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Kernel tests: a small bend's display mesh is graded on the display mesh alone
a_small_bend_on_a_large_sheet_is_meshed_round also pinned the chord-only mesh (exactly two stations across each bend, its sag over 0.29 r) and required every flat side face to keep the chord-only mesh's triangle count: facts about another mesh, not what the display shows (the chord-only mesh now puts three stations across the r1 bend). It keeps what the display mesh must do: each bend a quarter turn in more than five facets, each turning at most DISPLAY_ANGLE, sagging at most r (1 - cos(angle / 2)) and less than the chord tolerance. It passes today. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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@@ -150,13 +150,16 @@ fn rim(m: &Mesh, centre: Vec2, radius: f64, z: f64) -> (usize, f64) {
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(segments, widest)
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}
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/// What the display mesh of a bent sheet 3000 mm long shows at its r1 and r3 bends, whose
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/// sagitta is below the chord tolerance: each bend round, a quarter turn in facets that each turn
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/// at most `DISPLAY_ANGLE` and so sag at most 1 − cos(angle / 2) of the radius, within the chord
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/// tolerance.
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#[test]
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fn a_small_bend_on_a_large_sheet_is_meshed_round() {
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let b = bent_sheet(3000.0);
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let tol = display_tol(&b);
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// The tolerance is larger than either side's sagitta: 1 - cos 45° of the radius.
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assert!(tol > 3.0 * (1.0 - (PI / 4.0).cos()));
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let coarse = b.mesh(&crate::MeshTolerance::chord(tol)).unwrap();
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let round = b.mesh(&crate::MeshTolerance { chord: tol, angle: Some(DISPLAY_ANGLE) }).unwrap();
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// A quarter turn in facets of at most DISPLAY_ANGLE.
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let facets = (FRAC_PI_2 / DISPLAY_ANGLE).ceil() as usize;
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@@ -165,9 +168,6 @@ fn a_small_bend_on_a_large_sheet_is_meshed_round() {
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let faces = cylinder_faces(&b, radius);
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assert_eq!(faces.len(), 1, "one bend face of radius {radius}");
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let (face, origin, axis) = faces[0];
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// The chord tolerance alone: one flat strip from tangent line to tangent line.
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assert_eq!(angles_around(&coarse, face, origin, *axis).len(), 2, "radius {radius}");
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assert!(sag(&coarse, face, origin, *axis, radius) > 0.29 * radius);
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let a = angles_around(&round, face, origin, *axis);
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assert!(a.len() > facets, "radius {radius}: {} facets across the bend", a.len() - 1);
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assert!((a[a.len() - 1] - FRAC_PI_2).abs() < 1e-6, "the bend is a quarter turn: {a:?}");
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@@ -178,19 +178,6 @@ fn a_small_bend_on_a_large_sheet_is_meshed_round() {
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let s = sag(&round, face, origin, *axis, radius);
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assert!(s <= radius * (1.0 - (DISPLAY_ANGLE / 2.0).cos()) * 1.001 && s < tol, "radius {radius}: sag {s}");
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}
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// The flat faces along the sheet meet the bends in straight lines and need nothing more:
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// only the bends, and the two ends where their arcs now have more points, gain triangles.
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let count = |m: &Mesh, face: usize| m.tri_face.iter().filter(|f| **f as usize == face).count();
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let mut along = 0;
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for face in 0..b.face_count() {
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if let Some(FaceSurface::Plane { normal, .. }) = face_surface(&b, face)
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&& normal.dot(Vec3::Z).abs() < 0.5
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{
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along += 1;
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assert_eq!(count(&round, face), count(&coarse, face), "face {face}");
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}
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}
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assert_eq!(along, 6);
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}
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#[test]
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