A big problem in triangular remeshing is to generate meshes when the triangle size approaches the feature size in the mesh. The main obstacle for Centroidal Voronoi Tessellation (CVT)-based remeshing is to compute a suitable Voronoi diagram. In this paper, we introduce the localized restricted Voronoi diagram (LRVD) on mesh surfaces. The LRVD is an extension of the restricted Voronoi diagram (RVD), but it addresses the problem that the RVD can contain Voronoi regions that consist of multiple disjoint surface patches. Our definition ensures that each Voronoi cell in the LRVD is a single connected region. We show that the LRVD is a useful extension to improve several existing mesh-processing techniques, most importantly surface remeshing with a low number of vertices. While the LRVD and RVD are identical in most simple configurations, the LRVD is essential when sampling a mesh with a small number of points and for sampling surface areas that are in close proximity to other surface areas, e.g., nearby sheets. To compute the LRVD, we combine local discrete clustering with a global exact computation. © 1995-2012 IEEE.
|Number of pages
|IEEE Transactions on Visualization and Computer Graphics
|Published - Oct 1 2014
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors thank the anonymous reviewers for their valuable comments and suggestions. They are grateful to Sebastien Valette for the ACVD software and to Xiaohu Guo for the HCVT results. This work was supported by the KAUST Visual Computing Center, the National Natural Science Foundation of China (nos. 61372168, 61331018, 61271431 and 61272327), and the US National Science Foundation (NSF).
ASJC Scopus subject areas
- Signal Processing
- Computer Graphics and Computer-Aided Design
- Computer Vision and Pattern Recognition