P2M++: Enhanced Solver for Point-to-Mesh Distance Queries

TL;DR

P2M++ significantly improves point-to-mesh distance query efficiency by optimizing Voronoi-based localization, interference detection, and search algorithms, reducing preprocessing and query times especially on symmetric geometries.

Contribution

The paper introduces P2M++, a novel method that enhances Voronoi-based point-to-mesh distance queries through adaptive vertex augmentation, sphere-triangle collision reformulation, and faster search techniques.

Findings

P2M++ is 3x-10x faster in preprocessing than P2M.

Query times are reduced by 1.5x with P2M++.

Performance gains are especially notable on symmetric geometries.

Abstract

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.