The 3D network originated by the faces of irregular Poissonian Voronoi polyhedra may represent the backbone on which the galaxies are originated. As a consequence the spatial appearance of the catalogs of galaxies can be reproduced. The selected catalogs to simulate are the 2dF Galaxy Redshift Survey and the Third Reference Catalog of Bright Galaxies. In order to explain the number of observed ...

We consider stationary Poisson line processes in the Euclidean plane and analyze properties of Voronoi tessellations induced by Poisson point processes on these lines. In particular, we describe and test an algorithm for the simulation of typical cells of this class of Cox–Voronoi tessellations. Using random testing, we validate our algorithm by comparing theoretical values of functionals of th...

Given a tesselation of the plane, defined by a planar straightline graph G, we want to find a minimal set S of points in the plane, such that the Voronoi diagram associated with S ‘fits’ G. This is the Generalized Inverse Voronoi Problem (GIVP), defined in [12] and rediscovered recently in [3]. Here we give an algorithm that solves this problem with a number of points that is linear in the size...

The ability to build maps of indoor environments is extremely important for autonomous mobile robots. In this paper we introduce Voronoi random fields (VRFs), a novel technique for mapping the topological structure of indoor environments. Our maps describe environments in terms of their spatial layout along with information about the different places and their connectivity. To build these maps,...

This paper proposes a non-photorealistic rendering method that creates an artistic effect called mosaicing. The proposed method converts images provided by the user into the mosaic images. Commercial image editing applications also provide a similar function. However, these applications often trade results for low-cost computing. It is desirable to create high quality images even if the computa...

Euclidean Voronoi diagram of spheres in 3-dimensional space has not been explored as much as it deserves even though it has significant potential impacts on diverse applications in both science and engineering. In addition, studies on the data structure for its topology have not been reported yet. Presented in this paper is the topological representation for Euclidean Voronoi diagram of spheres...

In this paper, we present a method to navigate a mobile robot using a webcam. This method determines the shortest path for the robot to transverse to its target location, while avoiding obstacles along the way. The environment is first captured as an image using a webcam. Image processing methods are then performed to identify the existence of obstacles within the environment. Using the Voronoi...

A reduced-order modeling methodology based on centroidal Voronoi tessellations (CVTs) is introduced. CVTs are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. For discrete data sets, CVTs are closely related to the h-means and k-means clustering techniques. A discussion of reduced-order modelin...

The Voronoi network is known to be a useful tool for the structural description of voids in the packings of spheres produced by computer simulations. In this article we extend the Voronoi-Delaunay analysis to packings of nonspherical convex objects. Main properties of the Voronoi network, which are known for systems of spheres, are valid for systems of any convex objects. A general numerical al...