We first develop and analyze a finite volume scheme for the discretization of partial differential equations (PDEs) on the sphere; the scheme uses Voronoi tessellations of the sphere. For a model convection–diffusion problem, the finite volume scheme is shown to produce first-order accurate approximations with respect to a mesh-dependent discrete firstderivative norm. Then, we introduce the not...

This paper aims to study the mechanical behaviour and failure mechanism of intact rocks under different loading conditions using the grain based model implemented in the universal distinct element code (UDEC). The grain based numerical model is a powerful tool to investigate complicated micro-structural mechanical behaviour of rocks. In the UDEC grain based model, the intact material is simulat...

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an exis...

Shell nacre (mother of pearl) of Pinctada margaritifera was analyzed by scanning electron microscopy. The originality of this work concerns the sampling performed to observe incipient nacre on the mantle side. The whole animal is embedded in methyl methacrylate followed by separation of the shell from the hardened mantle. It is revealed this way how each future nacre layer pre-exists as a film ...

In an attempt to escape some of the limitations of traditional GIS data structures, the Voronoi diagram was selected as an attractive alternative. It is a space-filling topological structure, eliminating problems of the line-intersection spatial model. It has been extensively studied by experts in computational geometry. Various versions have been developed in differing dimensions and metrics, ...

We present techniques for fast motion planning by using discrete approximations of generalized Voronoi diagrams, computed with graphics hardware. Approaches based on this diagram computation are applicable to both static and dynamic environments of fairly high complexity. We compute a discrete Voronoi diagram by rendering a three-dimensional distance mesh for each Voronoi site. The sites can be...

Updating an abstract Voronoi diagram in linear time, after deletion of one site, has been an open problem for a long time. Similarly for various concrete Voronoi diagrams of generalized sites, other than points. In this paper we present a simple, expected linear-time algorithm to update an abstract Voronoi diagram after deletion. We introduce the concept of a Voronoi-like diagram, a relaxed ver...

In recent years, the literature shows an increasing interest to tessellation methods based on Voronoi diagrams to model different structures as packing of spheres. Voronoi diagrams have found numerous practical and theoretical applications in a large number of fields in science and technology as well as in computer graphics. A useful property of Voronoi diagrams is that they represent cellular ...