Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm
- Univ. of Maryland, College Park, MD (United States). Dept. of Computer Science
- Univ. of Texas, Austin, TX (United States). Dept. of Computer Science
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
- Univ. of California, Davis, CA (United States). Dept. of Electrical and Computer Engineering
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Univ. of California, Davis, CA (United States). Dept. of Electrical and Computer Engineering
We study the problem of decomposing a volume with a smooth boundary into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained elusive. VoroCrust leverages ideas from weighted α-shapes and the power crust algorithm to produce unweighted Voronoi cells conforming to the surface, yielding the first provably-correct algorithm for this problem. Given a κ-sparse ε-sample, we work with the balls of radius δ times the local feature size centered at each sample. The corners of the union of these balls on both sides of the surface are the Voronoi sites and the interface of their cells is a watertight surface reconstruction embedded in the dual shape of the union of balls. With the surface protected, the enclosed volume can be further decomposed by generating more sites inside it. Compared to clipping-based algorithms, VoroCrust cells are full Voronoi cells, with convexity and fatness guarantees. Compared to the power crust algorithm, VoroCrust cells are not filtered, are unweighted, and offer greater flexibility in meshing the enclosed volume by either structured or randomly genenerated samples.
- Research Organization:
- Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
- Grant/Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1502453
- Alternate ID(s):
- OSTI ID: 1526526
- Report Number(s):
- SAND--2018-3812J; 670144
- Journal Information:
- LIPIcs-Leibniz International Proceedings in Informatics, Journal Name: LIPIcs-Leibniz International Proceedings in Informatics Vol. 99; ISSN 1868-8969
- Publisher:
- Dagstuhl Research Online Publication Server (DROPS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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