Title :
Low-Resolution Remeshing Using the Localized Restricted Voronoi Diagram
Author :
Dong-Ming Yan ; Guanbo Bao ; Xiaopeng Zhang ; Wonka, Peter
Author_Institution :
King Abdullah Univ. of Sci. & Technol., Thuwal, Saudi Arabia
Abstract :
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.
Keywords :
computational geometry; mesh generation; rendering (computer graphics); CVT-based remeshing; LRVD; centroidal Voronoi tessellation; local discrete clustering; localized restricted Voronoi diagram; low-resolution remeshing; multiple disjoint surface patches; triangular remeshing; Algorithm design and analysis; Approximation algorithms; Approximation methods; Euclidean distance; Surface treatment; Three-dimensional displays; Localized restricted Voronoi diagram; Poisson-disk sampling; centroidal Voronoi tessellation; remeshing;
Journal_Title :
Visualization and Computer Graphics, IEEE Transactions on
DOI :
10.1109/TVCG.2014.2330574