Meshless power diagrams

Abstract

The computation of power diagrams (or weighted Voronoi diagrams) is a fundamental task in computational geometry and computer graphics. To accomplish the computation, we provide a different way from the existing ones for lifting the weighted seeds to a set of points in the space of one dimension higher, then the power cells can be directly obtained by computing the intersections of the Voronoi cells of these lifting points and the original space. This property enables us to apply the method based on the k-nearest neighbors query to the generation of power diagrams. Each power cell is obtained by sequentially clipping the input domain using the bisectors between its seed and the k-nearest neighbors. Experimental results demonstrate that our method outperforms the state-of-the-art one based on regular triangulation in terms of efficiency for general cases in the 2D and 3D spaces.