Estimation of the necessary number of points in Riemannian Voronoi

G. Leibon and D. Letscher showed that for general and sufficiently dense point set its Delaunay triangulation and Voronoi diagram in Riemannian manifold exist. They also proposed an algorithm to construct them for a given set. In this paper we estimate the necessary number of points for computing the Voronoi diagram in the manifold by using sectional curvature of the manifold. Moreover, we show how many Voronoi regions exist around a Voronoi region.

• Type: Conference
• Year: 2003
• Where: CCCG
• Authors: Kensuke Onishi, Jin-ichi Itoh
• Keywords: CCCG 2003, CCCG 2007, Riemannian Manifold, Voronoi Diagram, Voronoi Region