coarser than the size field; the
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//! clearances keep the packing argument for termination.
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//!
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//! Every loop is bounded (walk steps, cavity rounds, flips, refinement passes and the triangle
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//! count), and a cavity is checked before it is retriangulated: the new triangles all have
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//! positive exact orientation and no constrained edge is removed.
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use std::collections::VecDeque;
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use super::domain::Region;
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use crate::predicates::{Point2, Sign, incircle, orient2d, snap_to_domain};
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use crate::size::{SizeField, checked_size};
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use crate::{Error, Result};
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const NONE: u32 = u32::MAX;
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/// Rounds of cavity shrinking before an insertion is rejected.
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const MAX_CAVITY_ROUNDS: usize = 32;
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/// Refinement passes over the triangles.
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const MAX_REFINE_PASSES: usize = 64;
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#[derive(Debug, Clone, Copy)]
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struct Tri {
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/// Counterclockwise vertices.
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v: [u32; 3],
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/// `n[i]`: the neighbour across the edge opposite `v[i]` (from `v[i+1]` to `v[i+2]`).
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n: [u32; 3],
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/// Whether the edge opposite `v[i]` is a constrained (boundary) edge.
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fixed: [bool; 3],
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inside: bool,
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alive: bool,
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}
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/// The triangles of the region: counterclockwise vertex triples into `pts`.
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#[derive(Debug, Clone)]
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pub(crate) struct Triangulation {
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pub pts: Vec<[f64; 2]>,
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pub p2: Vec<Point2>,
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pub tris: Vec<[u32; 3]>,
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}
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pub(crate) struct Cdt {
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pts: Vec<[f64; 2]>,
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p2: Vec<Point2>,
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tris: Vec<Tri>,
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free: Vec<u32>,
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vt: Vec<u32>,
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last: u32,
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mark: Vec<u32>,
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epoch: u32,
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max_tris: usize,
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}
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/// Steiner points keep this fraction of the local size from vertices (and, through the
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/// caller's guard, from the boundary).
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pub(crate) const CLEARANCE: f64 = 0.3;
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/// A constructed point snapped into the predicates' domain, or `None` when it is outside the
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/// model's coordinate range.
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fn steiner_point(c: [f64; 2]) -> Option<Point2> {
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let c = [snap_to_domain(c[0]), snap_to_domain(c[1])];
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if !(c[0].abs() <= modelcraft_model::MAX_COORD && c[1].abs() <= modelcraft_model::MAX_COORD) {
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return None;
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}
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Point2::new(c[0], c[1]).ok()
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}
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fn err(what: &str) -> Error {
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Error::Failed(format!("triangulation: {what}"))
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}
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/// The edge index `i` of `tri` that runs from `a` to `b` (opposite `v[i]`).
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fn edge_index(tri: &Tri, a: u32, b: u32) -> Option<usize> {
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(0..3).find(|&i| tri.v[(i + 1) % 3] == a && tri.v[(i + 2) % 3] == b)
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}
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/// Every edge of `tri` keeps `p` on its left or on it (exact).
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fn contains(tri: &Tri, p2: &[Point2], p: &Point2) -> bool {
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(0..3).all(|i| match (p2.get(tri.v[(i + 1) % 3] as usize), p2.get(tri.v[(i + 2) % 3] as usize)) {
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(Some(a), Some(b)) => orient2d(a, b, p) != Sign::Negative,
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_ => false,
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})
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}
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impl Cdt {
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fn t(&self, t: u32) -> Result<&Tri> {
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self.tris.get(t as usize).ok_or_else(|| err("triangle index out of range"))
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}
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fn tm(&mut self, t: u32) -> Result<&mut Tri> {
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self.tris.get_mut(t as usize).ok_or_else(|| err("triangle index out of range"))
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}
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fn p(&self, v: u32) -> Result<&Point2> {
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self.p2.get(v as usize).ok_or_else(|| err("vertex index out of range"))
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}
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fn xy(&self, v: u32) -> Result<[f64; 2]> {
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self.pts.get(v as usize).copied().ok_or_else(|| err("vertex index out of range"))
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}
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/// Triangulate `region`'s boundary points (ids preserved) and recover its loops as
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/// constrained edges; triangles inside the region are marked.
