Fix crossingsRemoved failures and optimize intersection hot paths#141
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hfutrell wants to merge 5 commits into
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Fix crossingsRemoved failures and optimize intersection hot paths#141hfutrell wants to merge 5 commits into
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…ng iteration budget - testCrossingsRemovedTwoOverlappingCircles: two near-circular overlapping components; checks that crossingsRemoved preserves the union bounding box. - testCrossingsRemovedTwoOverlappingCircles2: similar test with an irregular 5-segment second component. - testCrossingsRemovedFourthRealWorldCase: 27-element self-intersecting path that previously caused crossingsRemoved to return an empty/degenerate result. - testTempE10E12Direct: diagnostic test capturing two known-hard intersection pairs (E10∩E12, E13∩E16) in the fourth real-world path. - Raise maximumIterations 64→512 in bezierClipping to give the overlapping- circle tests enough budget to converge. Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
- Add Arc.swift: Arc struct, arc detection (asArc), arcParameter, arc-arc, arc-line, arc-quadratic, and arc-cubic intersection routines using Bernstein polynomial root finding - Add BernsteinPolynomial6 with BezierClippingPolynomial conformance to support degree-6 polynomial roots in arcCubicIntersections - Add ArcTests.swift: unit tests for arcParameter including CCW/CW arcs where endAngle crosses the atan2 branch cut (> π and < -π) - Document angle range conventions in Arc.swift: startAngle ∈ (-π,π] from atan2; endAngle can exceed 2π (CCW crossing branch cut) or be negative (CW crossing branch cut) - Add regression tests for crossingsRemoved on overlapping near-circles and a self-intersecting 27-element path - Add testTempE10E12Direct to catch false-positive intersection between a degenerate near-point cubic and a large-radius arc cubic Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
Three changes work together to correctly handle closed components with self-intersections in removeCrossings: 1. Wrap-around edges: closed components with intersections now use a single wrap-around edge from the last intersection node back to the first, bypassing the seam. This prevents inconsistent classification of arcs that straddle the component seam. 2. Gap-nodes-first ordering: in performOperation, intersection nodes whose own forward arc is not in solution are processed before other intersection nodes, ensuring they find their cycles before those arcs are consumed by other traversals. 3. preferNeighbors DFS: for removeCrossings, findUnvisitedPath tries neighbor (cross-component) forward arcs before the node's own forward arc, so cross-component edges are explored first. Neighbor arcs leading directly to the goal are deferred last to avoid trivial one-arc cycles that would split correct multi-arc cycles. Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
- CoincidenceInterval struct: replace [Intersection]? return type with a plain 4-CGFloat value type; callers materialize [Intersection] only when needed. Confirmed via assembly: 0 swift_allocObject in all four coincidenceCheck specializations. - coincidenceCheck bounding-box guard: skip the expensive project() root-find when an endpoint clearly lies outside the other curve's bounding box. - tangent-parallelness pre-filter: only call coincidenceCheck from the clipping result path when result.count==1 and sin²(angle) ≤ 0.1 (angle ≤ ~18°). Genuine transverse crossings are never coincidences. - asArc closed-form midpoint: compute t=0.5 algebraically instead of allocating a [CGPoint] array; replace the loop over 5 sampled points with explicit checks at t=0.25 and t=0.75 only (p0/pMid/p3 lie on the circumcircle by construction). - asArc R<5×chord filter: reject nearly-linear cubics that pass the distance checks but gain nothing from the arc intersection path. Performance (release build, Apple M-series): testCubicIntersectionsPerformance: 0.571 s → 0.486 s (−15 %) testQuadraticCubicIntersectionsPerformance: unchanged at 0.039 s Accuracy (exhaustive t-grid sweep): Cubic×Cubic (1884 pairs): max error 6.87e-16, avg 1.36e-16 Quad×Cubic (1934 pairs): max error 6.21e-16 Quad×Quad (1980 pairs): max error 6.87e-16 Line×Cubic (1960 pairs): max error 0 (exact) All errors at or below float64 machine epsilon (2.22e-16 ulp). Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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Summary
This branch resolves correctness failures in
crossingsRemovedfor overlapping circular arc paths, and adds performance optimizations to the cubic intersection engine.Bug fixes
coincidenceCheck.crossingsRemovedtest cases from multi-circle paths that were failing before these fixes.New feature: arc-based cubic intersection path (
Arc.swift)When both input cubics approximate a circular arc (detected via circumcircle fit), the engine switches from iterative bezier clipping to an algebraic arc–arc intersection formula, then refines with Newton–Raphson. This is both faster and more accurate for the common case of circle-based paths.
CubicCurve.asArc(accuracy:)— detects whether a cubic lies withinaccuracyof a circle; uses the circumcircle of p0/pMid/p3arcArcIntersections,arcLineIntersections,arcCubicIntersections,arcQuadraticIntersections— closed-form intersection formulas for arc pairsarcParameter— maps a point back to a t-value on an arcPerformance optimizations
CoincidenceIntervalstruct (BezierCurve+Intersection.swift)coincidenceCheckpreviously returned[Intersection]?, allocating a heap array on every hit (and in specializations, even on miss paths). Replaced with a plain 4-CGFloatvalue typeCoincidenceInterval; callers call.asIntersections()or.asMappedIntersections(t1Range:t2Range:)only when they actually need the array.Assembly verification (release build, whole-module optimization):
swift_allocObjectin the cubic×cubic specializationswift_allocObjectin all four specializationscoincidenceCheckbounding-box guardSkip the expensive
project()(degree-5 root find) when an endpoint lies clearly outside the other curve's bounding box. Only enters the slow path when the boxes overlap.Tangent-parallelness pre-filter before
coincidenceCheckAfter bezier clipping,
coincidenceCheckwas called unconditionally wheneverresultwas non-empty. Now it is called only whenresult.count == 1andsin²(angle) ≤ 0.1(angle ≤ ~18°). Genuine transverse crossings (two curves crossing at a meaningful angle) are structurally incapable of being coincidence artifacts.asArcclosed-form midpoint + linear-curve filterasArcpreviously allocated a 5-element[CGPoint]array for sampled points. Replaced with:Performance results (release build, Apple M-series)
testCubicIntersectionsPerformancetestQuadraticCubicIntersectionsPerformanceAccuracy results (exhaustive t-grid sweep, float64)
All errors are at or below float64 machine epsilon (2.22e-16). No accuracy regression vs. clipping-only baseline.
Test plan
swift test)crossingsRemovedregression tests added and passingswift_allocObject, 0swift_beginAccess, 0 indirect dispatch in hot intersection paths🤖 Generated with Claude Code