fix Screw3D Lipschitz under-correction at high taper

render/screw_test.go

@@ -145,6 +145,61 @@ func Test_Screw_Watertight_Tapered(t *testing.T) {
 	}
 }
 
+// Test_Screw_Watertight_HighTaperHighRes pins the configurations from the
+// screw_assortment example that produced boundary edges on Linux at the
+// example's cells=300 resolution: high-taper screws where the cone narrows
+// far enough that the closest surface r at any query may be much smaller
+// than r_query - threadDepth. Without clamping rEff at rSurfaceMin, the
+// Lipschitz correction underestimates σ_max for those queries and the
+// octree isEmpty check skips cubes that contain surface.
+//
+// Cell count matches the example so the borderline FP regime that
+// surfaces these failures is exercised here too.
+//
+// Coverage:
+//   - the four originally-reported failing configs
+//   - a wider taper sweep (35°, 40°) at standard pitch/length
+//   - multi-start at high taper
+//   - alternative thread profiles (acme, plastic-buttress) at high taper
+//   - varied length (longer cone narrows further)
+//   - very fine pitch at high taper (small rEff → huge σ_max)
+func Test_Screw_Watertight_HighTaperHighRes(t *testing.T) {
+	cases := []screwTestConfig{
+		// Originally-reported failing configs.
+		{"taper_45", 5, 2, 20, 45, 1, 300, "iso"},
+		{"taper_30_coarse", 5, 5, 20, 30, 1, 300, "iso"},
+		{"taper_30_buttress", 5, 2, 20, 30, 1, 300, "buttress"},
+		{"taper_30_left_buttress", 5, 2, 20, 30, -1, 300, "buttress"},
+		// Wider taper sweep at standard pitch/length.
+		{"taper_35_iso", 5, 2, 20, 35, 1, 300, "iso"},
+		{"taper_40_iso", 5, 2, 20, 40, 1, 300, "iso"},
+		{"taper_45_buttress", 5, 2, 20, 45, 1, 300, "buttress"},
+		// High-taper multi-start.
+		{"taper_30_4start", 5, 2, 20, 30, 4, 300, "iso"},
+		{"taper_30_8start", 5, 2, 20, 30, 8, 300, "iso"},
+		// Alternative profiles at high taper.
+		{"taper_30_acme", 5, 2, 20, 30, 1, 300, "acme"},
+		{"taper_30_plastic_butt", 5, 2, 20, 30, 1, 300, "plastic-buttress"},
+		{"taper_30_iso_internal", 5, 2, 20, 30, 1, 300, "iso-int"},
+		// Longer cone — narrows further.
+		{"taper_30_long_l40", 5, 2, 40, 30, 1, 300, "iso"},
+		// Fine pitch + high taper — small rEff at the tip → huge σ_max
+		// without rSurfaceMin floor.
+		{"taper_30_fine_p1", 5, 1, 20, 30, 1, 300, "iso"},
+	}
+	for _, c := range cases {
+		t.Run(c.name, func(t *testing.T) {
+			screw := buildScrew(t, c)
+			tris := CollectTriangles(screw, NewMarchingCubesOctree(c.cells))
+			be := CountBoundaryEdges(tris)
+			if be != 0 {
+				t.Errorf("octree mesh has %d boundary edges (want 0 for watertight)", be)
+			}
+			t.Logf("%d tris, %d boundary edges", len(tris), be)
+		})
+	}
+}
+
 func Test_Screw_EndCap_Position(t *testing.T) {
 	// Verify octree and uniform renderers agree on end-cap Z positions.
 	configs := straightScrewConfigs()

sdf/screw.go

@@ -394,6 +394,7 @@ type ScrewSDF3 struct {
 	tanTaper    float64 // tan(taper), precomputed
 	tan2Taper   float64 // tan²(taper), precomputed
 	threadDepth float64 // radial extent of thread profile (max.Y - min.Y)
+	rSurfaceMin float64 // lower bound on surface r anywhere on the screw
 	starts      int     // number of thread starts
 	bb          Box3    // bounding box
 }
@@ -469,6 +470,18 @@ func Screw3D(
 	// add the taper increment
 	r += s.length * s.tanTaper
 	s.bb = Box3{v3.Vec{-r, -r, -s.length}, v3.Vec{r, r, s.length}}
+	// Lower bound on surface r anywhere on the screw, used to clamp rEff
+	// in Evaluate. For a cylindrical screw this equals the root radius
+	// (thread.Max.Y - threadDepth). For a tapered screw the cone narrows
+	// toward the top: at z = +length/2 the crest sits at thread.Max.Y −
+	// length·tan(taper), and the root is threadDepth shallower than that.
+	// At sharp tapers the cone may pinch to or past the axis — floor at
+	// 5% of the crest radius so σ_max stays bounded; the renderer will
+	// over-evaluate cubes near the cone tip but won't punch holes.
+	s.rSurfaceMin = bb.Max.Y - s.length*s.tanTaper - s.threadDepth
+	if floor := bb.Max.Y * 0.05; s.rSurfaceMin < floor {
+		s.rSurfaceMin = floor
+	}
 	return &s, nil
 }
 
@@ -552,11 +565,23 @@ func (s *ScrewSDF3) Evaluate(p v3.Vec) float64 {
 	// be at a smaller r where the stretch is larger. Using r reduced by the
 	// thread depth gives a conservative bound: the nearest surface point
 	// on the thread can be at most threadDepth closer to the axis.
+	//
+	// For tapered screws the cone narrows along z, so the closest surface
+	// point at any query may sit at a much smaller r than r_query allows
+	// for — e.g. a query at the wide end can have its closest surface at
+	// the narrow end of the cone if the cube spans z. Clamping rEff at
+	// rSurfaceMin (the smallest surface r anywhere on the screw) keeps
+	// the bound conservative across the full z range. Cylindrical screws
+	// have rSurfaceMin = root radius and this clamp is a no-op for queries
+	// inside the screw radius, a small extra correction outside.
 	if r > 0 {
 		rEff := r - s.threadDepth
 		if rEff < r*0.5 {
 			rEff = r * 0.5
 		}
+		if rEff > s.rSurfaceMin {
+			rEff = s.rSurfaceMin
+		}
 		k2 := s.leadOver2π / rEff
 		k2 *= k2
 		a := 1 + k2