Cascading upper bounds for triangle soup Pompeiu-Hausdorff distance

TL;DR

This paper introduces a novel method for approximating the Pompeiu-Hausdorff distance between triangle soups using multiple upper bounds, significantly improving speed over previous methods.

Contribution

It proposes a new approach employing four upper bounds for efficient distance approximation, with three being newly developed, enhancing computational speed and accuracy.

Findings

Method is faster than previous accurate methods

Uses four upper bounds for better approximation

Effective in discarding non-maximizing triangles

Abstract

We propose a new method to accurately approximate the Pompeiu-Hausdorff distance from a triangle soup A to another triangle soup B up to a given tolerance. Based on lower and upper bound computations, we discard triangles from A that do not contain the maximizer of the distance to B and subdivide the others for further processing. In contrast to previous methods, we use four upper bounds instead of only one, three of which newly proposed by us. Many triangles are discarded using the simpler bounds, while the most difficult cases are dealt with by the other bounds. Exhaustive testing determines the best ordering of the four upper bounds. A collection of experiments shows that our method is faster than all previous accurate methods in the literature.