Polynomial-Size Nonobtuse Triangulation of Polygons

We describe methods for triangulating polygonal regions of the plane so that no triangle has a large angle. Our main result is that a polygon with n sides can be triangulated with O(n2) nonobtuse triangles. We also show that any triangulation (without Steiner points) of a simple polygon has a refinement with O(n4) nonobtuse triangles. Finally we show that a triangulation whose dual is a path has a refinement with only O(n2) nonobtuse triangles.

• Type: Conference
• Year: 1991
• Where: COMPGEOM
• Authors: Marshall W. Bern, David Eppstein
• Keywords: COMPGEOM 1991, Discrete Geometry, Nonobtuse Triangles, Polygonal Regions, Simple Polygon