An $O(n^2 \log n)$ Time Algorithm for the Minmax Angle Triangulation

Abstract

It is shown that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time $O(n^2 \log n)$ and space $O(n)$. The algorithm is fairly easy to implement and is based on the edge-insertion scheme that iteratively improves an arbitrary initial triangulation. It can be extended to the case where edges are prescribed, and, within the same time- and space-bounds, it can lexicographically minimize the sorted angle vector if the point set is in general position. Experimental results on the efficiency of the algorithm and the quality of the triangulations obtained are included.