Modelled threads: shuffle the faceted boolean's polygons before the BSP (#1250) (#1395)

The groove's facets came in sweep order, and the BSP takes each list's first
polygon as its splitter, so the tree was as deep as the list: quadratic time and
memory. An M8 x 60 mm thread ran out of tree depth after 12.9 GB. A fixed shuffle
gives a shallow tree and the same result (volume and faces equal to 1e-9).

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

crates/kernel/src/polybool.rs

@@ -356,6 +356,11 @@ pub fn faceted_boolean(a: &Body, b: &Mesh, op: BoolOp, tol: f64) -> Result<Optio
     // whether the pieces' boundaries come out consistent: try a few tolerances, and take the
     // first whose result is watertight and agrees with the complementary boolean (A − B and
     // A ∩ B add up to A; A ∪ B is A plus B less A ∩ B).
+    // The BSP takes each list's first polygon as its splitting plane. Facets in sweep order
+    // (a thread's groove, turn after turn) make every splitter cut nothing, so the tree is as
+    // deep as the list is long: quadratic time and memory, and a long thread ran out of depth
+    // (#1250). The same lists in a fixed shuffled order give a shallow tree.
+    let (pa, pb) = (shuffled(pa), shuffled(pb));
     let (va, vb) = (polys_volume(&pa), polys_volume(&pb));
     let mut last = KernelError::Failed("faceted boolean".into());
     for rel in [1e-8, 1e-7, 3e-8, 1e-9, 3e-7] {
@@ -383,6 +388,23 @@ pub fn faceted_boolean(a: &Body, b: &Mesh, op: BoolOp, tol: f64) -> Result<Optio
     Err(last)
 }
 
+/// `polys` in a fixed pseudo-random order (the same every run, so results are reproducible).
+fn shuffled(mut polys: Vec<Poly>) -> Vec<Poly> {
+    let mut state = 0x9E37_79B9_7F4A_7C15u64 ^ polys.len() as u64;
+    let mut next = || {
+        // SplitMix64.
+        state = state.wrapping_add(0x9E37_79B9_7F4A_7C15);
+        let mut z = state;
+        z = (z ^ (z >> 30)).wrapping_mul(0xBF58_476D_1CE4_E5B9);
+        z = (z ^ (z >> 27)).wrapping_mul(0x94D0_49BB_1331_11EB);
+        z ^ (z >> 31)
+    };
+    for i in (1..polys.len()).rev() {
+        polys.swap(i, (next() % (i as u64 + 1)) as usize);
+    }
+    polys
+}
+
 /// Boolean of two all-planar bodies.
 pub fn planar_boolean(a: &Body, b: &Body, op: BoolOp) -> Result<Option<Body>> {
     a.require_brep("a boolean")?;

crates/kernel/src/thread_tests.rs

@@ -44,3 +44,21 @@ fn faceted_cut_into_a_bore() {
     let want = 4.0 * PI * 0.2 * (1.5f64.powi(2) - 1.23f64.powi(2));
     assert!((removed - want).abs() < 0.03 * want, "{removed} vs {want}");
 }
+
+/// #1250: a long thread (48 turns of an M8 groove on a 60 mm shaft). The groove's facets come in
+/// sweep order; taken as BSP splitters in that order they made the tree as deep as the facet
+/// list ("planar boolean: tree too deep", after minutes and gigabytes). It cuts now, closed.
+#[test]
+fn a_long_thread_cuts_without_a_deep_tree() {
+    let (r, len, p) = (4.0, 60.0, 1.25);
+    let shaft = cylinder(Vec3::ZERO, Vec3::new(0.0, 0.0, 1.0), r, len).unwrap();
+    let k = Vec3::new(0.0, 0.0, 1.0);
+    let base = Vec3::new(0.0, 0.0, -p);
+    let plane = Plane { origin: base, x: Vec3::new(1.0, 0.0, 0.0), y: k };
+    let section = [Vec2::new(3.3, -0.08), Vec2::new(4.1, -0.5), Vec2::new(4.1, 0.5), Vec2::new(3.3, 0.08)];
+    let groove = sweep_helix_mesh(&plane, &section, base, k, p, len / p + 2.0, 48).unwrap();
+    let cut = faceted_boolean(&shaft, &groove, BoolOp::Cut, p * 0.005).unwrap().unwrap();
+    let v = cut.tessellate(0.01).unwrap().measure().volume;
+    let v0 = PI * r * r * len;
+    assert!(v < v0 * 0.95 && v > v0 * 0.6, "{v} of {v0}");
+}