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.

翻译：由于Voronoi图在众多应用领域中频繁出现，提升其计算效率的研究课题持续受到关注。本文提出一种新颖且高效的方法，用于计算给定边界域内的Voronoi图，即裁剪或受限Voronoi图。通过从边界域中移除位于单元外部的部分，可生成边界域与Voronoi单元的交集（域-单元交集），该过程可通过多次裁剪操作实现。与现有方法不同，我们提出一种基于边的搜索方案来寻找裁剪平面（等分面）。首先建立一种称为"点-单元测试"的判定方法，用于判断空间点是否位于目标Voronoi单元内。随后，对于中间域-单元交集的每条边，仅当其两个端点分别位于对应Voronoi单元的内部和外部时，才会触发裁剪操作，此时可通过数次点-单元测试确定裁剪所需的等分面。因此，本方法仅涉及对最终结果有贡献的裁剪操作，相较于现有先进方法具有显著优势。此外，由于每个域-单元交集均可独立生成，我们将所提方法扩展至GPU平台以实现并行化的Voronoi图计算。实验结果表明，无论站点分布情况如何，本方法均展现出优于现有先进算法的性能表现。本文已首次投稿至SIGGRAPH Asia 2025会议。