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Guaranteed Quality Isotropic Surface Remeshing Based on Uniformization

Ma, Ming, Xiaokang Yu, Na Lei, Hang Si, Xianfeng Gu

Proceedings, 26th International Meshing Roundtable, Elsevier, Science Direct, September 18-21 2017

INTERNATIONAL
MESHING
ROUNTABLE

26th International Meshing Roundtable
Barcelona, Spain
September 18-21, 2017

Ming Ma, Department of Computer Science, Stony Brook University, US, minma@cs.stonybrook.edu
Xiaokang Yu, College of Computer Science and Technology, Qingdao University, CN, xyu_qdu@163.com
Na Lei, School of Software and Technology, Dalian University of Technology, CN, nalei@dlut.edu.cn
Hang Si, Weierstrass Institute for Applied Analysis and Stochastics, DE, si@wias-berlin.de
Xianfeng Gu, Department of Computer Science, Stony Brook University, US, gu@cs.stonybrook.edu

Abstract
Surface remeshing plays a significant role in computer graphics and visualization. Numerous surface remeshing methods have been developed to produce high quality meshes. Generally, the mesh quality is improved in terms of vertex sampling, regularity, triangle size and triangle shape. Many of such surface remeshing methods are based on Delaunay refinement. In particular, some surface remeshing methods generate high quality meshes by performing the planar Delaunay refinement on the conformal uniformization domain. However, most of these methods can only handle topological disks. Even though some methods can cope with high-genus surfaces, they require partitioning a high-genus surface into multiple simply connected segments, and remesh each segment in the parameterized domain. In this work, we propose a novel surface remeshing method based on uniformization theorem using dynamic discrete Yamabe flow and Delaunay refinement, which is capable of handling surfaces with complicated topologies, without the need of partitioning. The proposed method has the following merits: Dimension deduction, it converts all 3D surface remeshing to 2D planar meshing; Curvature convergence, it can be shown that the Gaussian and mean curvature measures of the generated meshes converge to the smooth curvature measures; Theoretic rigor, the existence of the constant curvature measures, the lower bound of the corner angles of the generated meshes and the curvature measure convergence can be proven. Experimental results demonstrate the efficiency and efficacy of our proposed method.

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