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Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram

Dong-Ming Yan () a12, Bruno Lévy () b1, Yang Liu () b1, Feng Sun () 2, Wenping Wang () 2

Computer Graphics Forum 28, 5 (2009) 1445-1454

Résumé : We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations of RVD. In this paper, we introduce an efficient algorithm that computes RVD exactly and robustly. As a consequence, we achieve better remeshing quality than approximation-based approaches, without sacrificing efficiency. Our method for RVD computation uses a simple procedure and a kd-tree to quickly identify and compute the intersection of each triangle face with its incident Voronoi cells. Its time complexity is O(mlogn), where n is the number of seed points and m is the number of triangles of the input mesh. Fast convergence of CVT is achieved using a quasi-Newton method, which proved much faster than Lloyd's iteration. Examples are presented to demonstrate the better quality of remeshing results with our method than with the state-of-art approaches.

  • a –  University of Hong Kong / Hong Kong
  • b –  INRIA
  • 1 :  ALICE (INRIA Lorraine - LORIA)
  • INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
  • 2 :  Department of Computer Science [Hong Kong]
  • City University of Hong Kong
  • Domaine : Informatique/Synthèse d'image et réalité virtuelle
 
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  • oai:hal.inria.fr:inria-00547790
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  • Soumis le : Vendredi 17 Décembre 2010, 15:10:47
  • Dernière modification le : Lundi 20 Décembre 2010, 09:35:28