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pub fn build(region: &Region, max_tris: usize) -> Result<Cdt> {
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let n = region.pts.len();
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let (lo, hi) = super::domain::bbox(region.pts.iter().copied());
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let c = [0.5 * (lo[0] + hi[0]), 0.5 * (lo[1] + hi[1])];
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let d = (hi[0] - lo[0]).max(hi[1] - lo[1]).max(1.0);
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let corners = [[c[0] - 20.0 * d, c[1] - 10.0 * d], [c[0] + 20.0 * d, c[1] - 10.0 * d], [c[0], c[1] + 20.0 * d]];
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let mut pts = region.pts.clone();
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let mut p2 = region.p2.clone();
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for k in corners {
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let k = [snap_to_domain(k[0]), snap_to_domain(k[1])];
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p2.push(Point2::new(k[0], k[1])?);
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pts.push(k);
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}
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let s = n as u32;
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let mut cdt = Cdt {
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vt: vec![NONE; pts.len()],
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pts,
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p2,
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tris: vec![Tri { v: [s, s + 1, s + 2], n: [NONE; 3], fixed: [false; 3], inside: false, alive: true }],
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free: Vec::new(),
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last: 0,
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mark: vec![0],
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epoch: 0,
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max_tris,
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};
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for v in [s, s + 1, s + 2] {
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if let Some(x) = cdt.vt.get_mut(v as usize) {
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*x = 0;
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}
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}
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// Insert in Morton order (short walks), ties by id.
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let span = [(hi[0] - lo[0]).max(f64::MIN_POSITIVE), (hi[1] - lo[1]).max(f64::MIN_POSITIVE)];
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let key = |p: &[f64; 2]| {
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let q = |x: f64, l: f64, s: f64| ((((x - l) / s) * 65535.0) as u32).min(65535);
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let (mut x, mut y) = (q(p[0], lo[0], span[0]), q(p[1], lo[1], span[1]));
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let mut k = 0u64;
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for bit in 0..16 {
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k |= u64::from(x & 1) << (2 * bit) | u64::from(y & 1) << (2 * bit + 1);
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x >>= 1;
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y >>= 1;
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}
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k
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};
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let mut order: Vec<(u64, u32)> = region.pts.iter().enumerate().map(|(i, p)| (key(p), i as u32)).collect();
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order.sort_unstable();
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for (_, v) in order {
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if !cdt.insert(v, None)? {
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return Err(err("a boundary point could not be inserted"));
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}
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}
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for l in ®ion.loops {
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for (i, &a) in l.iter().enumerate() {
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let b = l.get((i + 1) % l.len()).copied().ok_or_else(|| err("loop"))?;
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cdt.recover(a, b)?;
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}
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}
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cdt.classify()?;
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#[cfg(test)]
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assert_eq!(cdt.verify(), Ok(()), "after build");
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Ok(cdt)
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}
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fn alloc(&mut self, tri: Tri) -> Result<u32> {
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if let Some(t) = self.free.pop() {
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*self.tm(t)? = tri;
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return Ok(t);
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}
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if self.tris.len() >= self.max_tris {
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return Err(Error::Limit(format!("the triangulation exceeds {} triangles", self.max_tris)));
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}
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self.tris.push(tri);
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self.mark.push(0);
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Ok(self.tris.len() as u32 - 1)
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}
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/// The triangle containing `p` (on its boundary counts), by a visibility walk from `start`
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/// with a linear scan as the fallback.
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fn locate(&self, p: &Point2, start: u32) -> Result<u32> {
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let mut t = if self.t(start).is_ok_and(|x| x.alive) { start } else { self.any_alive()? };
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let cap = 64 + 4 * self.tris.len();
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'walk: for step in 0..cap {
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let tri = *self.t(t)?;
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for k in 0..3 {
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let i = (k + step) % 3;
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let (a, b) = (tri.v[(i + 1) % 3], tri.v[(i + 2) % 3]);
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if orient2d(self.p(a)?, self.p(b)?, p) == Sign::Negative {
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let next = tri.n[i];
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if next == NONE {
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return Err(err("point outside the super-triangle"));
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}
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t = next;
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continue 'walk;
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}
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}
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return Ok(t);
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}
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self.tris.iter().position(|tri| tri.alive && contains(tri, &self.p2, p)).map(|i| i as u32).ok_or_else(|| err("point location failed"))
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}
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fn any_alive(&self) -> Result<u32> {
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self.tris.iter().position(|t| t.alive).map(|i| i as u32).ok_or_else(|| err("no triangles"))
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}
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/// Insert vertex `v` (already in `pts`). Boundary points (`steiner == None`) must be inserted.
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/// Steiner points (`Some(min_distance)`) may be rejected (outside the region, closer than
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/// `min_distance` to a vertex, or no valid cavity), leaving the triangulation unchanged;
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/// returns whether the point went in.
