Linear-size nonobtuse triangulation of polygons

We give an algorithm for triangulating n-vertex polygonal regions (with holes) so that no angle in the final triangulation measures more than π/2. The number of triangles in the triangulation is only O(n), improving a previous bound of O(n 2), and the running time is O(n log2 n). The basic technique used in the algorithm, recursive subdivision by disks, is new and may have wider application in mesh generation. We also report on an implementation of our algorithm. © 1995 Springer-Verlag New York Inc.