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,...

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...

Describing macro-molecular interfaces is key to improve our understanding of the specificity and of the stability of macro-molecular interactions, and also to predict complexes when little structural information is known. Ideally, an interface model should provide easy-tocompute geometric and topological parameters exhibiting a good correlation with important bio-physical quantities. It should ...

A two part probabilistic model for polycrystalline microstructures is described. The model utilizes a Poisson–Voronoi tessellation for the grain geometry and a vector random field model for the crystallographic orientation. The grain geometry model is calibrated to experimental data through the intensity of the Poisson point field underlying the Poisson–Voronoi tessellation and the orientation ...

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...

This paper presents a novel optimal location selection problem, which can be applied to a wide range of applications. After providing a formal definition of the novel query type, we explore an intuitive approach that sequentially scans all possible object combinations in the search space. Then, we propose an Overlapping Voronoi Diagram (OVD) model that defines OVDs and Minimum OVDs, and constru...

To efficiently store and analyse spatial data at a global scale, the digital expression of the Earth’s data must be global, continuous and conjugate, i.e., a spherical dynamic data model is needed. The Voronoi data structure is the only published attempt and only solution (which is currently available) for dynamic GIS. The complexity of the Voronoi algorithms for line and area data sets in a ve...

The Voronoi diagram is a widely used partition of space which may be implemented in a variety of unconventional computing prototypes, sharing in common the uniform propagation of information via fronts emanating from data point sources. The giant single-celled amoeboid organism Physarum polycephalum constructs minimising transport networks but can also approximate the Voronoi diagram using two ...

We present a fluid particle model based on the Voronoi tessellation that allows one to represent an inviscid fluid in a Lagrangian description. The discrete model has all the required symmetries and structure of the continuum equations and can be understood as a linearly consistent discretization of Euler’s equations. Although the model is purely inviscid, we observe that the probability distri...

Traditional vector and raster spatial models as used in many computer systems are examined to determine what is meant by the term “neighbour”. The limitations are examined and the Voronoi spatial model is proposed as a consistent alternative to both. It is then asked whether this new computer model of space bears any resemblance to human spatial reasoning and perception processes. Examination o...