From e4290c736670b66d524016ea658d77b619e72be1 Mon Sep 17 00:00:00 2001 From: jyviko <2501648+jyviko@users.noreply.github.com> Date: Fri, 16 Oct 2026 19:26:42 -0400 Subject: [PATCH] mesh: faster tet improvement (#84) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Profile-driven (thin-ribs: 76% of the improvement in the topological operations, most of it in face removal walking whole edge rings to find one neighbour; pinhole-block: 44% in the smoothing passes). Same results, less work: - face removal finds the sandwiched face across a ring edge through the tetrahedron it already holds (O(1) instead of an edge ring), keeps the candidate tetrahedra of ring edges between rounds and updates the removed worst incrementally; - Klincsek's table for edge removal starts at the quality to beat, so triangles that cannot help are never evaluated; - a change clock per vertex: a topological operation (per tetrahedron, per edge, per face and side) or a smoothing that failed is not tried again until a tetrahedron it reads changes (exact: the operations are functions of that region; checked by re-running them); - the quality of a live tetrahedron is cached per slot until one of its vertices is touched; - smoothing line searches stop at the first tetrahedron that does not beat the worst, and gradients are computed only near the worst; - the journal saves the free list's tail instead of the whole list. For the clock to be exact, the quality is the same bits for every listing of a tetrahedron with the same orientation (corners in a canonical even order), and a closed edge ring starts at its smallest vertex. Changed results: - smoothing uses the analytic gradient of the smallest dihedral sine (Klingner and Shewchuk 2007 §3.1; Freitag and Ollivier-Gooch 1997) instead of central differences (kept for flat or inverted tetrahedra); - the composite insertion runs its topological passes on the new vertex's tetrahedra below the threshold, and smooths the neighbours whose star has one, as the passes do. Tests: analytic gradient against central differences, quality the same for every even reordering, cached qualities equal fresh ones after improvement, rollbacks restore every slot; the washer fingerprint moves (the same on arm64 and x86-64). Co-Authored-By: Claude Opus 5.5 Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo --- crates/mesh/src/tet/complex.rs | 174 +++++++++++++++++++++++- crates/mesh/src/tet/improve.rs | 61 +++++---- crates/mesh/src/tet/measure.rs | 171 +++++++++++++++++++++-- crates/mesh/src/tet/ops.rs | 139 ++++++++++++------- crates/mesh/src/tet/smooth.rs | 74 ++++++++-- crates/mesh/src/tet/tests.rs | 61 ++++++++- docs/meshing/literature.md | 9 +- docs/meshing/skill-results.md | 4 +- docs/meshing/skill/filleted-bracket.png | Bin 85588 -> 84149 bytes docs/meshing/skill/sphere-on-plate.png | Bin 109417 -> 107257 bytes 10 files changed, 587 insertions(+), 106 deletions(-) diff --git a/crates/mesh/src/tet/complex.rs b/crates/mesh/src/tet/complex.rs index 7bdfee6..012a205 100644 --- a/crates/mesh/src/tet/complex.rs +++ b/crates/mesh/src/tet/complex.rs @@ -170,7 +170,9 @@ pub enum Step { pub struct Raw { slots: Vec<(u32, [u32; 4], [u32; 4], [u32; 4])>, tets_len: usize, - free: Vec, + /// The free list's length, and its last entries (those the change may take). + free_len: usize, + free_tail: Vec, vtets: Vec<(u32, Vec)>, live: usize, } @@ -199,6 +201,21 @@ pub struct TetComplex { frozen: Vec, mark: Vec, epoch: u32, + /// Change clock: `touched[v]` is the clock of the last change to a tetrahedron of `v`'s star + /// (made, removed, reshaped or restored), `failed[t]` the clock at which every topological + /// operation on slot `t` last failed ([`Self::known_to_fail`]). + clock: u64, + touched: Vec, + failed: Vec, + /// The clock at which removing an edge `(a, b)` (sorted), or a face from apex `a`'s side to apex `b` (sorted face) + /// last failed: the operation reads only the tetrahedra holding both apexes. + failed_edges: IdMap<(u32, u32), u64>, + failed_faces: IdMap<(u32, u32, [u32; 3]), u64>, + /// Per slot: the quality ([`super::measure::quality`]) and one more than the clock it was + /// computed at; current while no vertex of the tetrahedron was touched since. + quality_cache: std::cell::RefCell>, + /// The clock at which smoothing a vertex last found no move. + failed_smoothing: Vec, live: usize, max_tets: usize, max_points: usize, @@ -281,6 +298,13 @@ impl TetComplex { frozen: Vec::new(), mark: vec![0; tets.len()], epoch: 0, + clock: 0, + touched: vec![0; points.len()], + failed: Vec::new(), + failed_edges: IdMap::default(), + failed_faces: IdMap::default(), + failed_smoothing: Vec::new(), + quality_cache: std::cell::RefCell::new(Vec::new()), live: tets.len(), max_tets, max_points, @@ -355,6 +379,125 @@ impl TetComplex { if let Some(s) = self.kinds.get_mut(v as usize) { *s = k; } + self.touch_star(v); + } + + // ---- change clock ---- + + fn touch(&mut self, vs: &[u32]) { + self.clock += 1; + for &v in vs { + if let Some(s) = self.touched.get_mut(v as usize) { + *s = self.clock; + } + } + } + + /// Touch `v` and every vertex of its star (moving `v` reshapes those tetrahedra). + fn touch_star(&mut self, v: u32) { + let mut vs = vec![v]; + for &t in self.vtets.get(v as usize).map(Vec::as_slice).unwrap_or_default() { + vs.extend(self.tets.get(t as usize).copied().unwrap_or([NONE; 4])); + } + self.touch(&vs); + } + + /// The last change near tetrahedron `t`: in the stars of its vertices and of its neighbours' + /// vertices, the region every topological operation on `t` reads. + fn stamp(&self, t: u32) -> Result { + let mut m = 0; + let mut look = |vs: [u32; 4]| { + for v in vs { + m = m.max(self.touched.get(v as usize).copied().unwrap_or(u64::MAX)); + } + }; + look(self.tet(t)?); + for n in self.adj(t)? { + if n != NONE { + look(self.tet(n)?); + } + } + Ok(m) + } + + fn touched_at(&self, v: u32) -> u64 { + self.touched.get(v as usize).copied().unwrap_or(u64::MAX) + } + + /// Record that removing edge `ab` failed now. + pub fn mark_edge_failed(&mut self, a: u32, b: u32) { + self.failed_edges.insert(sorted2(a, b), self.clock); + } + + /// Whether removing edge `ab` failed and no tetrahedron around `a` or `b` changed since. + pub fn edge_known_to_fail(&self, a: u32, b: u32) -> bool { + self.failed_edges.get(&sorted2(a, b)).is_some_and(|&f| self.touched_at(a).max(self.touched_at(b)) <= f) + } + + /// Record