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fn insert(&mut self, v: u32, steiner: Option<f64>) -> Result<bool> {
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let p = *self.p(v)?;
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let t0 = self.locate(&p, self.last)?;
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let tri0 = *self.t(t0)?;
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for &u in &tri0.v {
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if self.p(u)?.coords() == p.coords() {
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return match steiner {
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Some(_) => Ok(false),
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None => Err(err("repeated point")),
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};
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}
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}
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if steiner.is_some() && !tri0.inside {
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return Ok(false);
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}
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let mut excluded: Vec<u32> = Vec::new();
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for _ in 0..MAX_CAVITY_ROUNDS {
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let (cavity, edges) = self.cavity(t0, &p, &excluded)?;
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let mut bad: Vec<u32> = Vec::new();
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// A constrained edge inside the cavity: drop the triangle on the far side from p.
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for &t in &cavity {
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let tri = *self.t(t)?;
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for i in 0..3 {
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if tri.fixed[i] && tri.n[i] != NONE && self.marked(tri.n[i]) {
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let (a, b) = (tri.v[(i + 1) % 3], tri.v[(i + 2) % 3]);
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if orient2d(self.p(a)?, self.p(b)?, &p) != Sign::Positive {
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bad.push(t);
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}
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}
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}
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}
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// Every new triangle (a, b, p) must be counterclockwise.
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for &(a, b, _, _, owner) in &edges {
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if orient2d(self.p(a)?, self.p(b)?, &p) != Sign::Positive {
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bad.push(owner);
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}
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}
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if let Some(min_distance) = steiner {
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let pc = p.coords();
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for &(a, _, _, _, _) in &edges {
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let pa = self.xy(a)?;
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if (pa[0] - pc[0]).powi(2) + (pa[1] - pc[1]).powi(2) < min_distance * min_distance {
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return Ok(false);
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}
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}
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}
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if bad.is_empty() && edges.len() == cavity.len() + 2 {
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self.retriangulate(v, &cavity, &edges, tri0.inside)?;
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return Ok(true);
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}
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if bad.contains(&t0) || bad.is_empty() {
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break;
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}
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excluded.extend(bad);
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excluded.sort_unstable();
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excluded.dedup();
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}
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match steiner {
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Some(_) => Ok(false),
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None => Err(err("no valid cavity for a boundary point")),
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}
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}
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fn marked(&self, t: u32) -> bool {
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self.mark.get(t as usize).is_some_and(|&m| m == self.epoch)
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}
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/// The Bowyer–Watson cavity of `p` from `t0` (never crossing constrained edges, skipping
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/// `excluded`), marked with the current epoch, and its boundary edges `(a, b, outside
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/// neighbour, constrained, owner)` with the cavity on their left.
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#[allow(clippy::type_complexity)]
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fn cavity(&mut self, t0: u32, p: &Point2, excluded: &[u32]) -> Result<(Vec<u32>, Vec<(u32, u32, u32, bool, u32)>)> {
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self.epoch = self.epoch.wrapping_add(1);
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if self.epoch == 0 {
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self.mark.iter_mut().for_each(|m| *m = 0);
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self.epoch = 1;
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}
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let epoch = self.epoch;
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let set = |mark: &mut Vec<u32>, t: u32| {
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if let Some(m) = mark.get_mut(t as usize) {
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*m = epoch;
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}
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};
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set(&mut self.mark, t0);
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let mut cavity = vec![t0];
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let mut k = 0;
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while let Some(&t) = cavity.get(k) {
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k += 1;
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let tri = *self.t(t)?;
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for i in 0..3 {
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let nb = tri.n[i];
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if nb == NONE || tri.fixed[i] || self.marked(nb) || excluded.binary_search(&nb).is_ok() {
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continue;
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}
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let o = *self.t(nb)?;
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if incircle(self.p(o.v[0])?, self.p(o.v[1])?, self.p(o.v[2])?, p) == Sign::Positive {
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set(&mut self.mark, nb);
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cavity.push(nb);
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}
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}
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}
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let mut edges = Vec::new();
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for &t in &cavity {
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let tri = *self.t(t)?;
|
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for i in 0..3 {
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let nb = tri.n[i];
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// Shared with another cavity triangle (a constrained one is reported by `insert`).
