Voronoi diagrams, and their more general weighted counterpart, power diagrams, are fundamental geometric constructs with wide-ranging applications. Recently, they have gained renewed attention in mesh-based neural rendering. Despite being extensively studied, the construction of 3D Voronoi diagrams for large-scale point sets remains computationally expensive, limiting their adoption in large-scale applications. Existing CPU-based approaches typically rely on computing its dual, the Delaunay tetrahedralization, but are prohibitively slow for large diagrams, while GPU-based methods either struggle to scale efficiently to large point sets or assume homogeneous point distributions. The weighted case, power diagrams, is even less explored in this context. Existing approaches are typically tailored to the application at hand, assuming homogeneous point distributions and small weight variations, making them unsuitable for general use in more complex heterogeneous data. In this paper, we present a highly parallelizable GPU algorithm for the fast construction of large-scale 3D Voronoi and power diagrams. Our approach constructs each convex cell from a weighted 3D point by progressively clipping an initial cell volume against bisecting planes induced by candidate neighboring points. To efficiently identify candidate neighbors under arbitrary spatial distributions, we introduce a culling criterion based on directional geometric bounds of the evolving cell, combined with a hierarchical best-first traversal of bounding volumes. We achieve performance on par with state-of-the-art Delaunay tetrahedralization methods on small and moderate problem sizes, while exhibiting robust scalability to large point sets and diverse spatial distributions. Moreover, our method naturally generalizes to power diagrams without additional assumptions. See https://research.zenseact.com/publications/paragram .

翻译：Voronoi图及其更具一般性的加权版本——Power图，是基础性的几何结构，具有广泛的应用场景。近年来，它们在基于网格的神经渲染中重新受到关注。尽管已有深入研究，但大规模点集的3D Voronoi图构建仍存在计算开销过大的问题，限制了其在大型应用中的采用。现有基于CPU的方法通常依赖计算其对偶结构——Delaunay四面体剖分，但对大规模图而言计算速度极慢；而基于GPU的方法要么难以高效扩展至大规模点集，要么假设点分布均匀。加权情况下的Power图在此领域的探索更为不足。现有方法通常针对特定应用场景，假设均匀点分布与小幅权值变化，难以适用于更复杂的异质性数据。本文提出一种高度并行化的GPU算法，用于快速构建大规模3D Voronoi图与Power图。该方法通过逐步利用候选邻近点诱导的平分平面对初始胞体体积进行裁剪，从加权3D点构建每个凸胞。为在任意空间分布下高效识别候选邻近点，我们引入基于动态胞体方向几何边界的剔除准则，并结合层次化最佳优先遍历的包围体结构。在中小规模问题上，本方法性能与最先进的Delaunay四面体剖分方法相当，同时在处理大规模点集及多样化空间分布时展现出稳健的可扩展性。此外，本方法无需额外假设即可自然推广至Power图。详见 https://research.zenseact.com/publications/paragram 。