PVD: A Stable Implementation for Computing Voronoi Diagrams of Polygonal Pockets
نویسندگان
چکیده
منابع مشابه
Generalized Voronoi Diagrams on Polyhedral Terrains
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) ...
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 کاملPolygonal Approximation of Voronoi Diagrams of a Set of Triangles in Three Dimensions
We describe a robust adaptive marching tetrahedra type algorithm for constructing a polygonal approximation of the Voronoi Diagram of an arbitrary set of triangles in three dimensions. Space is adaptively subdivided into a set of tetrahedral cells, and the set of Voronoi regions which intersect each cell is determined exactly using a simple primitive we introduce. We obtain a small number of di...
متن کاملThe Complexity of Finding Minimal Voronoi Covers with Applications to Machine Learning
Our goal in this paper is to examine the application of Voronoi diagrams, a fundamental concept of computational geometry, to the nearest neighbor algorithm used in machine learning. We consider the question “Given a planar polygonal tessellation T and an integer k, is there a set of k points whose Voronoi diagram contains every edge in T?” We show that this question is NP-hard. We encountered ...
متن کاملOptimizing Voronoi Diagrams for Polygonal Finite Element Computations
We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectively removes the major reason for numerical instabilities—short edges in the Voronoi diagram. We evaluate o...
متن کامل