Chase algorithm
Track edge on each polygon. Advance whichever's edge is 'behind'. Detect + record intersection points. Complexity O(N+M).
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Concave polygons
Weiler-Atherton or Vatti's algorithm. General polygon clipping. O((N+M) log(N+M)).
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Sutherland-Hodgman
Clip subject polygon against convex clipper polygon. O(N × edges of clipper). Standard in graphics.
Boolean operations
Union, intersection, difference, symmetric difference. Reduce to clipping + traversal.