Abdelkader Ahmed, Bajaj Chandrajit L, Ebeida Mohamed S, Mahmoud Ahmed H, Mitchell Scott A, Owens John D, Rushdi Ahmad A
University of Maryland, College Park.
University of Texas, Austin.
ACM Trans Graph. 2020 May;39(3). doi: 10.1145/3337680.
Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrary curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably correct algorithm for conforming Voronoi meshing for non-convex and possibly non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while all sharp features are preserved in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.
多面体网格正日益成为一种有吸引力的选择，在某些应用中相对于传统网格具有特殊优势。一直缺少的是一种强大的多面体网格划分算法，它能够处理具有任意弯曲边界和尖锐特征的广泛类别的域。此外，以Voronoi-Delaunay网格为代表的原始-对偶网格对的作用，在众多公式中已被视为一个重要因素。VoroCrust算法是首个可证明正确的算法，用于对非凸且可能非流形的域进行符合要求的Voronoi网格划分，并能保证表面和体积单元的质量。一个强大的细化过程会估计一个合适的尺寸场，该尺寸场能够在表面上精心放置Voronoi种子，从而避免裁剪的需要并避免其诸多缺点。该算法具有灵活性，可以通过结构化或随机采样来填充内部，同时所有尖锐特征都会保留在输出网格中。我们在各种模型上展示了该算法的能力，并与基于裁剪Voronoi单元的最新多面体网格划分方法进行比较，确立了VoroCrust输出的明显优势。
