Kernel tests: the #871 part's fitting rounds take their exact volume

rounds_that_fit_are_closed counted faces (the input's plus one per picked
edge: 38, where SMLib makes 50 with its corner faces). It now keeps
validity and no crossed loops and holds the R0.5 rounds on all 24 end-face
edges to the exact volume.

Proof. The part (plate 14 x 21.5 x 10, block 14 x 9.948 x 10 on it, the
5.2 x 7.1 window through both along x) is
14 (215 + 10 (b - a) - 36.92). At depth u into an end face's rounds the
section is that face's outline moved in by d = r - sqrt(r^2 - (r - u)^2),
each edge parallel to itself: the area less L d, L = 2 (21.5 + 20) +
2 (5.2 + 7.1) = 107.6 (the stepped outline's perimeter is its box's), plus
d^2 at each of the six convex corners (two rounds mitred), less pi d^2 / 4
at each of the six concave ones (the two shoulders and the window's four
corners: rounds meeting at a concave corner beside an unpicked sharp edge
are swept round it, the owner's ruling of 2026-10-30). The wall between
window and block side is 1.256 > 2 r, so the offsets stay apart. Over the
round the integrals of d and d^2 are r^2 (1 - pi/4) and r^3 (5/3 - pi/2),
so both ends remove
2 (L r^2 (1 - pi/4) - (6 - 6 pi/4) r^3 (5/3 - pi/2)) = 11.514718.
Graded at 1e-7 of the part's volume. It passes today (aarch64, SMLib).

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

crates/kernel/src/issue_871_tests.rs

@@ -49,12 +49,28 @@ fn overlapping_rounds_are_refused() {
     }
 }
 
-/// Below half the wall the rounds fit: a closed solid with a round on every edge.
+/// Below half the wall the rounds fit: a closed solid with a round on every edge. Each end face's
+/// round section at depth u into the round is the end face's outline moved in by
+/// d = r − √(r² − (r − u)²), each edge parallel to itself: the area less L d (L the outline's
+/// and the window's length together, 2 · 41.5 + 2 · 12.3 = 107.6), plus d² at each of the six
+/// convex corners (two rounds mitred) and less π d² / 4 at each of the six concave ones, the two
+/// shoulders and the window's four corners (two rounds meeting at a concave corner beside an
+/// unpicked sharp edge are swept round it, the owner's ruling of 2026-10-30). Over the round,
+/// ∫ d = r² (1 − π/4) and ∫ d² = r³ (5/3 − π/2), at both ends.
 #[test]
 fn rounds_that_fit_are_closed() {
+    use std::f64::consts::{FRAC_PI_2, FRAC_PI_4};
     let p = part();
-    let b = crate::fillet(&p, &edges(), 0.5).unwrap();
+    let r = 0.5;
+    let b = crate::fillet(&p, &edges(), r).unwrap();
     assert!(b.validity().is_empty(), "{:?}", b.validity());
     assert_eq!(b.crossed_face_loops().unwrap(), 0);
-    assert_eq!(b.face_count(), p.face_count() + edges().len());
+    let (a, top) = (12.74437365538526, 22.69275963366936);
+    let part_volume = 14.0 * (21.5 * 10.0 + (top - a) * 10.0 - 5.2 * 7.1);
+    assert!((crate::measure(&p).unwrap().volume - part_volume).abs() < 1e-9 * part_volume);
+    let length = 2.0 * (21.5 + 20.0) + 2.0 * (5.2 + 7.1);
+    let corners = 6.0 - 6.0 * FRAC_PI_4;
+    let removed = 2.0 * (length * r * r * (1.0 - FRAC_PI_4) - corners * r * r * r * (5.0 / 3.0 - FRAC_PI_2));
+    let v = crate::measure(&b).unwrap().volume;
+    assert!((v - (part_volume - removed)).abs() < 1e-7 * part_volume, "{v} vs {}", part_volume - removed);
 }