that removing `face` between apexes `a` and `b` failed now. + pub fn mark_face_failed(&mut self, a: u32, b: u32, face: [u32; 3]) { + self.failed_faces.insert((a, b, sorted3(face)), self.clock); + } + + /// Whether removing `face` between `a` and `b` failed and nothing around them changed since. + pub fn face_known_to_fail(&self, a: u32, b: u32, face: [u32; 3]) -> bool { + self.failed_faces.get(&(a, b, sorted3(face))).is_some_and(|&f| self.touched_at(a).max(self.touched_at(b)) <= f) + } + + /// The quality of live tetrahedron `t`, computed once per change of its vertices. + pub fn slot_quality(&self, t: u32) -> Result { + let vs = self.tet(t)?; + let stamp = vs.iter().map(|&v| self.touched_at(v)).max().unwrap_or(u64::MAX); + let i = t as usize; + if let Some(&(c, q)) = self.quality_cache.borrow().get(i) + && c > stamp + { + return Ok(q); + } + let q = super::measure::quality(&self.coords(vs)?); + let mut cache = self.quality_cache.borrow_mut(); + if cache.len() <= i { + cache.resize(i + 1, (0, 0.0)); + } + if let Some(e) = cache.get_mut(i) { + *e = (self.clock + 1, q); + } + Ok(q) + } + + /// Record that smoothing `v` found no move now. + pub fn mark_smoothing_failed(&mut self, v: u32) { + let i = v as usize; + if self.failed_smoothing.len() <= i { + self.failed_smoothing.resize(i + 1, 0); + } + if let Some(f) = self.failed_smoothing.get_mut(i) { + *f = self.clock; + } + } + + /// Whether smoothing `v` found no move and no tetrahedron around it changed since. + pub fn smoothing_known_to_fail(&self, v: u32) -> bool { + self.failed_smoothing.get(v as usize).is_some_and(|&f| f > 0 && self.touched_at(v) <= f) + } + + /// Record that every topological operation on `t` failed now. + pub fn mark_failed(&mut self, t: u32) { + let i = t as usize; + if self.failed.len() <= i { + self.failed.resize(i + 1, 0); + } + if let Some(f) = self.failed.get_mut(i) { + *f = self.clock; + } + } + + /// Whether the topological operations on `t` failed and nothing they read has changed + /// since, so trying again would fail the same way (they are deterministic functions of that + /// region). + pub fn known_to_fail(&self, t: u32) -> Result { + let Some(&f) = self.failed.get(t as usize) else { return Ok(false) }; + Ok(f > 0 && self.stamp(t)? <= f) } pub fn slots(&self) -> usize { @@ -424,6 +567,7 @@ impl TetComplex { pub fn set_curve(&mut self, a: u32, b: u32, curve: Option) { let key = sorted2(a, b); + self.touch(&[a, b]); let before = match curve { Some(c) => self.curves.insert(key, c), None => self.curves.remove(&key), @@ -688,6 +832,7 @@ impl TetComplex { self.pts.push(p); self.kinds.push(kind); self.vtets.push(Vec::new()); + self.touched.push(self.clock); if self.journal.recording { self.journal.steps.push(Step::Added { v }); } @@ -695,7 +840,7 @@ impl TetComplex { } /// The data a change of `slots` and of the incidence of `verts` would overwrite. - fn snapshot(&self, slots: &[u32], verts: &[u32]) -> Raw { + fn snapshot(&self, slots: &[u32], verts: &[u32], takes: usize) -> Raw { let mut ids: Vec = slots.to_vec(); ids.sort_unstable(); ids.dedup(); @@ -711,7 +856,8 @@ impl TetComplex { }) .collect(), tets_len: self.tets.len(), - free: self.free.clone(), + free_len: self.free.len(), + free_tail: self.free.get(self.free.len().saturating_sub(takes)..).unwrap_or_default().to_vec(), vtets: vs.into_iter().filter_map(|v| Some((v, self.vtets.get(v as usize)?.clone()))).collect(), live: self.live, } @@ -719,6 +865,12 @@ impl TetComplex { /// Put back what [`Self::snapshot`] saved. fn restore(&mut self, raw: Raw) { + let mut touched: Vec = raw.vtets.iter().map(|(v, _)| *v).collect(); + for (t, vs, _, _) in &raw.slots { + touched.extend(self.tets.get(*t as usize).copied().unwrap_or([NONE; 4])); + touched.extend(vs); + } + self.touch(&touched); for (v, l) in raw.vtets { if let Some(s) = self.vtets.get_mut(v as usize) { *s = l; @@ -734,7 +886,8 @@ impl TetComplex { self.adj.truncate(raw.tets_len); self.tags.truncate(raw.tets_len); self.mark.truncate(raw.tets_len); - self.free = raw.free; + self.free.truncate(raw.free_len.saturating_sub(raw.free_tail.len())); + self.free.extend(raw.free_tail); self.live = raw.live; } @@ -744,6 +897,7 @@ impl TetComplex { self.pts.pop(); self.kinds.pop(); self.vtets.pop(); + self.touched.pop(); return Ok(()); } Err(corrupt("dropping a vertex in use")) @@ -755,6 +909,7 @@ impl TetComplex { let slot = self.pts.get_mut(v as usize).ok_or_else(|| corrupt("vertex id"))?; let from = *slot; *slot = p; + self.touch_star(v); if self.journal.recording { self.journal.steps.push(Step::Moved { v, from }); } @@ -962,7 +1117,7 @@ impl TetComplex { for &t in old { verts.extend(self.tet(t)?); } - Some(Box::new(self.snapshot(&slots, &verts))) + Some(Box::new(self.snapshot(&slots, &verts, change.new.len()))) } else { None }; @@ -1002,6 +1157,9 @@ impl TetComplex { } } } + let mut changed: Vec = removed.iter().flat_map(|r| r.vs).collect(); + changed.extend(change.new.iter().flatten()); + self.touch(&changed); self.live = self.live - old.len() + ids.len(); if self.journal.recording { self.journal.steps.push(Step::Replaced { removed, added: change.new.clone(), raw: raw.unwrap_or_default() }); @@ -1044,7 +1202,7 @@ impl TetComplex { return Ok(false); } } - let raw = self.journal.recording.then(|| Box::new(self.snapshot(&[t, ns[k], ns[l]], &vs))); + let raw = self.journal.recording.then(|| Box::new(self.snapshot(&[t, ns[k], ns[l]], &vs, 0))); for m in [k, l] { let n = ns[m]; let nn = self.adj(n)?; @@ -1055,6 +1213,7 @@ impl TetComplex { } } self.unlink(t, vs); + self.touch(&vs); if let Some(s) = self.tets.get_mut(t as usize) { *s = [DEAD; 4]; } @@ -1122,15 +1281,18 @@ impl TetComplex { if let Some(s) = self.pts.get_mut(v as usize) { *s = from; } + self.touch_star(v); } Step::Added { v } => { if v as usize + 1 == self.pts.len() { self.pts.pop(); self.kinds.pop(); self.vtets.pop(); + self.touched.pop(); } } Step::Curve { edge, curve } => { + self.touch(&[edge.0, edge.1]); match curve { Some(c) => self.curves.insert(edge, c), None => self.curves.remove(&edge), diff --git a/crates/mesh/src/tet/improve.rs b/crates/mesh/src/tet/improve.rs index d515f69..8eaa910 100644 --- a/crates/mesh/src/tet/improve.rs +++ b/crates/mesh/src/tet/improve.rs @@ -24,7 +24,7 @@ use super::complex::{EDGES, IdMap, NONE, Step, TetComplex, VertexKind, Walk, fac use super::measure::{self, P}; use