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.

翻译：我们提出了一种新方法，用于在给定容差范围内精确逼近从一个三角形网格A到另一个三角形网格B的Pompeiu-Hausdorff距离。该方法基于下界和上界的计算，首先剔除A中不包含到B距离最大化点的三角形，并对剩余三角形进行细分以进一步处理。与先前方法仅使用一个上界不同，我们采用了四个上界，其中三个为我们新提出的上界。通过较简单的上界可剔除大量三角形，而最困难的情况则由其他上界处理。通过详尽测试确定了这四个上界的最佳使用顺序。一系列实验表明，我们的方法比文献中所有现有精确方法更为快速。