標題: A Novel Algorithm for Volume-Preserving Parameterizations of 3-Manifolds
作者: Yueh, Mei-Heng
Li, Tiexiang
Lin, Wen-Wei
Yau, Shing-Tung
應用數學系
Department of Applied Mathematics
關鍵字: volumetric stretch energy minimization;volume-preserving parameterization;simply connected 3-manifold;manifold parameterization;genus-zero closed surface
公開日期: 1-Jan-2019
摘要: Manifold parameterizations have been applied to various fields of commercial industries. Several efficient algorithms for the computation of triangular surface mesh parameterizations have been proposed in recent years. However, the computation of tetrahedral volumetric mesh parameterizations is more challenging due to the fact that the number of mesh points would become enormously large when the higher-resolution mesh is considered and the bijectivity of parameterizations is more difficult to guarantee. In this paper, we develop a novel volumetric stretch energy minimization algorithm for volume-preserving parameterizations of simply connected 3-manifolds with a single boundary under the restriction that the boundary is a spherical area-preserving mapping. In addition, our algorithm can also be applied to compute spherical angle- and area-preserving parameterizations of genus-zero closed surfaces, respectively. Several numerical experiments indicate that the developed algorithms are more efficient and reliable compared to other existing algorithms. Numerical results on applications of the manifold partition and the mesh processing for three-dimensional printing are demonstrated thereafter to show the robustness of the proposed algorithm.
URI: http://dx.doi.org/10.1137/18M1201184
http://hdl.handle.net/11536/152226
ISSN: 1936-4954
DOI: 10.1137/18M1201184
期刊: SIAM JOURNAL ON IMAGING SCIENCES
Volume: 12
Issue: 2
起始頁: 1071
結束頁: 1098
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