Computing the Voronoi diagram of a given set of points in a restricted domain (e.g., inside a 2D polygon, on a 3D surface, or within a volume) has many applications. Although existing algorithms can compute 2D and surface Voronoi diagrams in parallel on graphics hardware, computing clipped Voronoi diagrams within volumes remains a challenge. This article proposes an efficient GPU algorithm to tackle this problem. A preprocessing step discretizes the input volume into a tetrahedral mesh. Then, unlike existing approaches which use the bisecting planes of the Voronoi cells to clip the tetrahedra, we use the four planes of each tetrahedron to clip the Voronoi cells. This strategy drastically simplifies the computation, and as a result, it outperforms state-of-the-art CPU methods up to an order of magnitude.

中文翻译：

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3D 裁剪 Voronoi 图的并行计算

计算受限域（例如，在 2D 多边形内、在 3D 表面上或在体积内）的一组给定点的 Voronoi 图有许多应用。尽管现有算法可以在图形硬件上并行计算 2D 和表面 Voronoi 图，但计算体积内的裁剪 Voronoi 图仍然是一个挑战。本文提出了一种高效的 GPU 算法来解决这个问题。预处理步骤将输入体积离散化为四面体网格。然后，与使用 Voronoi 单元的二等分平面来裁剪四面体的现有方法不同，我们使用每个四面体的四个平面来裁剪 Voronoi 单元。这种策略极大地简化了计算，因此，它的性能比最先进的 CPU 方法高出一个数量级。