Tessellation: a whole sphere's loop starts off its poles when its seam has two segments

A whole sphere as one face has its seam as its only edge, used both ways. In a body many times
its size the seam gets two segments at the body's chord (pole, equator, pole), so no node off
the poles follows a node off them, and the loop kept its first node, a pole: its closing step
crossed the other pole, which the drift unwrapped to a whole turn ("boundary winds around the
surface"). The sphere was left out of the mesh (cut_beside_a_sealed_void_keeps_the_body: a void
r 2 in a 75 mm part, "1 face(s) don't mesh"). The loop now starts, failing a node with an
off-pole predecessor, at a node whose predecessor is a pole on the same edge, so the step into
it is that edge's own and the step into the pole is unwrapped in the loop like any other.

Regression test a_small_sphere_void_in_a_large_block_meshes (tess tests): watertight, no face
left out.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

crates/kernel/src/tess/mod.rs

@@ -356,7 +356,14 @@ fn boundary(
         }
         let n = uvs.len();
         let pole = |q: &[f64; 2]| (0..2).any(|d| pole_along(*q, d));
-        if let Some(k) = (0..n).find(|&k| uvs.get(k).is_some_and(|q| !pole(q)) && uvs.get((k + n - 1) % n).is_some_and(|q| !pole(q))) {
+        let off = |k: usize| uvs.get(k).is_some_and(|q| !pole(q));
+        // A node off the poles whose predecessor is off them too; failing that (a whole sphere's
+        // seam in two segments: pole, equator, pole), one whose predecessor is a pole on the same
+        // edge, so the step into it is the edge's own and the step into that pole, from the
+        // edge before, is in the loop where it is unwrapped like any other.
+        let same_edge = |k: usize| segs.get((k + n - 1) % n).zip(segs.get(k)).is_some_and(|(a, b)| a.0 == b.0);
+        let start = (0..n).find(|&k| off(k) && off((k + n - 1) % n)).or_else(|| (0..n).find(|&k| off(k) && same_edge(k)));
+        if let Some(k) = start {
             uvs.rotate_left(k);
             pts.rotate_left(k);
             segs.rotate_left(k);

crates/kernel/src/tess/tests.rs

@@ -888,3 +888,23 @@ fn a_loop_corner_within_its_tolerance_of_a_pole_is_a_pole() {
     let Err(e) = plan(&pyramid_past_a_near_pole(1e-8), 0.01, None) else { panic!("no pole without the tolerance") };
     assert!(e.to_string().contains("winds around the surface"), "{e}");
 }
+
+/// A whole sphere as one face (its seam the only edge) in a body many times its size: at the
+/// body's chord the seam gets two segments, pole to equator to pole, and every node off the poles
+/// follows a pole. The loop used to start at a pole and close across the other, which unwrapped
+/// to a whole turn: "boundary winds around the surface", and the sphere was left out (a sealed
+/// void r 2 in a 60 mm block). It meshes closed.
+#[test]
+fn a_small_sphere_void_in_a_large_block_meshes() {
+    let block = ok(crate::box_solid(Vec3::new(-30.0, -30.0, 0.0), Vec3::new(30.0, 30.0, 60.0)));
+    let ball = ok(crate::sphere(Vec3::new(0.0, 0.0, 30.0), 2.0));
+    let hollow = cut(&block, &ball);
+    let tol = hollow.size() * 0.01;
+    let (m, stats) = match plan(&record(&hollow), tol, None) {
+        Ok((p, stats)) => (p.evaluate(), stats),
+        Err(e) => panic!("plan: {e}"),
+    };
+    assert!(stats.unmeshed.is_empty(), "{:?}", stats.unmeshed.iter().map(|u| &u.reason).collect::<Vec<_>>());
+    assert_watertight(&m, "block with a sphere void");
+    assert_eq!(hollow.unmeshed_faces(), 0);
+}