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if nb != NONE && self.marked(nb) {
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continue;
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}
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edges.push((tri.v[(i + 1) % 3], tri.v[(i + 2) % 3], nb, tri.fixed[i], t));
|
||||
}
|
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}
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Ok((cavity, edges))
|
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}
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fn retriangulate(&mut self, v: u32, cavity: &[u32], edges: &[(u32, u32, u32, bool, u32)], inside: bool) -> Result<()> {
|
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for &t in cavity {
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self.tm(t)?.alive = false;
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self.free.push(t);
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}
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let mut made: Vec<(u32, u32, u32)> = Vec::with_capacity(edges.len()); // (a, b, tri)
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for &(a, b, nb, fixed, _) in edges {
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let t = self.alloc(Tri { v: [a, b, v], n: [NONE, NONE, nb], fixed: [false, false, fixed], inside, alive: true })?;
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made.push((a, b, t));
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if nb != NONE {
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self.relink(nb, a, b, t)?;
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||||
}
|
||||
}
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let mut by_a: Vec<(u32, u32)> = made.iter().map(|&(a, _, t)| (a, t)).collect();
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let mut by_b: Vec<(u32, u32)> = made.iter().map(|&(_, b, t)| (b, t)).collect();
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by_a.sort_unstable();
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||||
by_b.sort_unstable();
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let find = |list: &[(u32, u32)], key: u32| -> Result<u32> {
|
||||
let i = list.binary_search_by_key(&key, |e| e.0).map_err(|_| err("cavity boundary is not a closed loop"))?;
|
||||
list.get(i).map(|e| e.1).ok_or_else(|| err("cavity lookup"))
|
||||
};
|
||||
for &(a, b, t) in &made {
|
||||
let next = find(&by_a, b)?; // the triangle (b, c, v): shares edge b–v
|
||||
let prev = find(&by_b, a)?; // the triangle (z, a, v): shares edge v–a
|
||||
let tri = self.tm(t)?;
|
||||
tri.n[0] = next;
|
||||
tri.n[1] = prev;
|
||||
for u in [a, b, v] {
|
||||
if let Some(x) = self.vt.get_mut(u as usize) {
|
||||
*x = t;
|
||||
}
|
||||
}
|
||||
self.last = t;
|
||||
}
|
||||
Ok(())
|
||||
}
|
||||
|
||||
/// In triangle `t`, point the edge from `b` to `a` at `to`.
|
||||
fn relink(&mut self, t: u32, a: u32, b: u32, to: u32) -> Result<()> {
|
||||
let tri = self.tm(t)?;
|
||||
let i = edge_index(tri, b, a).ok_or_else(|| err("neighbour does not share the edge"))?;
|
||||
tri.n[i] = to;
|
||||
Ok(())
|
||||
}
|
||||
|
||||
/// Visit the triangles around vertex `v` counterclockwise, each with `v`'s local index,
|
||||
/// until `visit` returns a value (or the rotation closes: `None`).
|
||||
fn around<R>(&self, v: u32, mut visit: impl FnMut(u32, &Tri, usize) -> Result<Option<R>>) -> Result<Option<R>> {
|
||||
let start = self.vt.get(v as usize).copied().ok_or_else(|| err("vertex"))?;
|
||||
let mut t = start;
|
||||
for _ in 0..self.tris.len() + 1 {
|
||||
let tri = self.t(t)?;
|
||||
let k = tri.v.iter().position(|&x| x == v).ok_or_else(|| err("vertex map is stale"))?;
|
||||
if let Some(r) = visit(t, tri, k)? {
|
||||
return Ok(Some(r));
|
||||
}
|
||||
t = tri.n[(k + 1) % 3];
|
||||
if t == NONE || t == start {
|
||||
return Ok(None);
|
||||
}
|
||||
}
|
||||
Err(err("vertex rotation did not close"))
|
||||
}
|
||||
|
||||
/// The triangle and local index of the directed edge `a → b` (the edge opposite `v[i]` runs
|
||||
/// from `v[i+1]` to `v[i+2]`).
|
||||
fn find_edge(&self, a: u32, b: u32) -> Result<Option<(u32, usize)>> {
|
||||
self.around(a, |t, tri, k| Ok((tri.v[(k + 1) % 3] == b).then_some((t, (k + 2) % 3))))
|
||||
}
|
||||
|
||||
/// Flip the edge opposite `v[i]` of `t`. Returns the new edge's end points.
|
||||
fn flip(&mut self, t: u32, i: usize) -> Result<(u32, u32)> {
|
||||
let a = *self.t(t)?;
|
||||
let (p, q, r) = (a.v[i], a.v[(i + 1) % 3], a.v[(i + 2) % 3]);
|
||||
let t2 = a.n[i];
|
||||
let b = *self.t(t2)?;
|
||||
let j = edge_index(&b, r, q).ok_or_else(|| err("flip: neighbour mismatch"))?;
|
||||
let s = b.v[j];
|
||||
let (n_pq, f_pq) = (a.n[(i + 2) % 3], a.fixed[(i + 2) % 3]);
|
||||
let (n_rp, f_rp) = (a.n[(i + 1) % 3], a.fixed[(i + 1) % 3]);
|
||||
let (n_sr, f_sr) = (b.n[(j + 2) % 3], b.fixed[(j + 2) % 3]);
|
||||
let (n_qs, f_qs) = (b.n[(j + 1) % 3], b.fixed[(j + 1) % 3]);
|
||||
*self.tm(t)? = Tri { v: [p, q, s], n: [n_qs, t2, n_pq], fixed: [f_qs, false, f_pq], inside: a.inside, alive: true };
|
||||
*self.tm(t2)? = Tri { v: [p, s, r], n: [n_sr, n_rp, t], fixed: [f_sr, f_rp, false], inside: b.inside, alive: true };
|
||||
if n_qs != NONE {
|
||||
self.relink(n_qs, q, s, t)?;
|
||||
}
|
||||
if n_rp != NONE {
|
||||
self.relink(n_rp, r, p, t2)?;
|
||||
}
|
||||
for (u, x) in [(p, t), (q, t), (s, t2), (r, t2)] {
|
||||
if let Some(y) = self.vt.get_mut(u as usize) {
|
||||
*y = x;
|
||||
}
|
||||
}
|
||||
Ok((p, s))
|
||||
}
|
||||
|
||||
/// The edge opposite `v[i]` of `t` with its far vertex, when it is flippable (strictly convex
|
||||
/// quadrilateral).
