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 arbitrarily 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 polyhedral Voronoi meshing for non-convex and 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 preserving all sharp features 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.

翻译：多面体网格正日益成为一种具有吸引力的选择，在某些应用中较传统网格具有特定优势。然而，目前仍缺乏一种鲁棒的多面体网格生成算法，能够处理包含任意弯曲边界和尖锐特征的广泛域类型。此外，以沃罗诺伊-德劳内网格为代表的原始-对偶网格对在众多公式中被视为关键要素。VoroCrust算法是首个经证明正确的算法，可对非凸和非流形域进行保形多面体沃罗诺伊网格划分，同时保证表面和体积单元的质量。该算法通过鲁棒的细化过程估算合适的尺寸场，从而在曲面表面精心放置沃罗诺伊种子，避免裁剪需求并规避其诸多缺陷。该算法具有灵活性，可通过结构化或随机采样填充内部区域，同时保留输出网格中的所有尖锐特征。我们通过多种模型展示了该算法的能力，并与基于裁剪沃罗诺伊单元的最新多面体网格生成方法进行了对比，证明了VoroCrust输出结果的显著优势。