Generalized Voronoi Diagrams on Polyhedral Terrains
نویسندگان
چکیده
We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a polyhedral terrain in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral terrain with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites.
منابع مشابه
Approximations of 3D generalized Voronoi diagrams
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...
متن کاملComputing generalized higher-order Voronoi diagrams on triangulated surfaces
We present an algorithm for computing exact shortest paths, and consequently distance functions, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex triangulated polyhedral surface. The algorithm is generalized to the case when a set of generalized sites is considered, providing their distance field that implicitly represents the Voronoi diag...
متن کاملMobile Robot Online Motion Planning Using Generalized Voronoi Graphs
In this paper, a new online robot motion planner is developed for systematically exploring unknown environ¬ments by intelligent mobile robots in real-time applications. The algorithm takes advantage of sensory data to find an obstacle-free start-to-goal path. It does so by online calculation of the Generalized Voronoi Graph (GVG) of the free space, and utilizing a combination of depth-first an...
متن کاملStraight Skeletons by Means of Voronoi Diagrams Under Polyhedral Distance Functions
We consider the question under which circumstances the straight skeleton and the Voronoi diagram of a given input shape coincide. More precisely, we investigate convex distance functions that stem from centrally symmetric convex polyhedra as unit balls and derive sufficient and necessary conditions for input shapes in order to obtain identical straight skeletons and Voronoi diagrams with respec...
متن کاملGeneralized Source Shortest Paths on Polyhedral Surfaces
We present an algorithm for computing shortest paths and distances from a single generalized source (point, segment, polygonal chain or polygon) to any query point on a possibly non-convex polyhedral surface. The algorithm also handles the case in which polygonal chain or polygon obstacles on the polyhedral surface are allowed. Moreover, it easily extends to the case of several generalized sour...
متن کامل