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Interactive hausdorff distance computation for general polygonal models (2009)
| Venue: | In ACM Transactions on Graphics (TOG), SIGGRAPH ’09 |
| Citations: | 8 - 0 self |
BibTeX
@INPROCEEDINGS{Tang09interactivehausdorff,
author = {Min Tang and Minkyoung Lee and Young J. Kim},
title = {Interactive hausdorff distance computation for general polygonal models},
booktitle = {In ACM Transactions on Graphics (TOG), SIGGRAPH ’09},
year = {2009},
pages = {74--174}
}
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Abstract
Figure 1: Interactive Hausdorff Distance Computation. Our algorithm can compute Hausdorff distance between complicated models at interactive rates (the first three figures). Here, the green line denotes the Hausdorff distance. This algorithm can also be used to find penetration depth (PD) for physically-based animation (the last two figures). It takes only a few milli-seconds to run on average. We present a simple algorithm to compute the Hausdorff distance between complicated, polygonal models at interactive rates. The algorithm requires no assumptions about the underlying topology and geometry. To avoid the high computational and implementa-tion complexity of exact Hausdorff distance calculation, we approx-imate the Hausdorff distance within a user-specified error bound. The main ingredient of our approximation algorithm is a novel polygon subdivision scheme, called Voronoi subdivision, combined with culling between the models based on bounding volume hier-archy (BVH). This cross-culling method relies on tight yet simple computation of bounds on the Hausdorff distance, and it discards unnecessary polygon pairs from each of the input models alterna-tively based on the distance bounds. This algorithm can approxi-mate the Hausdorff distance between polygonal models consisting of tens of thousands triangles with a small error bound in real-time, and outperforms the existing algorithm by more than an order of magnitude. We apply our Hausdorff distance algorithm to the mea-surement of shape similarity, and the computation of penetration depth for physically-based animation. In particular, the penetration depth computation using Hausdorff distance runs at highly interac-tive rates for complicated dynamics scene.
Keyphrases
hausdorff distance interactive hausdorff distance computation general polygonal model polygonal model interactive rate physically-based animation penetration depth penetration depth computation volume hier-archy green line user-specified error bound voronoi subdivision exact hausdorff distance calculation main ingredient interac-tive rate cross-culling method relies input model complicated dynamic scene thousand triangle underlying topology hausdorff distance run simple computation unnecessary polygon pair approximation algorithm high computational shape similarity novel polygon subdivision scheme small error bound hausdorff distance algorithm implementa-tion complexity simple algorithm