super::ops::{self, Site, remove_edge_at, remove_face, tet_quality}; use super::refine::{Context, MAX_CAVITY, MIN_GAP}; -use super::smooth::smooth_vertex; +use super::smooth::{smooth_vertex, smooth_vertex_below}; /// Settings of the schedule. #[derive(Debug, Clone, Copy, PartialEq)] @@ -53,6 +53,8 @@ pub struct ImproveStats { pub smoothed: usize, pub topological: usize, pub inserted: usize, + /// Insertions tried (kept or undone). + pub attempted: usize, /// The worst quality (smallest dihedral sine) after each pass. pub worst: Vec, pub stopped: Option, @@ -81,8 +83,8 @@ fn indicators(cx: &TetComplex) -> Result<[f64; 8]> { let mut out = [0.0; 8]; out[0] = f64::INFINITY; let mut n = 0usize; - for (_, vs) in cx.live_tets() { - let q = tet_quality(cx, vs)?; + for (t, _) in cx.live_tets() { + let q = cx.slot_quality(t)?; out[0] = out[0].min(q); for (i, s) in SIN_DEG.iter().enumerate() { out[i + 1] += q.min(*s); @@ -102,8 +104,8 @@ fn progressed(now: &[f64; 8], before: &[f64; 8]) -> bool { /// Smooth every movable vertex of a tetrahedron below `good`. Returns the moves. fn smoothing_pass(cx: &mut TetComplex, ctx: &Context, good: f64) -> Result { let mut want = vec![false; cx.point_count()]; - for (_, vs) in cx.live_tets() { - if tet_quality(cx, vs)? < good { + for (t, vs) in cx.live_tets() { + if cx.slot_quality(t)? < good { for v in vs { if let Some(w) = want.get_mut(v as usize) { *w = true; @@ -149,7 +151,7 @@ fn delete_flat(cx: &mut TetComplex, t: u32) -> Result { /// edge ([`ops::collapse`]), which takes the tetrahedron away. fn collapse_into_crease(cx: &mut TetComplex, t: u32) -> Result { let vs = cx.tet(t)?; - if tet_quality(cx, vs)? > 0.1 { + if cx.slot_quality(t)? > 0.1 { return Ok(false); } let (ns, tags) = (cx.adj(t)?, cx.tags(t)?); @@ -182,7 +184,7 @@ fn collapse_into_crease(cx: &mut TetComplex, t: u32) -> Result { pub fn topological_pass(cx: &mut TetComplex, list: &[u32]) -> Result { let mut changes = 0; for &t in list { - if !cx.is_live(t) { + if !cx.is_live(t) || cx.known_to_fail(t)? { continue; } let vs = cx.tet(t)?; @@ -201,20 +203,25 @@ pub fn topological_pass(cx: &mut TetComplex, list: &[u32]) -> Result { changes += 1; continue; } + let mut removed = false; for k in 0..4 { if remove_face(cx, t, k)? { changes += 1; + removed = true; break; } } + if !removed { + cx.mark_failed(t); + } } Ok(changes) } fn below(cx: &TetComplex, good: f64) -> Result> { let mut out = Vec::new(); - for (t, vs) in cx.live_tets() { - if tet_quality(cx, vs)? < good { + for (t, _) in cx.live_tets() { + if cx.slot_quality(t)? < good { out.push(t); } } @@ -288,7 +295,8 @@ fn change_quality(cx: &mut TetComplex, len: usize) -> Result<(f64, f64)> { } /// The composite insertion of §3.5 (see the module docs). Returns whether it was kept. -fn attempt_insert(cx: &mut TetComplex, ctx: &Context, p: Point3, kind: VertexKind, site: Site) -> Result { +fn attempt_insert(cx: &mut TetComplex, ctx: &Context, attempted: &mut usize, good: f64, p: Point3, kind: VertexKind, site: Site) -> Result { + *attempted += 1; let was = cx.journal.recording; cx.journal.recording = true; let len = cx.journal.steps.len(); @@ -303,8 +311,15 @@ fn attempt_insert(cx: &mut TetComplex, ctx: &Context, p: Point3, kind: VertexKin if !cx.is_used(v) { break; } - let star = cx.star(v)?; - if topological_pass(cx, &star)? == 0 { + // Only the tetrahedra below the threshold, as in the passes. + let mut star = cx.star(v)?; + let mut keep = Vec::with_capacity(star.len()); + for &t in &star { + keep.push(cx.slot_quality(t)? < good); + } + let mut flags = keep.into_iter(); + star.retain(|_| flags.next().unwrap_or(false)); + if star.is_empty() || topological_pass(cx, &star)? == 0 { break; } } @@ -312,7 +327,7 @@ fn attempt_insert(cx: &mut TetComplex, ctx: &Context, p: Point3, kind: VertexKin let mut around: Vec = cx.neighbours(v)?; around.push(v); for u in around { - smooth_vertex(cx, ctx, u)?; + smooth_vertex_below(cx, ctx, u, good)?; } } let (before, after) = change_quality(cx, len)?; @@ -337,7 +352,7 @@ fn attempt_insert(cx: &mut TetComplex, ctx: &Context, p: Point3, kind: VertexKin } /// Try inserting a vertex in each tetrahedron of `list` (§4.2). Returns the insertions kept. -fn insertion_pass(cx: &mut TetComplex, ctx: &Context, list: &[u32], budget: usize, good: f64) -> Result { +fn insertion_pass(cx: &mut TetComplex, ctx: &Context, list: &[u32], budget: usize, good: f64, attempted: &mut usize) -> Result { let mut kept = 0; for &t in list { if kept >= budget { @@ -347,7 +362,7 @@ fn insertion_pass(cx: &mut TetComplex, ctx: &Context, list: &[u32], budget: usiz continue; } let vs = cx.tet(t)?; - if tet_quality(cx, vs)? >= good { + if cx.slot_quality(t)? >= good { continue; } let ns = cx.adj(t)?; @@ -374,7 +389,7 @@ fn insertion_pass(cx: &mut TetComplex, ctx: &Context, list: &[u32], budget: usiz let target = measure::add(measure::mid(pa, pb), measure::scale(inward, 0.4 * l / len)); if let Ok(p) = Point3::try_from(target) && let Some(Walk::Inside(at)) = cx.walk(t, &p, 1 << 12)? - && attempt_insert(cx, ctx, p, VertexKind::Interior, Site::Interior(at))? + && attempt_insert(cx, ctx, attempted, good, p, VertexKind::Interior, Site::Interior(at))? { done = true; } @@ -391,7 +406,7 @@ fn insertion_pass(cx: &mut TetComplex, ctx: &Context, list: &[u32], budget: usiz let kind = VertexKind::Face(tags[k]); if let Some(p) = ctx.place(kind, g) && cx.is_live(t) - && attempt_insert(cx, ctx, p, kind, Site::Face(t, k))? + && attempt_insert(cx, ctx, attempted, good, p, kind, Site::Face(t, k))? { done = true; } @@ -400,7 +415,7 @@ fn insertion_pass(cx: &mut TetComplex, ctx: &Context, list: &[u32], budget: usiz if !done && cx.is_live(t) && cx.tet(t)? == vs { let g = measure::centroid(&cx.coords(vs)?); if let Ok(p) = Point3::try_from(g) - && attempt_insert(cx, ctx, p, VertexKind::Interior, Site::Interior(t))? + && attempt_insert(cx, ctx, attempted, good, p, VertexKind::Interior, Site::Interior(t))? { done = true; } @@ -430,7 +445,7 @@ fn insertion_pass(cx: &mut TetComplex, ctx: &Context, list: &[u32], budget: usiz }; let m = measure::mid(cx.xyz(a)?, cx.xyz(b)?); if let Some(p) = ctx.place(kind, m) - && attempt_insert(cx, ctx, p, kind, Site::Edge(a, b))? + && attempt_insert(cx, ctx, attempted, good, p, kind, Site::Edge(a, b))? { done = true; break; @@ -479,8 +494,8 @@ pub fn improve(cx: &mut TetComplex, ctx: &Context, o: &ImproveOptions) -> Result // The worst 3.5% of the tetrahedra, or (desperation pass, §4.2) every one with a // dihedral angle below 40° or above 140° (sine below sin 40°). let mut scored: Vec<(f64, u32)> = Vec::new(); - for (t, vs) in cx.live_tets() { - scored.push((tet_quality(cx, vs)?, t)); + for (t, _) in cx.live_tets() { + scored.push((cx.slot_quality(t)?, t)); } scored.sort_by(|a, b| a.0.total_cmp(&b.0).then(a.1.cmp(&b.1))); let list: Vec = if failed == 1 { @@ -490,7 +505,7 @@ pub fn improve(cx: &mut TetComplex, ctx: &Context, o: &ImproveOptions) -> Result scored.iter().take(n).map(|s| s.1).collect() }; let budget = o.max_insertions - stats.inserted; - stats.inserted += insertion_pass(cx, ctx, &list, budget, o.good)?; + stats.inserted += insertion_pass(cx, ctx, &list, budget, o.good, &mut stats.attempted)?; } let now = indicators(cx)?; carried = Some(now); @@ -548,7 +563,7 @@ mod tests { let q = Point3::try_from(q).unwrap(); if let Some(Walk::Inside(at)) = cx.walk(t, &q, 1 << 12).unwrap() { tried += 1; - assert!(!attempt_insert(&mut cx, &ctx, q, VertexKind::Interior, Site::Interior(at)).unwrap()); + assert!(!attempt_insert(&mut cx, &ctx, &mut 0, SIN_40, q, VertexKind::Interior, Site::Interior(at)).unwrap()); } } } diff --git a/crates/mesh/src/tet/measure.rs b/crates/mesh/src/tet/measure.rs index 98640f2..1a76f95 100644 --- a/crates/mesh/src/tet/measure.rs +++ b/crates/mesh/src/tet/measure.rs @@ -76,13 +76,39 @@ pub fn dihedral_cosines(x: &[P; 4]) -> [f64; 6] { /// The quality objective of a valid tetrahedron: the smaller of its smallest dihedral sine and /// its weighted scaled Jacobian ([`JACOBIAN_WEIGHT`]; the regular tetrahedron scores -/// √(8/9) ≈ 0.943). The dihedral sine catches slivers and caps; it does not see needles, whose -/// dihedral angles can all be fine while a corner is nearly flat (Shewchuk 2002), and the scaled -/// Jacobian `√2 · 6V / (ℓ₁ℓ₂ℓ₃)` at the worst corner, the measure analysts check (the skill's -/// limit, [`crate::quality`]), does. 0 for a flat tetrahedron; for an inverted one the negative -/// sine of largest magnitude, so worse inversions score lower. Extremes are found on squared -/// lengths and areas, with one square root each. +/// √(8/9) ≈ 0.943). The dihedral sine +/// catches slivers and caps; it does not see needles, whose dihedral angles can all be fine +/// while a corner is nearly flat (Shewchuk 2002), and the scaled Jacobian +/// `√2 · 6V / (ℓ₁ℓ₂ℓ₃)` at the worst corner, the measure analysts check (the skill's ≥ 0.2, +/// [`crate::quality`]), does. 0 for a flat tetrahedron; for an inverted one the negative sine of +/// largest magnitude, so worse inversions score lower. Extremes are found on squared lengths and +/// areas, with one square root each. pub fn quality(x: &[P; 4]) -> f64 { + quality_in_order(&canonical_order(x)) +} + +/// The corners reordered by an even permutation that depends only on the corners' positions +/// (sorted by coordinates, the last two swapped back when the sort was odd), so a measure +/// computed on it gives the same bits for every listing of a tetrahedron with the same +/// orientation: a removal tried from either side of a ring sees the same qualities. +fn canonical_order(x: &[P; 4]) -> [P; 4] { + let less = |a: &P, b: &P| a[0] < b[0] || (a[0] == b[0] && (a[1] < b[1] || (a[1] == b[1] && a[2] < b[2]))); + let mut y = *x; + let mut odd = false; + // A sorting network on four (pairs 01, 23, 02, 13, 12), counting swaps for the parity. + for (i, j) in [(0, 1), (2, 3), (0, 2), (1, 3), (1, 2)] { + if less(&y[j], &y[i]) { + y.swap(i, j); + odd = !odd; + } + } + if odd { + y.swap(2, 3); + } + y +} + +fn quality_in_order(x: &[P; 4]) -> f64 { let v6 = volume6(x); if v6 == 0.0 || !v6.is_finite() { return 0.0; @@ -102,12 +128,6 @@ pub fn quality(x: &[P; 4]) -> f64 { if q.is_finite() { q } else { 0.0 } } -/// The weight of the scaled Jacobian in [`quality`]: the meshing skill's limit, a scaled -/// Jacobian of 0.3, counts as much as a 30° dihedral angle (sin 30°, the improvement's target, -/// [`super::improve::ImproveOptions::target`]), so the Jacobian decides only for tetrahedra near -/// that limit (needles) and the dihedral sine everywhere else. -pub const JACOBIAN_WEIGHT: f64 = 0.5 / 0.3; - /// The corners of a tetrahedron and the other three corners of each. const CORNERS: [(usize, [usize; 3]); 4] = [(0, [1, 2, 3]), (1, [0, 2, 3]), (2, [0, 1, 3]), (3, [0, 1, 2])]; @@ -128,6 +148,100 @@ fn scaled_jacobian(x: &[P; 4], v6: f64) -> f64 { std::f64::consts::SQRT_2 * v6 / worst.sqrt() } +/// The weight of the scaled Jacobian in [`quality`]: the meshing skill's limit, a scaled +/// Jacobian of 0.3, counts as much as a 30° dihedral angle (sin 30°, the improvement's target, +/// [`super::improve::ImproveOptions::target`]), so the Jacobian decides only for tetrahedra near +/// that limit (needles) and the dihedral sine everywhere else. +pub const JACOBIAN_WEIGHT: f64 = 0.5 / 0.3; + +/// [`quality`] and its gradient with respect to corner `i`, for a positive tetrahedron: the +/// gradient of the term [`quality`] picks (the smallest dihedral sine, or the scaled Jacobian at +/// the worst corner, `∇ ln J = ∇V₆ / V₆ − Σ ∇ℓ / ℓ` over that corner's edges), analytic, as Klingner and +/// Shewchuk (§3.1) and Freitag and Ollivier-Gooch use for smoothing. With +/// `s = V₆ ℓ / (N_k N_l)` (`N` twice a face's area), +/// `∇s = s (∇V₆ / V₆ + ∇ℓ / ℓ − ∇N_k / N_k − ∇N_l / N_l)`, where `∇V₆` at a corner is its +/// opposite face's area vector, `∇ℓ` the unit edge vector at an end of the edge and, for a face +/// `(p, q, r)` with unit normal `n̂`, `∇_p N = (q − r) × n̂`. A flat or inverted tetrahedron +/// gets a zero gradient (smoothing only moves within valid positions). +pub fn quality_gradient(x: &[P; 4], i: usize) -> (f64, P) { + let q = quality(x); + let v6 = volume6(x); + if !