Point-to-mesh distance queries are fundamental in computer graphics and geometric modeling. While the state-of-the-art P2M method achieves high-speed queries via Voronoi-based localization, it suffers from prohibitive precomputation costs. Its iterative Voronoi sweep for interference detection leads to redundant predicate evaluations and scales poorly on rotationally symmetric structures (e.g., spheres, cones or cylinders), where candidate counts grow quadratically. We propose P2M++ to address these limitations through three key contributions. First, we adaptively augment the set of mesh vertices with auxiliary sites in regions of high Voronoi vertex density to localize complex interference within minimal spatial regions. Second, we reformulate interference detection as a series of sphere-triangle collision tests centered at Voronoi cell corners, which are efficiently resolved using the base mesh's BVH. Finally, we enhance runtime performance by replacing the standard kd-tree search with a faster recursive dynamic programming implementation. Experimental results demonstrate that P2M++ is 3x-10x faster than the original P2M during preprocessing and 1.5x faster in queries, with even more pronounced gains on rotationally symmetric geometries.

翻译：点-网格距离查询是计算机图形学和几何建模中的基础操作。当前最先进的P2M方法通过基于Voronoi的定位实现了高速查询，但其预计算开销过高。该方法在干涉检测中使用的迭代式Voronoi扫描会导致冗余谓词评估，且在旋转对称结构（如球体、圆锥体或圆柱体）上扩展性差，候选点数量呈二次增长。我们提出P2M++通过三项关键贡献来解决这些限制。首先，我们在Voronoi顶点密度高的区域自适应地用辅助站点扩充网格顶点集合，以在最小空间区域内定位复杂干涉。其次，我们将干涉检测重新表述为一系列以Voronoi单元角落为中心的球-三角形碰撞测试，并利用基础网格的BVH高效求解。最后，我们通过用更快的递归动态规划实现替换标准kd树搜索来提升运行时性能。实验结果表明，P2M++的预处理速度比原始P2M快3-10倍，查询速度快1.5倍，且在旋转对称几何体上效果尤为显著。