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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...

The geometry of circles in the plane is inextricably tied with the group of Möbius transformations, which take circles to circles. This geometry can be seen in a more symmetric after transforming the plane to the sphere, by stereographic projection. Interpretations will be discussed for Voronoi diagrams, Delaunay triangulations,etc. from this point of view. Fortune’s algorithm for constructing ...

Generalized Voronoi diagrams of objects are di cult to compute in a robust way, especially in higher dimensions. For a number of applications an approximation of the real diagram within some predetermined precision is su cient. In this paper we study the computation of such approximate Voronoi diagrams. The emphasis is on practical applicability, therefore we are mainly concerned with fast (in ...

The Hausdorff Voronoi diagram of a set of clusters of points in the plane is a generalization of the classic Voronoi diagram, where distance between a point t and a cluster P is measured as the maximum distance, or equivalently the Hausdorff distance between t and P . The size of the diagram for non-crossing clusters is O(n ), where n is the total number of points in all clusters. In this paper...

adequate coverage is one of the main problems for distributed wireless sensor networks and the effectiveness of that highly depends on the sensor deployment scheme. given a finite number of sensors, optimizing the sensor deployment will provide sufficient sensor coverage and save power of sensors for movement to target location to adequate coverage. in this paper, we apply fuzzy logic system to...

We present a novel algorithm to compute a homotopy preserving bounded-error approximate Voronoi diagram of a 3D polyhedron. Our approach uses spatial subdivision to generate an adaptive volumetric grid and computes an approximate Voronoi diagram within each grid cell. Moreover, we ensure each grid cell satisfies a homotopy preserving criterion by computing an arrangement of 2D conics within a p...

We introduce a new approach to approximate generalized 3D Voronoi diagrams for different site shapes (points, spheres, segments, lines, polyhedra, etc) and different distance functions (Euclidean metrics, convex distance functions, etc). The approach is based on an octree data structure denoted Voronoi-Octree (VO) that encodes the information required to generate a polyhedral approximation of t...