(v6 > 0.0 && q > 0.0) || i > 3 { + return (q, [0.0; 3]); + } + let crosses = [0, 1, 2, 3].map(|k| face_cross(x, k)); + let n2 = crosses.map(|c| dot(c, c)); + // The edge whose sine is smallest (the same comparison as `quality`). + let mut pick = (f64::INFINITY, EDGE_FACES[0]); + for e in EDGE_FACES { + let (a, b, k, l) = e; + let d = sub(x[a], x[b]); + let r = dot(d, d) / (n2[k] * n2[l]); + if r < pick.0 { + pick = (r, e); + } + } + // The scaled Jacobian branch, when it is the smaller. + let products = corner_products(x); + let (c, cp) = products.iter().enumerate().fold((0, 0.0_f64), |m, (c, &p)| if p > m.1 { (c, p) } else { m }); + let sj = JACOBIAN_WEIGHT * std::f64::consts::SQRT_2 * v6 / cp.sqrt(); + let sine = v6 * pick.0.sqrt(); + let face = |k: usize| -> [usize; 3] { + match k { + 0 => [1, 2, 3], + 1 => [0, 2, 3], + 2 => [0, 1, 3], + _ => [0, 1, 2], + } + }; + // ∇V₆ at corner i: the area vector of the face opposite i, signed so that V₆ grows along it. + let gi = crosses[i]; + let gv = if dot(gi, sub(x[i], x[face(i)[0]])) < 0.0 { scale(gi, -1.0) } else { gi }; + if sj < sine { + // ∇ ln sj = ∇V₆ / V₆ − Σ ∇ℓ / ℓ over the corner's edges at i. + let (corner, others) = CORNERS[c]; + let mut g = scale(gv, 1.0 / v6); + for j in others { + let (p, o) = if i == corner { + (x[i], x[j]) + } else if i == j { + (x[i], x[corner]) + } else { + continue; + }; + let e = sub(p, o); + g = sub(g, scale(e, 1.0 / dot(e, e))); + } + let g = scale(g, q); + return if g.iter().all(|c| c.is_finite()) { (q, g) } else { (q, [0.0; 3]) }; + } + let (a, b, k, l) = pick.1; + let len = dist(x[a], x[b]); + let gl = if i == a { + scale(sub(x[a], x[b]), 1.0 / len) + } else if i == b { + scale(sub(x[b], x[a]), 1.0 / len) + } else { + [0.0; 3] + }; + // ∇N of the face opposite m at corner i (zero when the face does not hold i). + let gn = |m: usize| -> P { + let f = face(m); + let Some(pos) = f.iter().position(|&c| c == i) else { return [0.0; 3] }; + let n = crosses[m]; + let nn = norm(n); + if !(nn > 0.0) { + return [0.0; 3]; + } + let (qv, rv) = (x[f[(pos + 1) % 3]], x[f[(pos + 2) % 3]]); + scale(cross(sub(qv, rv), n), 1.0 / nn) + }; + let (nk, nl) = (n2[k].sqrt(), n2[l].sqrt()); + let g = add(add(scale(gv, 1.0 / v6), scale(gl, 1.0 / len)), scale(add(scale(gn(k), 1.0 / nk), scale(gn(l), 1.0 / nl)), -1.0)); + let g = scale(g, q); + if g.iter().all(|c| c.is_finite()) { (q, g) } else { (q, [0.0; 3]) } +} + /// The smallest and largest dihedral angle in degrees (reports only). pub fn dihedral_range(x: &[P; 4]) -> (f64, f64) { let (s, c) = (dihedral_sines(x), dihedral_cosines(x)); @@ -251,6 +365,16 @@ mod tests { assert!(circumcenter(&flat).is_none()); } + /// Every even reordering of the corners gives the same quality, bit for bit. + #[test] + fn quality_does_not_depend_on_the_corner_order() { + let x = positive([[0.1, 0.0, 0.05], [1.0, 0.2, 0.0], [0.3, 0.9, 0.1], [0.4, 0.35, 0.7]]); + let q = quality(&x); + for p in [[1, 2, 0, 3], [2, 0, 1, 3], [0, 2, 3, 1], [3, 1, 0, 2], [1, 0, 3, 2], [2, 3, 0, 1]] { + assert_eq!(quality(&p.map(|i| x[i])).to_bits(), q.to_bits(), "{p:?}"); + } + } + /// A needle: every dihedral angle above 20°, yet one corner nearly flat; the objective sees /// it through the scaled Jacobian. #[test] @@ -261,6 +385,29 @@ mod tests { assert!(quality(&x) < 0.15 * JACOBIAN_WEIGHT, "{}", quality(&x)); } + /// The analytic gradient matches central differences of the quality away from ties, on + /// either branch. + #[test] + fn quality_gradient_matches_central_differences() { + let sliverish = positive([[0.1, 0.0, 0.05], [1.0, 0.2, 0.0], [0.3, 0.9, 0.1], [0.4, 0.35, 0.7]]); + let needle = positive([[0.0, 0.0, 0.0], [1.0, 0.1, 0.0], [0.45, 0.85, 0.05], [0.55, 0.3, 6.0]]); + for x in [sliverish, needle] { + for i in 0..4 { + let (q, g) = quality_gradient(&x, i); + assert_eq!(q, quality(&x)); + let h = 1e-7; + for c in 0..3 { + let (mut a, mut b) = (x, x); + a[i][c] += h; + b[i][c] -= h; + let fd = (quality(&a) - quality(&b)) / (2.0 * h); + assert!((fd - g[c]).abs() < 1e-6, "corner {i} axis {c}: {fd} vs {}", g[c]); + } + } + } + assert_eq!(quality_gradient(&[[0.0; 3]; 4], 0).1, [0.0; 3]); + } + #[test] fn sliver_scores_low() { let x = positive([[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [1.0, 1.0, 0.01]]); diff --git a/crates/mesh/src/tet/ops.rs b/crates/mesh/src/tet/ops.rs index a2a2261..d0b6928 100644 --- a/crates/mesh/src/tet/ops.rs +++ b/crates/mesh/src/tet/ops.rs @@ -31,7 +31,7 @@ pub fn tet_quality(cx: &TetComplex, vs: [u32; 4]) -> Result { pub fn worst(cx: &TetComplex, tets: &[u32]) -> Result { let mut q = f64::INFINITY; for &t in tets { - q = q.min(tet_quality(cx, cx.tet(t)?)?); + q = q.min(cx.slot_quality(t)?); } Ok(q) } @@ -47,13 +47,17 @@ pub const MAX_RING: usize = 10; pub const BOUNDARY_FLIP_COS: f64 = 0.939_692_620_785_908_4; /// Klincsek's table: the best worst quality of a triangulation of the chain `v_i … v_j` -/// (with the closing edge `v_i v_j`), and the apex `k` that achieves it. -fn klincsek(m: usize, q: &mut dyn FnMut(usize, usize, usize) -> Result) -> Result<(Vec, Vec)> { +/// (with the closing edge `v_i v_j`), and the apex `k` that achieves it. Only triangulations +/// better than `floor` matter: an entry that cannot beat it holds `floor`, and a triangle is +/// evaluated only when its two sub-chains beat it, which skips most of the table when the +/// removal cannot pay off (the decision and the triangulation chosen are the same as without +/// the floor). +fn klincsek(m: usize, floor: f64, q: &mut dyn FnMut(usize, usize, usize) -> Result) -> Result<(Vec, Vec)> { let mut best = vec![f64::INFINITY; m * m]; let mut arg = vec![0usize; m * m]; for i in (0..m.saturating_sub(2)).rev() { for j in i + 2..m { - let mut b = f64::NEG_INFINITY; + let mut b = floor; let mut a = i + 1; for k in i + 1..j { let sub = best.get(i * m + k).copied().unwrap_or(f64::NEG_INFINITY).min(best.get(k * m + j).copied().unwrap_or(f64::NEG_INFINITY)); @@ -115,12 +119,31 @@ pub fn remove_edge_at(cx: &mut TetComplex, t: u32, a: u32, b: u32) -> Result Result { let Some(ring) = cx.edge_ring_at(t, a, b)? else { return Ok(false) }; let m = ring.verts.len(); if m < 3 || m > MAX_RING + usize::from(!ring.closed) { return Ok(false); } - let v = ring.verts.clone(); + let mut v = ring.verts.clone(); + if ring.closed { + // Start a closed ring at its smallest vertex, so the triangulation chosen does not + // depend on the tetrahedron the ring was walked from. + let first = v.iter().enumerate().min_by_key(|(_, id)| **id).map_or(0, |(i, _)| i); + v.rotate_left(first); + } let x = |id: u32| cx.xyz(id); let (xa, xb) = (x(a)?, x(b)?); // An open ring runs from boundary face (a, b, v_0) to (a, b, v_{m−1}): both must lie on one @@ -150,7 +173,7 @@ pub fn remove_edge_at(cx: &mut TetComplex, t: u32, a: u32, b: u32) -> Result before) { return Ok(false); @@ -199,37 +222,59 @@ pub fn remove_face(cx: &mut TetComplex, t: u32, k: usize) -> Result { let us = cx.tet(u)?; let