|
||||
fn flippable(&self, t: u32, i: usize) -> Result<Option<u32>> {
|
||||
let a = *self.t(t)?;
|
||||
let t2 = a.n[i];
|
||||
if t2 == NONE || a.fixed[i] {
|
||||
return Ok(None);
|
||||
}
|
||||
let (p, q, r) = (a.v[i], a.v[(i + 1) % 3], a.v[(i + 2) % 3]);
|
||||
let b = *self.t(t2)?;
|
||||
let s = b.v[edge_index(&b, r, q).ok_or_else(|| err("neighbour mismatch"))?];
|
||||
let (pp, ps) = (self.p(p)?, self.p(s)?);
|
||||
Ok((orient2d(pp, ps, self.p(q)?) * orient2d(pp, ps, self.p(r)?) == Sign::Negative).then_some(s))
|
||||
}
|
||||
|
||||
/// Make `a–b` an edge (Sloan 1993) and mark it constrained.
|
||||
fn recover(&mut self, a: u32, b: u32) -> Result<()> {
|
||||
if self.find_edge(a, b)?.is_none() {
|
||||
let crossing = self.crossing_edges(a, b)?;
|
||||
let (pa, pb) = (*self.p(a)?, *self.p(b)?);
|
||||
let mut queue: VecDeque<(u32, u32)> = crossing.into_iter().collect();
|
||||
let cap = 1000 + 16 * queue.len() * queue.len();
|
||||
let mut fresh = Vec::new();
|
||||
let mut steps = 0usize;
|
||||
while let Some((u, w)) = queue.pop_front() {
|
||||
steps += 1;
|
||||
if steps > cap {
|
||||
return Err(Error::Limit(format!("boundary edge recovery did not finish in {cap} flips")));
|
||||
}
|
||||
let (t, i) = self.find_edge(u, w)?.ok_or_else(|| err("crossing edge vanished"))?;
|
||||
match self.flippable(t, i)? {
|
||||
Some(_) => {
|
||||
let (x, y) = self.flip(t, i)?;
|
||||
let crosses =
|
||||
x != a && x != b && y != a && y != b && orient2d(&pa, &pb, self.p(x)?) * orient2d(&pa, &pb, self.p(y)?) == Sign::Negative;
|
||||
if crosses { queue.push_back((x, y)) } else { fresh.push((x, y)) }
|
||||
}
|
||||
None => queue.push_back((u, w)),
|
||||
}
|
||||
}
|
||||
self.mark_fixed(a, b)?;
|
||||
self.lawson(fresh)?;
|
||||
return Ok(());
|
||||
}
|
||||
self.mark_fixed(a, b)
|
||||
}
|
||||
|
||||
fn mark_fixed(&mut self, a: u32, b: u32) -> Result<()> {
|
||||
let (t, i) = self.find_edge(a, b)?.ok_or_else(|| err("recovered edge is missing"))?;
|
||||
let nb = self.t(t)?.n[i];
|
||||
self.tm(t)?.fixed[i] = true;
|
||||
if nb != NONE {
|
||||
let tri = self.tm(nb)?;
|
||||
if let Some(k) = edge_index(tri, b, a) {
|
||||
tri.fixed[k] = true;
|
||||
}
|
||||
}
|
||||
Ok(())
|
||||
}
|
||||
|
||||
/// The edges crossed by the open segment `a–b`, from `a` to `b`.
