Exact and efficient polyhedral envelope containment check
Exact and efficient polyhedral envelope containment check
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DOI：
10.1145/3386569.3392426
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发表时间：
2020-07
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影响因子：
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通讯作者：
Bolun Wang;T. Schneider;Yixin Hu;M. Attene;Daniele Panozzo
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文献类型：
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作者：
Bolun Wang;T. Schneider;Yixin Hu;M. Attene;Daniele Panozzo
我们引入了一种新技术，用于检查在围绕给定三角形网格构建的包络内三角形的包含情况。虽然现有方法保守地检查在欧几里得包络内的包含情况，但我们的方法利用了一种非欧几里得包络，在其中可以精确且高效地检查包含情况。精确性对于解决现有几何处理算法中的主要稳健性问题至关重要，我们通过将我们的技术集成到两个曲面三角形重新网格化算法和一个体四面体网格化算法中证明了这一点。我们对我们的方法和替代算法进行了定量比较，表明我们的解决方案除了精确之外，也更高效。实际上，虽然在大的包络内的包含情况可以在相当的时间内检查，但我们表明当包络变窄时我们的算法优于替代方法。
We introduce a new technique to check containment of a triangle within an envelope built around a given triangle mesh. While existing methods conservatively check containment within a Euclidean envelope, our approach makes use of a non-Euclidean envelope where containment can be checked both exactly and efficiently. Exactness is crucial to address major robustness issues in existing geometry processing algorithms, which we demonstrate by integrating our technique in two surface triangle remeshing algorithms and a volumetric tetrahedral meshing algorithm. We provide a quantitative comparison of our method and alternative algorithms, showing that our solution, in addition to being exact, is also more efficient. Indeed, while containment within large envelopes can be checked in a comparable time, we show that our algorithm outperforms alternative methods when the envelope becomes thin.