Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set on a plane, where the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work in conjunction with the first paper of the series dealing with the construction of the correct top...

The Voronoi diagram of a point set has been extensively used in various disciplines ever since it was first proposed. Its application realms have been even further extended to estimate the shape of point clouds when Edelsbrunner and Mücke introduced the concept of α-shape based on the Delaunay triangulation of a point set. In this paper, we present the theory of β-shape for a set of three-dimen...

We revisit a new type of a Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, and analyze the structure and complexity of the nearestand furthest-neighbor Voronoi diagrams of a point set with respect to these distance functions.

This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks. The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and independent Poisson point processes, conditionally on the Poisson lines, to model vehicles on the roads. We derive basic properties of the point process, in...

The Voronoi diagram is a fundamental geometry structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact 3D domain (i.e. a finite 3D volume), some Voronoi cells of their Voronoi diagram are infinite, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellatio...

In this paper we describe a generic C++ adaptor, that adapts a 2-dimensional triangulated Delaunay graph and to the corresponding a Voronoi diagram, represented as a doubly connected edge list (DCEL) data structure. Our adaptor has the ability to automatically eliminate, in a consistent manner, degenerate features of the Voronoi diagram, that are artifacts of the requirement that Delaunay graph...

Given a set of spheres in 3D, constructing its Voronoi diagram in Euclidean distance metric is not easy at all even though many mathematical properties of its structure are known. This Voronoi diagram has been known for many important applications from science and engineering. In this paper, we characterize the Voronoi diagram of spheres in three-dimensional Euclidean space, which is also known...