Efficient computation of Voronoi diagrams of general generators in general spaces and uses thereof

摘要

A computerized method of computing the Voronoi diagram has applications including communications networks, robotics, three-dimensional networks, materials science, searching image processing, data clustering, data compression, control of a groups of methods for image processing and the like, design of electronic circuits, geographic information systems, solutions of the efficient location problem, face recognition, mesh generation and re-meshing, curve and surface generation/reconstruction, solid modeling, collision detection, controlling motion of vehicles, navigation, accident prevention, data clustering and data processing, proximity operations, nearest neighbor search, numerical simulations, weather prediction, analyzing and modeling proteins and other biological structures, designing drugs, finding shortest paths, pattern recognition and as an artistic tool. The Voronoi diagram is a decomposed region X made into cells, the decomposition being induced by a set of generators (P_k)_k-K, and a distance function, and involves finding for each generator P_k a cell, which is a set of all the points in X satisfying the condition that the distance to the current generator P=P_k is not greater than the distance thereof to the union A of the other generators, The method comprising: for each generator, and for each point p in this generator, selecting a set of directions, then for each direction recursively testing a ray in that direction, until a certain interval on the ray is of length less than or equal to a given error parameter. A point corresponding to the interval on the ray is then selected as an end point, the cells are defined from the end points, thus forming the Voronoi diagram.