Angular and Aspect-Ratio Voronoi Diagram with Applications

Voronoi diagram (and aspect-ratio 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 (aspect ratio of a triangle defined by
the point and the line segment) is smallest (largest, resp.) among all
line segments. These Voronoi diagrams are different from an ordinary
Voronoi diagram for a point set. After introducing interesting
properties, we present two efficient algorithms, one for finding a point
to maximize the smallest visual angle and the other for computing
a point to minimize the largest aspect ratio.