A new efficient algorithm for volume-preserving parameterizations of genus-one 3-manifolds

Mei Heng Yueh*, Tiexiang Li, Wen Wei Lin, Shing Tung Yau

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

摘要

Parameterizations of manifolds are widely applied to the fields of numerical partial differential equations and computer graphics. To this end, in recent years several efficient and reliable numerical algorithms have been developed by different research groups for the computation of triangular and tetrahedral mesh parameterizations. However, it is still challenging when the topology of manifolds is nontrivial, e.g., the 3-manifold of a topological solid torus. In this paper, we propose a novel volumetric stretch energy minimization algorithm for volume-preserving parameterizations of toroidal polyhedra with a single boundary being mapped to a standard torus. In addition, the algorithm can also be used to compute the equiareal mapping between a genus-one closed surface and the standard torus. Numerical experiments indicate that the developed algorithm is effective and performs well on the bijectivity of the mapping. Applications on manifold registrations and partitions are demonstrated to show the robustness of our algorithms.

原文英語
頁(從 - 到)1536-1564
頁數29
期刊SIAM Journal on Imaging Sciences
13
發行號3
DOIs
出版狀態已發佈 - 2020

ASJC Scopus subject areas

  • 數學(全部)
  • 應用數學

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