|
||||
fn crossing_edges(&self, a: u32, b: u32) -> Result<Vec<(u32, u32)>> {
|
||||
let (pa, pb) = (*self.p(a)?, *self.p(b)?);
|
||||
let found = self.around(a, |t, tri, k| {
|
||||
let (u, w) = (tri.v[(k + 1) % 3], tri.v[(k + 2) % 3]);
|
||||
let (ou, ow) = (orient2d(&pa, self.p(u)?, &pb), orient2d(&pa, self.p(w)?, &pb));
|
||||
if ou.is_zero() || ow.is_zero() {
|
||||
let x = if ou.is_zero() { u } else { w };
|
||||
let px = self.xy(x)?;
|
||||
let (qa, qb) = (pa.coords(), pb.coords());
|
||||
if (px[0] - qa[0]) * (qb[0] - qa[0]) + (px[1] - qa[1]) * (qb[1] - qa[1]) > 0.0 {
|
||||
return Err(Error::Invalid("a point lies on a boundary edge".into()));
|
||||
}
|
||||
}
|
||||
Ok((ou == Sign::Positive && ow == Sign::Negative).then_some((t, u, w)))
|
||||
})?;
|
||||
let (mut t, mut right, mut left) = found.ok_or_else(|| err("segment start not found"))?;
|
||||
let mut out = vec![(right, left)];
|
||||
for _ in 0..self.tris.len() + 1 {
|
||||
let tri = *self.t(t)?;
|
||||
let i = tri.v.iter().position(|&x| x != right && x != left).ok_or_else(|| err("walk"))?;
|
||||
let next = tri.n[i];
|
||||
let nt = *self.t(next)?;
|
||||
let d = *nt.v.iter().find(|&&x| x != right && x != left).ok_or_else(|| err("walk"))?;
|
||||
if d == b {
|
||||
return Ok(out);
|
||||
}
|
||||
match orient2d(&pa, &pb, self.p(d)?) {
|
||||
Sign::Positive => left = d,
|
||||
Sign::Negative => right = d,
|
||||
Sign::Zero => return Err(Error::Invalid("a point lies on a boundary edge".into())),
|
||||
}
|
||||
out.push((right, left));
|
||||
t = next;
|
||||
}
|
||||
Err(err("segment walk did not reach its end"))
|
||||
}
|
||||
|
||||
/// Lawson flips from the given edges until every unconstrained edge is locally Delaunay.
|
||||
fn lawson(&mut self, edges: Vec<(u32, u32)>) -> Result<()> {
|
||||
let mut stack = edges;
|
||||
let cap = 1000 + 64 * self.tris.len();
|
||||
let mut steps = 0usize;
|
||||
while let Some((u, w)) = stack.pop() {
|
||||
steps += 1;
|
||||
if steps > cap {
|
||||
return Err(Error::Limit("Delaunay restoration did not finish".into()));
|
||||
}
|
||||
let Some((t, i)) = self.find_edge(u, w)? else { continue };
|
||||
let tri = *self.t(t)?;
|
||||
if tri.fixed[i] || tri.n[i] == NONE {
|
||||
continue;
|
||||
}
|
||||
let Some(s) = self.flippable(t, i)? else { continue };
|
||||
let [a, b, c] = tri.v;
|
||||
if incircle(self.p(a)?, self.p(b)?, self.p(c)?, self.p(s)?) != Sign::Positive {
|
||||
continue;
|
||||
}
|
||||
let (p, _) = self.flip(t, i)?;
|
||||
let (q, r) = (tri.v[(i + 1) % 3], tri.v[(i + 2) % 3]);
|
||||
stack.extend([(p, q), (q, s), (s, r), (r, p)]);
|
||||
}
|
||||
Ok(())
|
||||
}
|
||||
|
||||
/// Mark the triangles inside the region: those separated from the super-triangle by an odd
|
||||
/// number of constrained edges.
|
||||
fn classify(&mut self) -> Result<()> {
|
||||
let n = self.tris.len();
|
||||
let mut depth = vec![u32::MAX; n];
|
||||
let start = self.vt.get(self.pts.len().saturating_sub(1)).copied().ok_or_else(|| err("super vertex"))?;
|
||||
let mut current = vec![start];
|
||||
if let Some(d) = depth.get_mut(start as usize) {
|
||||
*d = 0;
|
||||
}
|
||||
let mut level = 0u32;
|
||||
while !current.is_empty() {
|
||||
let mut next = Vec::new();
|
||||
let mut k = 0;
|
||||
while let Some(&t) = current.get(k) {
|
||||
k += 1;
|
||||
let tri = *self.t(t)?;
|
||||
for i in 0..3 {
|
||||
let nb = tri.n[i];
|
||||
if nb == NONE || depth.get(nb as usize).is_none_or(|&d| d != u32::MAX) {
|
||||
continue;
|
||||
}
|
||||
if tri.fixed[i] {
|
||||
next.push(nb);
|
||||
} else {
|
||||
if let Some(d) = depth.get_mut(nb as usize) {
|
||||
*d = level;
|
||||
}
|
||||
current.push(nb);
|
||||
}
|
||||
}
|
||||
}
|
||||
level += 1;
|
||||
next.retain(|&t| depth.get(t as usize).is_some_and(|&d| d == u32::MAX));
|
||||
next.sort_unstable();
|
||||
next.dedup();
|
||||
for &t in &next {
|
||||
if let Some(d) = depth.get_mut(t as usize) {
|
||||
*d = level;
|
||||
}
|
||||
}
|
||||
current = next;
|
||||
if level > 4 {
|
||||
break;
|
||||
}
|
||||
}
|
||||
for (tri, d) in self.tris.iter_mut().zip(depth) {
|
||||
tri.inside = tri.alive && d == 1;
|
||||
}
|
||||
Ok(())
|
||||
}
|
||||
|
||||
/// Try to insert Steiner point `p` (located from `hint`), at least `min_distance` from the
|
||||
/// vertices of its cavity.
