📝 SummarXiv

Abstract

Since the Voronoi diagram appears in many applications, the topic of improving its computational efficiency remains attractive. We propose a novel yet efficient method to compute Voronoi diagrams bounded by a given domain, i.e., the clipped or restricted Voronoi diagrams. The intersection of the domain and a Voronoi cell (domain-cell intersection) is generated by removing the part outside the cell from the domain, which can be accomplished by several clippings. Different from the existing methods, we present an edge-based search scheme to find clipping planes (bisectors). A test called point-in-cell is first set up to tell whether a space point is in a target Voronoi cell or not. Then, for each edge of the intermediate domain-cell intersection, we will launch a clipping only if its two endpoints are respectively inside and outside the corresponding Voronoi cell, where the bisector for the clipping can be found by using a few times of point-in-cell tests. Therefore, our method only involves the clippings that contribute to the final results, which is a great advantage over the state-of-the-art methods. Additionally, because each domain-cell intersection can be generated independently, we extend the proposed method to the GPUs for computing Voronoi diagrams in parallel. The experimental results show the best performance of our method compared to state-of-the-art ones, regardless of site distribution. This paper was first submitted to SIGGRAPH Asia 2025.