Abstract
In this paper, we propose a simple-yet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation (CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing high-quality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient, and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-of- the-art techniques, but is significantly faster than conventional CPU-based implementations.
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Yuen-Shan Leung received her B.Eng. degree and her Ph.D. degree from the Chinese University of Hong Kong. She is currently a research fellow at the School of Computer Engineering, Nanyang Technological University, Singapore. Her research interests include geometric & solid modeling, computer-aided design & manufacturing, and computer graphics.
Xiaoning Wang received the B.Eng. degree from Tianjin University, China, in 2011. He is currently a Ph.D. candidate in the School of Computer Engineering, Nanyang Technological Univeristy, Singapore. His research interests are geometry analysis and computer graphics.
Ying He is currently an associate professor at the School of Computer Engineering, Nanyang Technological University, Singapore. He received the B.S. and M.S. degrees in electrical engineering from Tsinghua University, China, and the Ph.D. degree in computer science from Stony Brook University, USA. His research interests fall into the general area of visual computing, and he is particularly interested in the problems which require geometric analysis and computation. For more information, please visit http://www.ntu.edu.sg/home/yhe.
Yong-Jin Liu received his B.Eng. degree from Tianjin University, China, in 1998, and his M.Phil. and Ph.D. degrees from Hong Kong University of Science and Technology (HKUST), Hong Kong, China, in 2000 and 2004, respectively. He is now an associate professor at the Tsinghua National Laboratory for Information Science and Technology, the Department of Computer Science and Technology, Tsinghua University, China. His research interests include computational geometry, multimedia, computer graphics, and computer- aided design. For more information, please visit http://cg.cs.tsinghua.edu.cn/people/~Yongjin/yongjin.htm.
Charlie C. L. Wang is a Fellow of the American Society of Mechanical Engineers (ASME) with expertise in geometric computing, design, and manufacturing. He received his Ph.D. in mechanical engineering from HKUST in 2002. After that, he joined the Chinese University of Hong Kong in 2003, and is now a full professor of mechanical and automation engineering. His research interests include geometric computing, computer-aided design, advanced manufacturing, and computational physics.
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Leung, YS., Wang, X., He, Y. et al. A unified framework for isotropic meshing based on narrow-band Euclidean distance transformation. Comp. Visual Media 1, 239–251 (2015). https://doi.org/10.1007/s41095-015-0022-4
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DOI: https://doi.org/10.1007/s41095-015-0022-4