Angular Voronoi Diagram with Applications

Given a set of line segments in the plane, we define an angular Voronoi diagram as follows: a point belongs to a Voronoi region of a line segment if the visual angle of the line segment from the point is smallest among all line segments. The Voronoi diagram is interesting in itself and different from an ordinary Voronoi diagram for a point set. After introducing interesting properties, we present an efficient algorithms for finding a point to maximize the smallest visual angle. Some applications to mesh improvement are also mentioned.