|
||||
fn try_steiner(&mut self, p: Point2, hint: u32, min_distance: f64) -> Result<bool> {
|
||||
let v = self.pts.len() as u32;
|
||||
self.pts.push(p.coords());
|
||||
self.p2.push(p);
|
||||
self.vt.push(NONE);
|
||||
self.last = hint;
|
||||
let ok = self.insert(v, Some(min_distance))?;
|
||||
if !ok {
|
||||
self.pts.pop();
|
||||
self.p2.pop();
|
||||
self.vt.pop();
|
||||
}
|
||||
Ok(ok)
|
||||
}
|
||||
|
||||
/// Delaunay refinement of the inside triangles to `scale × size field`. A Steiner point `p`
|
||||
/// for local size `h` is skipped when `allows(p, h)` refuses it (the caller's clearance from
|
||||
/// the true boundary) or when it comes closer than [`CLEARANCE`]` × h` to a vertex.
|
||||
pub fn refine(&mut self, size: &dyn SizeField, scale: f64, allows: &dyn Fn(&Point2, f64) -> bool) -> Result<()> {
|
||||
for _ in 0..MAX_REFINE_PASSES {
|
||||
let mut inserted = 0usize;
|
||||
let n = self.tris.len();
|
||||
for t in 0..n as u32 {
|
||||
let tri = *self.t(t)?;
|
||||
if !tri.alive || !tri.inside {
|
||||
continue;
|
||||
}
|
||||
let [a, b, c] = [self.xy(tri.v[0])?, self.xy(tri.v[1])?, self.xy(tri.v[2])?];
|
||||
let centroid = [(a[0] + b[0] + c[0]) / 3.0, (a[1] + b[1] + c[1]) / 3.0];
|
||||
let h = scale * checked_size(size, [centroid[0], centroid[1], 0.0])?;
|
||||
let (bx, by, cx, cy) = (b[0] - a[0], b[1] - a[1], c[0] - a[0], c[1] - a[1]);
|
||||
let d = 2.0 * (bx * cy - by * cx);
|
||||
let (b2, c2) = (bx * bx + by * by, cx * cx + cy * cy);
|
||||
let (ux, uy) = ((cy * b2 - by * c2) / d, (bx * c2 - cx * b2) / d);
|
||||
let r = (ux * ux + uy * uy).sqrt();
|
||||
let shortest = b2.min(c2).min((cx - bx).powi(2) + (cy - by).powi(2)).sqrt();
|
||||
if !r.is_finite() || !(d > 0.0) {
|
||||
continue;
|
||||
}
|
||||
let too_big = r > 0.75 * h;
|
||||
let poor = r > std::f64::consts::SQRT_2 * shortest;
|
||||
if !too_big && !poor {
|
||||
continue;
|
||||
}
|
||||
let candidates = [Some([a[0] + ux, a[1] + uy]), too_big.then_some(centroid)];
|
||||
for c in candidates.into_iter().flatten() {
|
||||
if let Some(p) = steiner_point(c).filter(|p| allows(p, h))
|
||||
&& self.try_steiner(p, t, CLEARANCE * h)?
|
||||
{
|
||||
inserted += 1;
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
if inserted == 0 {
|
||||
break;
|
||||
}
|
||||
}
|
||||
#[cfg(test)]
|
||||
assert_eq!(self.verify(), Ok(()), "after refinement");
|
||||
Ok(())
|
||||
}
|
||||
|
||||
/// The inside triangles around vertex `v`.
|
||||
fn inside_fan(&self, v: u32) -> Result<Vec<u32>> {
|
||||
let mut fan = Vec::new();
|
||||
self.around(v, |t, tri, _| {
|
||||
if tri.inside {
|
||||
fan.push(t);
|
||||
}
|
||||
Ok(None::<()>)
|
||||
})?;
|
||||
Ok(fan)
|
||||
}
|
||||
|
||||
/// [`Cdt::ensure_fan`] for every vertex with its count in `need`.
