feat(extract): NURBS curve + patch surface tessellation#29
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First-party NurbsEval math unit + two MeshBuilder arms (curve→lines, patch→triangles with analytic normals), full periodic closed handling, convex-hull bounds. Closes NRB-1 for curve+patch; trimmed/swept/swung, interpolators, and 2D geometry deferred to follow-ups. Includes the 'why not a seam' rationale (I/O-free + spec-prescribed ⇒ no genericity payoff; externalGeometryResolver stays as the override).
Math-unit-first: open/closed curves -> open/closed surfaces with analytic normals (all formulas machine-verified) -> MeshBuilder arms -> bounds -> specimen swap -> docs -> CI. Each task ships verified golden values.
…ot double) Caught by adversarial workflow execution: the golden asserted |x^2+y^2-1|<1e-9 on float-stored points whose achievable error is ~1 ulp (6e-8). Math is exact (double accumulation, float output); only the test bound was impossible.
Caught by adversarial workflow execution: comparing the chord leaving the seam to the chord arriving caps the dot at ~0.923 (chords straddle the true tangent by the curvature), so >0.99 is impossible even for a correct C1 curve. Replaced with: seam chord-turning == diametrically-opposite vertex's (verified == 1e-16); a C0 kink would break that equality. Curve is genuinely C1.
- ci-preset -Werror=narrowing: finite-difference test used double h -> float brace-init; make h float (blocking; dev preset does not -Werror). - review (medium): prepareSurface wrapped closed surfaces unconditionally while prepareCurve guards on endsDiffer. Add the coincident-boundary guard so an already-closed control net is not duplicated into zero-area sliver triangles; + regression test (already-closed net + uClosed == unwrapped result). - review (low): guard the rational denominator in tessellateCurve/evalSurface so a degenerate/zero weight set emits a finite point, not NaN (which would poison the AABB).
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Implements first-party tessellation for
NurbsCurveandNurbsPatchSurface, closing NRB-1 for curve + patch. Previously both were generated stubs that the extractor silently dropped.What's in it
runtime/extract/NurbsEval.hpp— node-free NURBS math: Cox–de Boor basis + first-derivative basis, rational (weighted) curve/surface evaluation, clamped + periodic knot defaulting, fullclosed/uClosed/vClosedhandling, and analytic normals via the quotient rule(A' − w'C)/w.MeshBuilderarms —NurbsCurve→Topology::Lines;NurbsPatchSurface→Triangles+ analytic normals + implicit (u,v) texcoords. Registered inrecognizedGeometryType().GeometryBounds.hpp.externalGeometryResolverstays the unrecognized-fallback for the deferred surfaces), conformance NRB-1 → fixed (NRB-3 tracks deferred swept/swung/trimmed), extract subsystem page, v1-capabilities.Scope
Curve + patch only. Deferred to follow-ups:
NurbsTrimmedSurface, swept/swung, NURBS interpolators, authoredNurbsTextureCoordinate, 2D geometry.Verification
nurbs_eval_test) + integration (mesh_builder_nurbs_test);recognizedGeometryTypeoracle; unrecognized-specimen moved toNurbsTrimmedSurface.mise run cigreen (ci-preset build 111/111 with-Werror+ per-header isolation; Python suite 305 passed/1 skipped; golden/conformance/coverage/cli gates pass).Spec:
docs/superpowers/specs/2026-06-27-nurbs-curve-patch-design.md. Plan:docs/superpowers/plans/2026-06-27-nurbs-curve-patch.md.Note: the headless renderer needed an unrelated ADR-0039 namespace fix to build (it's out-of-CI); that's a separate PR (#28).