Abstract

The Graham scan is a fundamental backtracking technique in computational geometry which was originally designed to compute the convex hull of a set of point in the plane [9] and has since found application in several different contexts. In this note we show how to use the Graham scan to triangulate a simple polygon. The resulting algorithm triangulates an n-vertex polygon P in O( kn) time where k −1 is the number of concave vertices in P. Although the worst case running time of the algorithm is O( n 2), it is easy to implement and is therefore of practical interest.

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