Why it matters

Polygon operations underlie GIS + graphics. Understanding enables polygon-based work.

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The architecture

Shoelace: sum of signed triangles.

Ray casting: point-in-polygon via edge crossings.

Ear clipping: recursively remove ear triangles.

Polygon algorithmsAreashoelacePoint-in-polygonray castingTriangulationear clippingConvex polygons: many operations simpler than general polygon
Polygon operations.
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How it works end to end

Ray casting: shoot ray from point; count edge crossings; odd = inside.

Ear clipping: O(n²) simple triangulation; Delaunay for better quality.

Convex hull check: O(n) sequential turn checks.