2002/01/01 by Xianfeng Gu, Shing–Tung Yau · 3 citations
Computer Science · Engineering · Mathematics · #Digital Image Processing Techniques #Computer Graphics and Visualization Techniques #3D Shape Modeling and Analysis #Morphing #Conformal map #Euclidean geometry #Group (periodic table) #Transformation (genetics) #Euclidean space #Transformation group #Computer graphics #Graphics #Transformation geometry #Mathematics #Geometry #Division (mathematics) #Surface (topology) #Topology (electrical circuits) #Algebra over a field #Computer graphics (images) #Computer science #Pure mathematics #Combinatorics #Arithmetic #Physics
paper · pdf · doi:10.4310/cis.2002.v2.n2.a2
openalex publication_date 2002/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
This paper solves the problem of computing conformal structures of general 2manifolds represented as triangular meshes. We approximate the De Rham cohomology by simplicial cohomology and represent the Laplace-Beltrami operator, the Hodge star operator by linear systems. A basis of holomorphic one-forms is constructed explicitly. We then obtain a period matrix by integrating holomorphic differentials along a homology basis. We also study the global conformal mappings between genus zero surfaces and spheres, and between general surfaces and planes. Our method of computing conformal structures can be applied to tackle fundamental problems in computer aid geometry design and computer graphics, such as geometry classification and identification, and surface global parametrization.