2002/12/13 by Xianfeng Gu, Shing-Tung Yau, Shing–Tung Yau +2 · 1 citation
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Computer Graphics and Visualization Techniques #F.2.2 #FOS: Computer and information sciences #G.2.m #Graphics (cs.GR) #I.3.5 #cs.CG #cs.GR
paper · pdf · doi:10.48550/arxiv.cs/0212043
14 pages, 3 figures, simplified version, full version upon request
arxiv created 2002/12/13 · openalex publication_date 2002/12/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures, then construct dual cohomology bases and diffuse them to harmonic 1-forms. Next, we construct bases of holomorphic differentials. We then obtain period matrices by integrating holomorphic differentials along homology bases. We also study the global conformal mapping between genus zero surfaces and spheres, and between general meshes and planes. Our method of computing conformal structures can be applied to tackle fundamental problems in computer aid design and computer graphics, such as geometry classification and identification, and surface global parametrization.