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A spherical parameterization approach based on symmetry analysis of triangular meshes

Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第7期10卷 1009-1017页

作者： Jian-ping HU Xiu-ping LIU Zhi-xun SU Xi-quan SHI Feng-shan LIU School of Mathematical Sciences Dalian University of Technology Dalian 116024 China Department of Applied Mathematics and Theoretical Physics Delaware State University Dover DE 19901 USA

We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.

关键词： Triangular mesh spherical parameterization Symmetry analysis

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Processing of 3D meshed surfaces using spherical wavelets

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Computer Aided Drafting,Design and Manufacturing 2012年第1期22卷 20-26页

作者： Hu Jianping Liu Xiuping WangXiaochao and Xie Qi School of Science Northeast Dianli University Jilin 132012 China Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education J ilin University Changchun 130012 China School of Mathematical Sciences Dalian University of Technology Dalian 116024 China

This paper presents an efficient technique for processing of 3D meshed surfaces via spherical wavelets. More specifically, an input 3D mesh is firstly transformed into a spherical vector signal by a fast low distortion spherical parameterization approach based on symmetry analysis of 3D meshes. This signal is then sampled on the sphere with the help of an adaptive sampling scheme. Finally, the sampled signal is transformed into the wavelet domain according to spherical wavelet transform where many 3D mesh processing operations can be implemented such as smoothing, enhancement, compression, and so on. Our main contribution lies in incorporating a fast low distortion spherical parameterization approach and an adaptive sampling scheme into the frame for pro- cessing 3D meshed surfaces by spherical wavelets, which can handle surfaces with complex shapes. A number of experimental ex- amples demonstrate that our algorithm is robust and efficient.

关键词： mesh processing spherical parameterization adaptive sampling spherical wavelets

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