Abstract
This chapter describes fast polygon triangulation based on Seidel's algorithm. Computing the triangulation of a polygon is a fundamental algorithm in computational geometry. In computer graphics, polygon triangulation algorithms are widely used for tessellating curved geometries, such as those described by splines. Methods of triangulation include algorithms, convex hull differences, and horizontal decompositions. This chapter describes an implementation based on Seidel's algorithm for triangulating simple polygons having no holes. It is an incremental randomized algorithm whose expected complexity is O(n log*n). In practice, it is almost linear time for a simple polygon having n vertices. The triangulation does not introduce any additional vertices and decomposes the polygon into n − 2 triangles. Furthermore, the algorithm generates a query structure that can be used to determine the location of a point in logarithmic time. All the data structures used in the implementation are statically allocated.
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