face = face_toward(vs, k); let b = us.iter().copied().find(|v| !face.contains(v)).unwrap_or(NONE); - if b == NONE || cx.curve(a, b).is_some() || cx.edge_tet(a, b)?.is_some() { + if b == NONE || cx.curve(a, b).is_some() || cx.face_known_to_fail(a, b, face) || cx.edge_tet(a, b)?.is_some() { return Ok(false); } + let removed = remove_faces_between(cx, t, u, a, b, face)?; + if !removed { + cx.mark_face_failed(a, b, face); + } + Ok(removed) +} + +/// [`remove_face`] past its checks: tetrahedra `t` (apex `a`) and `u` (apex `b`) share `face`. +fn remove_faces_between(cx: &mut TetComplex, t: u32, u: u32, a: u32, b: u32, face: [u32; 3]) -> Result { // Sandwiched faces between a and b: faces f with tetrahedra (a ∪ f) and (b ∪ f). Grow the // set from the given face across shared edges while every new tetrahedron (a, b, e) on the // ring stays better than the worst removed one; take the best prefix found (a greedy form of // Shewchuk's optimal search, which visits the same candidates). - let mut faces: Vec<[u32; 3]> = vec![face]; + // Each face with the tetrahedron (a ∪ face). + let mut faces: Vec<([u32; 3], u32)> = vec![(face, t)]; let mut old: Vec = vec![t, u]; let mut best: Option<(f64, Vec, Vec<[u32; 4]>)> = None; + let mut removed_q = worst(cx, &old)?; + let mut made: IdMap<(u32, u32), ([u32; 4], f64)> = IdMap::default(); for _round in 0..8 { - let removed_q = worst(cx, &old)?; // The boundary edges of the face set (edges in exactly one face), oriented as in the face - // seen from a: each gives the new tetrahedron (a, b, e) positive. - let mut count: IdMap<(u32, u32), (u32, u32, usize)> = IdMap::default(); - for f in &faces { + // seen from a, with the face's tetrahedron on a's side: each gives the new tetrahedron + // (a, b, e) positive. + let mut count: IdMap<(u32, u32), (u32, u32, u32, usize)> = IdMap::default(); + for &(f, ta) in &faces { for i in 0..3 { let (p, q) = (f[i], f[(i + 1) % 3]); - let e = count.entry(sorted2(p, q)).or_insert((p, q, 0)); - e.2 += 1; + let e = count.entry(sorted2(p, q)).or_insert((p, q, ta, 0)); + e.3 += 1; } } - let mut ring: Vec<(u32, u32)> = count.values().filter(|e| e.2 == 1).map(|e| (e.0, e.1)).collect(); + let mut ring: Vec<(u32, u32, u32)> = count.values().filter(|e| e.3 == 1).map(|e| (e.0, e.1, e.2)).collect(); ring.sort_unstable(); let mut new = Vec::with_capacity(ring.len()); let mut q = f64::INFINITY; - for &(p, r) in &ring { - // face (p, r, x) has a on its positive side, so (p, r, a, b)… orient explicitly. - let cand = [p, r, b, a]; - let cand = if cx.orient(cand)? == Sign::Positive { cand } else { [r, p, b, a] }; - q = q.min(tet_quality(cx, cand)?); + for &(p, r, _) in &ring { + // A ring edge stays on the ring until a face grows across it: its tetrahedron is + // worked out once. + let (cand, cq) = match made.get(&(p, r)) { + Some(&c) => c, + None => { + // face (p, r, x) has a on its positive side, so (p, r, a, b)… orient explicitly. + let cand = [p, r, b, a]; + let cand = if cx.orient(cand)? == Sign::Positive { cand } else { [r, p, b, a] }; + let c = (cand, tet_quality(cx, cand)?); + made.insert((p, r), c); + c + } + }; + q = q.min(cq); new.push(cand); } if q > removed_q && best.as_ref().is_none_or(|(bq, _, _)| q > *bq) { @@ -237,11 +282,12 @@ pub fn remove_face(cx: &mut TetComplex, t: u32, k: usize) -> Result { } // Grow: a sandwiched neighbour face across a ring edge. let mut grown = false; - for &(p, r) in &ring { - if let Some((f, ta, tb)) = sandwiched_across(cx, a, b, p, r, &faces)? { - faces.push(f); - old.push(ta); - old.push(tb); + for &(p, r, ta) in &ring { + if let Some((f, na, nb)) = sandwiched_across(cx, a, b, p, r, ta, &faces)? { + faces.push((f, na)); + old.push(na); + old.push(nb); + removed_q = removed_q.min(worst(cx, &[na, nb])?); grown = true; break; } @@ -257,27 +303,28 @@ pub fn remove_face(cx: &mut TetComplex, t: u32, k: usize) -> Result { /// A face `(p, r, x)` sandwiched between `a` and `b` (tetrahedra `a ∪ f` and `b ∪ f` both exist) /// next to edge `pr`, not already in `faces`. -fn sandwiched_across(cx: &mut TetComplex, a: u32, b: u32, p: u32, r: u32, faces: &[[u32; 3]]) -> Result> { - let Some(ring) = cx.edge_ring(p, r)? else { return Ok(None) }; - // Tetrahedra around pr containing a, and containing b. - for &ta in &ring.tets { - let va = cx.tet(ta)?; - if !va.contains(&a) { - continue; - } - let x = va.iter().copied().find(|&v| v != a && v != p && v != r).unwrap_or(NONE); - if x == NONE || x == b { - continue; - } - let f = [p, r, x]; - if faces.iter().any(|g| sorted3(*g) == sorted3(f)) { - continue; - } - let k = va.iter().position(|&v| v == a).unwrap_or(0); - let tb = cx.adj(ta)?.get(k).copied().unwrap_or(NONE); - if tb != NONE && cx.tet(tb)?.contains(&b) { - return Ok(Some((f, ta, tb))); - } +fn sandwiched_across(cx: &TetComplex, a: u32, b: u32, p: u32, r: u32, ta: u32, faces: &[([u32; 3], u32)]) -> Result> { + // ta = (a, p, r, y) holds the face set's face on edge pr; the other tetrahedron of a around + // pr in a face set's neighbourhood lies across its face (a, p, r). + let va = cx.tet(ta)?; + let Some(ky) = va.iter().position(|&v| v != a && v != p && v != r) else { return Ok(None) }; + let n = cx.adj(ta)?.get(ky).copied().unwrap_or(NONE); + if n == NONE { + return Ok(None); + } + let vn = cx.tet(n)?; + let x = vn.iter().copied().find(|&v| v != a && v != p && v != r).unwrap_or(NONE); + if x == NONE || x == b || !vn.contains(&a) { + return Ok(None); + } + let f = [p, r, x]; + if faces.iter().any(|(g, _)| sorted3(*g) == sorted3(f)) { + return Ok(None); + } + let Some(k) = vn.iter().position(|&v| v == a) else { return Ok(None) }; + let tb = cx.adj(n)?.get(k).copied().unwrap_or(NONE); + if tb != NONE && cx.tet(tb)?.contains(&b) { + return Ok(Some((f, n, tb))); } Ok(None) } diff --git a/crates/mesh/src/tet/smooth.rs b/crates/mesh/src/tet/smooth.rs index 81060aa..3956dbb 100644 --- a/crates/mesh/src/tet/smooth.rs +++ b/crates/mesh/src/tet/smooth.rs @@ -207,6 +207,42 @@ impl LocalStar { measure::quality(&y) } + /// The quality of tetrahedron `k` with the vertex at `p`, and its gradient there: analytic + /// for a valid tetrahedron, central differences with step `delta` for a flat or inverted one + /// (whose signed measure has no single smooth branch). + fn quality_gradient_at(&self, k: usize, p: P, delta: f64) -> (f64, P) { + let Some((x, i)) = self.tets.get(k) else { return (f64::NEG_INFINITY, [0.0; 3]) }; + let mut y = *x; + if let Some(s) = y.get_mut(*i) { + *s = p; + } + let (q, g) = measure::quality_gradient(&y, *i); + if q > 0.0 { + return (q, g); + } + let mut g = [0.0; 3]; + for (c, gc) in g.iter_mut().enumerate() { + let (mut a, mut b) = (p, p); + a[c] += delta; + b[c] -= delta; + *gc = (self.quality_at(k, a) - self.quality_at(k, b)) / (2.0 * delta); + } + (q, g) + } + + /// The worst quality at `p` over the tetrahedra in `order`, or the first one found that is + /// not above `floor` (then the move is refused whatever the others are). + fn worst_above(&self, order: &[usize], p: P, floor: f64) -> f64 { + let mut w = f64::INFINITY; + for &k in order { + w = w.min(self.quality_at(k, p)); + if !