A new 2D tessellation for angle problems: The polar diagram

Abstract

The new approach we propose in this paper is a plane partition with similar features to those of the Voronoi Diagram, but the Euclidean minimum distance criterion is replaced for the minimal angle criterion. The result is a new tessellation of the plane in regions called Polar Diagram, in which every site is owner of a polar region as the locus of points with smallest polar angle respect to this site.

We prove that polar diagrams, used as preprocessing, can be applied to many problems in Computational Geometry in order to speed up their processing times. Some of these applications are the convex hull, visibility problems, and path planning problems.