Geodesic Voronoi diagrams on parametric surfaces

In this paper we extend the concept of Voronoi diagrams to parameterized surfaces where distance between two points is defined as infimum over the lengths of surface paths connecting these points. We present a method to compute Voronoi diagrams on these surfaces.

[1]  H. Piaggio.  Differential Geometry of Curves and Surfaces , 1952, Nature.

[2]  Rolf Klein,et al.  Concrete and Abstract Voronoi Diagrams , 1990, Lecture Notes in Computer Science.

[3]  Michael Ian Shamos,et al.  Closest-point problems , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[4]  Franz Aurenhammer,et al.  Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.

[5]  Franz-Erich Wolter.  Distance function and cut loci on a complete Riemannian manifold , 1979 .