(w > floor) { + return w; + } + } + w + } + fn worst_at(&self, p: P) -> f64 { (0..self.tets.len()).map(|k| self.quality_at(k, p)).fold(f64::INFINITY, f64::min) } @@ -215,7 +251,15 @@ impl LocalStar { /// Optimization-based smoothing of `v`: raise the worst quality of its star (see the module /// docs). Returns whether it moved. pub fn smooth_vertex(cx: &mut TetComplex, ctx: &Context, v: u32) -> Result { - if !cx.is_used(v) || cx.kind(v) == VertexKind::Corner { + smooth_vertex_below(cx, ctx, v, f64::INFINITY) +} + +/// [`smooth_vertex`], only when the worst tetrahedron around `v` is below `good` (Klingner and +/// Shewchuk smooth only around tetrahedra below their threshold). +pub fn smooth_vertex_below(cx: &mut TetComplex, ctx: &Context, v: u32, good: f64) -> Result { + // The optimization is a function of the star alone: one that found no move finds none + // again until a tetrahedron around `v` changes. + if !cx.is_used(v) || cx.kind(v) == VertexKind::Corner || cx.smoothing_known_to_fail(v) { return Ok(false); } let star = cx.star(v)?; @@ -237,25 +281,19 @@ pub fn smooth_vertex(cx: &mut TetComplex, ctx: &Context, v: u32) -> Result if !(len > 0.0 && len.is_finite()) { return Ok(false); } - let delta = 1e-6 * len; let mut x = x0; let mut worst = local.worst_at(x); + if !(worst < good) { + return Ok(false); + } let mut moved = false; for _ in 0..8 { - // Qualities and gradients (central differences) of the tetrahedra near the worst. + // Qualities and analytic gradients of the tetrahedra near the worst. let mut qs = Vec::with_capacity(local.tets.len()); for k in 0..local.tets.len() { let q = local.quality_at(k, x); - let mut g = [0.0; 3]; - if q <= worst + 0.1 { - for (c, gc) in g.iter_mut().enumerate() { - let (mut a, mut b) = (x, x); - a[c] += delta; - b[c] -= delta; - *gc = (local.quality_at(k, a) - local.quality_at(k, b)) / (2.0 * delta); - } - } - qs.push((q, restrict(g, f))); + let g = if q <= worst + 0.1 { restrict(local.quality_gradient_at(k, x, 1e-6 * len).1, f) } else { [0.0; 3] }; + qs.push((q, g)); } let active: Vec

= qs.iter().filter(|s| s.0 <= worst + 1e-4).map(|s| s.1).collect(); let d = min_norm(&active); @@ -272,10 +310,15 @@ pub fn smooth_vertex(cx: &mut TetComplex, ctx: &Context, v: u32) -> Result alpha = alpha.min((q - worst) / (dd - gd)); } } + // Trial positions check the worst tetrahedra first and stop at the first that does not + // beat the current worst. + let mut order: Vec = (0..qs.len()).collect(); + let q_of = |i: usize| qs.get(i).map_or(f64::INFINITY, |s| s.0); + order.sort_by(|&i, &j| q_of(i).total_cmp(&q_of(j)).then(i.cmp(&j))); let mut accepted = false; for _ in 0..6 { let Some(p) = ctx.place(cx.kind(v), add(x, scale(d, alpha))) else { break }; - let q = local.worst_at(p.coords()); + let q = local.worst_above(&order, p.coords(), worst); if p.coords() != x && q > worst && cx.move_is_valid(v, &p, &star)? { cx.move_point(v, p)?; x = p.coords(); @@ -290,5 +333,8 @@ pub fn smooth_vertex(cx: &mut TetComplex, ctx: &Context, v: u32) -> Result break; } } + if !moved { + cx.mark_smoothing_failed(v); + } Ok(moved) } diff --git a/crates/mesh/src/tet/tests.rs b/crates/mesh/src/tet/tests.rs index 91f50d3..7d31631 100644 --- a/crates/mesh/src/tet/tests.rs +++ b/crates/mesh/src/tet/tests.rs @@ -443,7 +443,7 @@ mod determinism { }) .fold(f64::INFINITY, f64::min); assert!(sj >= 0.3, "min scaled Jacobian {sj}"); - assert_eq!(fingerprint(&m), 11_252_377_805_886_396_373, "{} tets, {} nodes", m.elements.len(), m.points.len()); + assert_eq!(fingerprint(&m), 13_918_536_535_603_991_107, "{} tets, {} nodes", m.elements.len(), m.points.len()); } /// Listing the triangles, their corners and the vertices in another order, and numbering @@ -507,3 +507,62 @@ fn the_gate_refuses_a_detached_tetrahedron() { assert!(e.contains("share no face") && e.contains("(1, 2)"), "{e}"); assert!(super::linear_gate(&p, &tets[..1], v / 2.0).is_ok()); } + +/// Undoing an edge removal or a face removal puts every slot back as it was. +#[test] +fn rollback_restores_every_slot() { + use crate::cdt::{CdtOptions, tetrahedralize}; + use crate::surface::{BoundarySurface, SurfaceOptions}; + let (p, t, f) = determinism::washer(); + let s = BoundarySurface::new(&p, &t, &f, &SurfaceOptions::default()).unwrap(); + let cdt = tetrahedralize(&s, &CdtOptions::default()).unwrap(); + let (mut cx, _) = crate::tet::complex_from_cdt(&s, &cdt, &crate::tet::QualityOptions::default()).unwrap(); + let state = |cx: &TetComplex| -> Vec<([u32; 4], [u32; 4], [u32; 4])> { + (0..cx.slots() as u32).map(|t| (cx.tet(t).unwrap(), cx.adj(t).unwrap(), cx.tags(t).unwrap())).collect() + }; + let mut changed = 0; + for (t, vs) in cx.live_tets().collect::>() { + for &(i, j) in &EDGES { + for op in 0..2 { + let before = state(&cx); + cx.journal.recording = true; + let len = cx.journal.steps.len(); + let did = if op == 0 { remove_edge_at(&mut cx, t, vs[i], vs[j]).unwrap() } else { remove_face(&mut cx, t, i).unwrap() }; + changed += usize::from(did); + cx.rollback(len).unwrap(); + cx.journal.steps.truncate(len); + cx.journal.recording = false; + assert_eq!(state(&cx), before, "tet {t} edge {i}{j} op {op}"); + } + } + } + assert!