|
||||
pub fn ensure_fans(&mut self, need: &[usize]) -> Result<()> {
|
||||
for (v, &k) in need.iter().enumerate() {
|
||||
if k > 1 {
|
||||
self.ensure_fan(v as u32, k)?;
|
||||
}
|
||||
}
|
||||
#[cfg(test)]
|
||||
assert_eq!(self.verify(), Ok(()), "after fans");
|
||||
Ok(())
|
||||
}
|
||||
|
||||
/// Give boundary vertex `v` at least `count` inside triangles by inserting the centroid of
|
||||
/// its widest triangle (bounded attempts; the caller's validity gate judges the result).
|
||||
fn ensure_fan(&mut self, v: u32, count: usize) -> Result<()> {
|
||||
for _ in 0..count + 2 {
|
||||
let fan = self.inside_fan(v)?;
|
||||
if fan.len() >= count {
|
||||
return Ok(());
|
||||
}
|
||||
let pv = self.xy(v)?;
|
||||
let mut widest: Option<(f64, u32, [f64; 2])> = None;
|
||||
for &t in &fan {
|
||||
let tri = *self.t(t)?;
|
||||
let k = tri.v.iter().position(|&x| x == v).ok_or_else(|| err("fan"))?;
|
||||
let (a, b) = (self.xy(tri.v[(k + 1) % 3])?, self.xy(tri.v[(k + 2) % 3])?);
|
||||
let (u, w) = ([a[0] - pv[0], a[1] - pv[1]], [b[0] - pv[0], b[1] - pv[1]]);
|
||||
let cos = (u[0] * w[0] + u[1] * w[1]) / ((u[0] * u[0] + u[1] * u[1]).sqrt() * (w[0] * w[0] + w[1] * w[1]).sqrt());
|
||||
let c = [(pv[0] + a[0] + b[0]) / 3.0, (pv[1] + a[1] + b[1]) / 3.0];
|
||||
if widest.is_none_or(|(m, _, _)| cos < m) {
|
||||
widest = Some((cos, t, c));
|
||||
}
|
||||
}
|
||||
let Some((t, p)) = widest.and_then(|(_, t, c)| steiner_point(c).map(|p| (t, p))) else { return Ok(()) };
|
||||
if !self.try_steiner(p, t, 0.0)? {
|
||||
return Ok(());
|
||||
}
|
||||
}
|
||||
Ok(())
|
||||
}
|
||||
|
||||
/// Consistency check for tests: every live triangle counterclockwise (exact), neighbours
|
||||
/// mutual, constrained flags matching on both sides.
|
||||
#[cfg(test)]
|
||||
pub fn verify(&self) -> std::result::Result<(), String> {
|
||||
for (t, tri) in self.tris.iter().enumerate() {
|
||||
if !tri.alive {
|
||||
continue;
|
||||
}
|
||||
let [a, b, c] = tri.v;
|
||||
let o = orient2d(&self.p2[a as usize], &self.p2[b as usize], &self.p2[c as usize]);
|
||||
if o != Sign::Positive {
|
||||
return Err(format!("triangle {t} {:?} has orientation {o:?} (inside {})", tri.v, tri.inside));
|
||||
}
|
||||
for i in 0..3 {
|
||||
let nb = tri.n[i];
|
||||
if nb == NONE {
|
||||
continue;
|
||||
}
|
||||
let o = &self.tris[nb as usize];
|
||||
let (p, q) = (tri.v[(i + 1) % 3], tri.v[(i + 2) % 3]);
|
||||
let back = (0..3).find(|&j| o.v[(j + 1) % 3] == q && o.v[(j + 2) % 3] == p);
|
||||
match back {
|
||||
Some(j) if o.n[j] == t as u32 && o.alive && o.fixed[j] == tri.fixed[i] => {
|
||||
let s = o.v[j];
|
||||
if !tri.fixed[i]
|
||||
&& incircle(&self.p2[a as usize], &self.p2[b as usize], &self.p2[c as usize], &self.p2[s as usize]) == Sign::Positive
|
||||
{
|
||||
return Err(format!("triangle {t} edge {i} is not locally Delaunay (inside {})", tri.inside));
|
||||
}
|
||||
}
|
||||
_ => return Err(format!("triangle {t} edge {i}: neighbour {nb} does not match")),
|
||||
}
|
||||
}
|
||||
}
|
||||
Ok(())
|
||||
}
|
||||
|
||||
/// The inside triangles.
|
||||
pub fn into_triangulation(self) -> Triangulation {
|
||||
let tris = self.tris.iter().filter(|t| t.alive && t.inside).map(|t| t.v).collect();
|
||||
Triangulation { pts: self.pts, p2: self.p2, tris }
|
||||
}
|
||||
}
|
||||
Reference in new issue
Block a user