In Euclidean geometry, it is well-known that the k-order Voronoi diagram in R can be computed from the vertical projection of the k-level of an arrangement of hyperplanes tangent to a convex potential function in R: the paraboloid. Similarly, we report for the Klein ball model of hyperbolic geometry such a concave potential function: the northern hemisphere. Furthermore, we also show how to bui...

a new model is proposed for two-dimensional simulation of the concrete fracture in compression. the model generated by using the voronoi diagram method and with considering random shape and distribution of full graded aggregates at the mesoscopic level. the aggregates modeled by combining irregular polygons, which then is placed into the concrete with no intersection between them. by this new m...

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...

This paper intends to generate the approximate Voronoi diagram in the geodesic metric for some unbiased samples selected from original points. The mesh model of seeds is then constructed on basis of the Voronoi diagram. Rather than constructing the Voronoi diagram for all original points, the proposed strategy is to run around the obstacle that the geodesic distances among neighboring points ar...

We study the Voronoi and void statistics of superhomogeneous (or hyperuniform) point patterns in which the infinite-wavelength density fluctuations vanish. Superhomogeneous or hyperuniform point patterns arise in one-component plasmas, primordial density fluctuations in the Universe, and jammed hard-particle packings. We specifically analyze a certain one-dimensional model by studying size fluc...

Mobility models are one piece in a chain of models, which are used to simulate mobile communication networks. Thereby, mobility models are generated to create typical movement patterns for nodes in a given environment. The following paper proposes a new mobility model for urban areas. The model contains movement channels, which are calculated by the multiple application of Voronoi graphs. The c...

Crowd Sensing is a new business model which allows large number of smart phones to be used not only for exchanging information but also for activities that may have a huge social impact including traffic or road monitoring, urban planning, social networking and environmental monitoring. Here, we present a novel approach for developing a sensing application to collect a specific dataset where re...

Voronoi diagrams are a central topic in Computational Geometry. They can be generalized in many ways. Suppose S is a finite set of geometric objects and there is a notion of Voronoi diagram V or(S) that we want to compute. One approach to designing algorithms for V or(S) is to (1) assume some general properties of S, and (2) describe an abstract algorithm based on the Real RAM model that has so...