On the minimality of polygon triangulation

Abstract

The problem of triangulating a polygon using the minimum number of triangles is treated. We show that the minimum number of triangles required to partition a simple n-gon is equal to n + 2w - d - 2, where w is the number of holes and d is the maximum number of independent degenerate triangles of the n-gon. We also propose an algorithm for constructing the minimum triangulation of a simple hole-free n-gon. The algorithm takes O(nlog2n + DK 2) time, where D is the maximum number of vertices lying on the same line in the n-gon and K is the number of minimally degenerate triangles of the n-gon. CR subjects classifications: G. 1.6, I. 1.2, 1.3.5