(changed > 0); +} + +/// The cached qualities match a fresh computation after improvement (smoothing, flips, +/// insertions and the rollbacks of rejected insertions). +#[test] +fn cached_qualities_match_fresh_ones() { + use crate::cdt::{CdtOptions, tetrahedralize}; + use crate::size::UniformSize; + use crate::surface::{BoundarySurface, SurfaceOptions}; + use crate::tet::geometry::Tessellation; + use crate::tet::refine::Context; + let (p, t, f) = determinism::washer(); + let s = BoundarySurface::new(&p, &t, &f, &SurfaceOptions::default()).unwrap(); + let cdt = tetrahedralize(&s, &CdtOptions::default()).unwrap(); + let (mut cx, curve_faces) = crate::tet::complex_from_cdt(&s, &cdt, &crate::tet::QualityOptions::default()).unwrap(); + let (geometry, size) = (Tessellation::new(&s, Vec::new()), UniformSize(3.0)); + let ctx = Context { size: &size, geometry: &geometry, curve_faces: &curve_faces }; + // Fill the cache, then change the mesh. + for (t, _) in cx.live_tets().collect::>() { + cx.slot_quality(t).unwrap(); + } + let o = crate::tet::improve::ImproveOptions { max_passes: 3, ..Default::default() }; + let stats = crate::tet::improve::improve(&mut cx, &ctx, &o).unwrap(); + assert!(stats.attempted > 0 && stats.smoothed > 0, "{stats:?}"); + for (t, vs) in cx.live_tets().collect::>() { + assert_eq!(cx.slot_quality(t).unwrap().to_bits(), measure::quality(&cx.coords(vs).unwrap()).to_bits()); + } + cx.validate().unwrap(); +} diff --git a/docs/meshing/literature.md b/docs/meshing/literature.md index 386cb71..d8dc9e3 100644 --- a/docs/meshing/literature.md +++ b/docs/meshing/literature.md @@ -398,7 +398,8 @@ Delaunay methods with Voronoi/ODT improvement, then (2) all-hex and hex-dominant - **Implemented** in `fieldcraft-mesh::tet::{ops, improve}` from the two papers: Klincsek's dynamic programming for edge removal (interior edges; boundary edges of one flat B-rep face end in a 2-2 flip), multi-face removal grown greedily over the sandwiched faces, nonsmooth optimization smoothing (active set, smallest vector of the convex hull of the - active gradients, line search; gradients by central differences), and the composite vertex insertion with rollback + active gradients, line search; analytic gradients of the active measure, as §3.1 and Freitag–Ollivier-Gooch 1997 + use), and the composite vertex insertion with rollback (barycentres of boundary faces, of the tetrahedron, midpoints of boundary edges, and a point inside off a flat boundary edge). Deviations: the inserted vertex takes the Delaunay cavity rather than the optimal cut of §3.4; each pass smooths and flips the tetrahedra below sin 40° and inserts only when the worst did not improve; passes and the @@ -407,7 +408,11 @@ Delaunay methods with Voronoi/ODT improvement, then (2) all-hex and hex-dominant angle fine, one corner nearly flat; Shewchuk 2002); the scaled Jacobian analysts check (Knupp 2001, B6.6) catches them, and with the weight it decides only near that limit. Every operation is a checked replacement of a region (positive by exact `orient3d`, faces matched with opposite orientation, removed vertices fully inside), so the mesh is - valid after each step. + valid after each step. Speed (#84): an operation (topological, per tetrahedron, edge and face; or a smoothing) that + failed is not tried again until a tetrahedron it reads changes (a change clock per vertex; exact, because the + operations are functions of that region and the quality is computed on the corners in a canonical order), live + tetrahedra's qualities are cached, Klincsek's table starts at the quality to beat, and the composite insertion runs + its flips and neighbour smoothing only where a tetrahedron is below the threshold. **A3.7 Cheng, Dey, Edelsbrunner, Facello, Teng 2000, Sliver exudation.** **Verdict: reference.** - **Citation.** J. ACM 47(5):883–904, 2000. DOI [10.1145/355483.355487](https://doi.org/10.1145/355483.355487). diff --git a/docs/meshing/skill-results.md b/docs/meshing/skill-results.md index c40d9ae..5b528b2 100644 --- a/docs/meshing/skill-results.md +++ b/docs/meshing/skill-results.md @@ -31,7 +31,7 @@ Times are wall clock on the machine that ran it. | bolted-assembly | plan (sweep), mesh.hex.generate (auto) | – | 6272 (6272 hex8) | 0.583 | 0.939 | 3.6 | 2.0e-4 | 0 | 0 (not relaxed) | 8 coincident, 0 cracks | – | 3.7 | pass | [x=50.000](skill/bolted-assembly.png) | | cantilever-i-beam | plan (sweep) | – | 61600 (61600 hex8) | 1.000 | 1.000 | 1.0 | 0.0e0 | 0 | 0 (not relaxed) | none | – | 8.5 | pass | [x=100.000](skill/cantilever-i-beam.png) | | cross-cylinders | none | – | – | – | – | – | – | – | – | – | – | 27.2 | no mesh | – | -| filleted-bracket | tet10 | – | 19991 (19991 tet10) | 0.318 | 0.564 | 4.1 | -6.8e-6 | 0 | 0 (not relaxed) | none | – | 15.1 | pass (fallback) | [x=30.000](skill/filleted-bracket.png) | +| filleted-bracket | tet10 | – | 20020 (20020 tet10) | 0.320 | 0.562 | 4.1 | -6.8e-6 | 0 | 0 (not relaxed) | none | – | 12.7 | pass (fallback) | [x=30.000](skill/filleted-bracket.png) | | filleted-bracket-blocks | plan (sweep) | – | 75410 (75410 hex8) | 0.704 | 0.954 | 3.5 | 3.7e-5 | 0 | 0 (not relaxed) | none (after merging 2348 nodes) | – | 6.9 | pass | [x=30.000](skill/filleted-bracket-blocks.png) | | i-beam | plan (sweep) | – | 61600 (61600 hex8) | 1.000 | 1.000 | 1.0 | 0.0e0 | 0 | 0 (not relaxed) | none | – | 4.5 | pass | [z=100.000](skill/i-beam.png) | | loft-transition | plan (sweep) | – | 2873 (2873 hex8) | 0.189 | 0.959 | 1.7 | -2.1e-3 | 0 | 4 → 4 (4 relaxed, 0 undone; min SJ 0.189 → 0.189, max ratio 1.7 → 1.7) | none | – | 0.9 | fail (SJ) | [z=25.000](skill/loft-transition.png) | @@ -40,7 +40,7 @@ Times are wall clock on the machine that ran it. | rounded-box | plan (project) | 2 plane(s) | 11520 (11520 hex8) | 0.717 | 0.973 | 4.0 | -4.1e-3 | 0 | 0 (not relaxed) | none | – | 8.7 | pass | [x=20.000](skill/rounded-box.png) | | shallow-groove | plan (sweep) | – | 1960 (1960 hex8) | 0.991 | 0.999 | 1.1 | 2.7e-4 | 0 | 0 (not relaxed) | none | – | 0.2 | pass | [x=30.000](skill/shallow-groove.png) | | sharp-wedge | plan (sweep) | – | 1674 (1674 hex8) | 0.014 | 0.301 | 149.6 | 2.7e-15 | 0 | 1524 (not relaxed) | none | – | 0.2 | fail (SJ, ratio) | [x=40.000](skill/sharp-wedge.png) | -| sphere-on-plate | tet10 | – | 25613 (25613 tet10) | 0.335 | 0.607 | 4.4 | -8.8e-5 | 0 | 0 (not relaxed) | none | – | 7.7 | pass (fallback) | [y=0.000](skill/sphere-on-plate.png) | +| sphere-on-plate | tet10 | – | 24175 (24175 tet10) | 0.341 | 0.604 | 4.2 | -9.6e-5 | 0 | 0 (not relaxed) | none | – | 6.5 | pass (fallback) | [y=0.000](skill/sphere-on-plate.png) | | spline-vase | plan (sweep) | – | 4536 (4536 hex8) | 0.665 | 0.945 | 9.9 | -6.6e-3 | 0 | 0 (not relaxed) | none | – | 2.3 | pass | [z=-35.000](skill/spline-vase.png) | | stepped-block | plan (cells) | – | 1416 (1416 hex8) | 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