P2M: A Fast Solver for Querying Distance from Point to Mesh Surface

TL;DR

This paper introduces P2M, a novel point-to-mesh distance query algorithm that precomputes a KD tree and interception table, significantly accelerating the process compared to existing BVH-based methods.

Contribution

The paper presents a new algorithmic paradigm for point-to-mesh distance queries using interception inspection and flooding algorithms, differing from traditional BVH-based approaches.

Findings

Runs many times faster than state-of-the-art solvers

Uses precomputed KD tree and interception table for efficiency

Effective interception inspection rule and flooding algorithm

Abstract

Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point Query (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables one to eliminate the vast majority of triangles that do not help find the closest point. In this paper, we develop a totally different algorithmic paradigm, named P2M, to speed up point-to-mesh distance queries. Our original intention is to precompute a KD tree (KDT) of mesh vertices to approximately encode the geometry of a mesh surface containing vertices, edges and faces. However, it is very likely that the closest primitive to the query point is an edge e (resp., a face f), but the KDT reports a mesh vertex \u{psion} instead. We call \u{psion} an interceptor of e (resp., f). The main contribution of this paper is to invent a simple yet effective interception inspection rule and an efficient flooding interception inspection algorithm for quickly finding out all the interception pairs. Once the KDT and the interception table are precomputed, the query stage proceeds by first searching the KDT and then looking up the interception table to retrieve the closest geometric primitive. Statistics show that our query algorithm runs many times faster than the state-of-the-art solvers.