Fast and robust computation of the Hausdorff distance between triangle mesh and quad mesh for near-zero cases

Abstract

We introduce an algorithm for computing the two-sided Hausdorff distance between a triangle mesh and a quad mesh, guaranteed to be within the given error bound, which can be machine precision-level small. The algorithm expands upon a recent breakthrough that only calculates the one-sided Hausdorff distance from the triangle mesh to the quad mesh using what is called “matching” and “upper bounding” of candidate pieces. We complete the algorithm by accomplishing the computation of the one-sided Hausdorff distance in the opposite direction: from the quad mesh to the triangle mesh. We split each quad into two triangular pieces to simplify the breakdown of matching cases and provide additional matching methods for new cases. By fusing the two one-sided computation algorithms, one can compute the two-sided Hausdorff distance that, for instance, can properly evaluate a quad mesh approximation of a triangle mesh. Experimental results show that our algorithm can handle near-zero Hausdorff distance, which has always been known to be a much difficult task, in an interactive time. Moreover, the improvement in efficiency of the two-sided Hausdorff distance computation over the successive execution of the two one-sided computations is addressed.