Three Optimized Algorithms for Computing Polygonal Mesh Edges

This post presents three equivalent algorithms for computing the edges of a polygonal mesh, representing progressive optimization steps to achieve the same result with increasing efficiency. Starting with a description of mesh topology representation and edge concepts, it details three approaches: a map-based algorithm (O(n log n) complexity), a sort-based algorithm (O(n log n) complexity), and a novel minor valence algorithm (O(n) complexity). The author compares their performance, highlighting the innovative nature and potential game development applications of the minor valence algorithm.