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

2026-05-01

AI Summary

Existing point-to-mesh distance query methods suffer from high precomputation costs and quadratic growth in candidate counts when handling rotationally symmetric structures, leading to inefficiency. This work proposes an efficient query framework that adaptively introduces auxiliary sites to localize complex interference, transforming interference detection into sphere–triangle collision tests based on Voronoi cell corners. Instead of conventional kd-tree searches, the method employs recursive dynamic programming. Combined with BVH acceleration and optimized spatial partitioning, the approach achieves 3–10× speedup in preprocessing and 1.5× faster query times, with particularly notable gains on rotationally symmetric geometries such as spheres and cones.

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.

Problem

• point-to-mesh distance
• Voronoi-based localization
• precomputation cost
• rotational symmetry
• interference detection

Innovation

• Voronoi-based localization
• sphere-triangle collision
• BVH acceleration
• adaptive auxiliary sites
• recursive dynamic programming