×

Computing conformal structures of surfaces. (English) Zbl 1092.14514

Summary: This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangular meshes. We approximate the de Rham cohomology by simplicial cohomology and represent the Laplace-Beltrami operator and the Hodge star operator by linear systems. A basis of holomorphic one-forms is constructed explicitly. We then obtain a periodic 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 aided geometry design and computer graphics, such as geometry classification and identification, and surface global parametrization.

MSC:

14Q10 Computational aspects of algebraic surfaces
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
PDFBibTeX XMLCite
Full Text: DOI