期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 274, 期 -, 页码 23-34出版社
ELSEVIER
DOI: 10.1016/j.cam.2014.07.001
关键词
Surface sampling; Mesh quality; Delaunay triangulation; 2-manifold mesh reconstruction
资金
- Natural Science Foundation of China [61322206, 61373003]
- National Basic Research Program of China [2011CB302202]
- National High Technology Research and Development Program of China [2012AA011801]
- Beijing Higher Institution Engineering Research Center of Visual Media Intelligent Processing and Security
- Tsinghua University Initiative Scientific Research Program [20131089252]
Several sampling criteria had been proposed for C-2 smooth surfaces such that the reconstructed meshes from point samples are homeomorphic to the original surfaces. In this paper, based on a widely used sample criterion, we present proofs that give the upper and lower bounds of mesh quality (in terms of several triangle aspect ratios) for the reconstructed mesh. To make the proposed theoretical bounds useful in practical applications with real-world point data, we propose a novel mesh reconstruction method that works in three steps: (1) approximate Delaunay mesh reconstruction; (2) point data upsampling and (3) hole filling. Finally, examples are presented, which illustrate the effectiveness of the proposed method. (C) 2014 Elsevier B.V. All rights reserved.
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