Optimal global conformal surface parameterization

Miao Jin, Yalin Wang, Shing Tung Yau, Xianfeng Gu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

86 Scopus citations

Abstract

All orientable metric surfaces are Riemann surfaces and admit global conformal parameterizations. Riemann surface structure is a fundamental structure and governs many natural physical phenomena, such as heat diffusion and electro-magnetic fields on the surface. A good parameterization is crucial for simulation and visualization. This paper provides an explicit method for finding optimal global conformal parameterizations of arbitrary surfaces. It relies on certain holomorphic differential forms and conformal mappings from differential geometry and Riemann surface theories. Algorithms are developed to modify topology, locate zero points, and determine cohomology types of differential forms. The implementation is based on a finite dimensional optimization method. The optimal parameterization is intrinsic to the geometry, preserves angular structure, and can play an important role in various applications including texture mapping, remeshing, morphing and simulation. The method is demonstrated by visualizing the Riemann surface structure of real surfaces represented as triangle meshes.

Original languageEnglish (US)
Title of host publicationIEEE Visualization 2004 - Proceedings, VIS 2004
EditorsH. Rushmeier, G. Turk, J.J. Wijk
Pages267-274
Number of pages8
StatePublished - Dec 1 2004
Externally publishedYes
EventIEEE Visualization 2004 - Proceedings, VIS 2004 - Austin, TX, United States
Duration: Oct 10 2004Oct 15 2004

Publication series

NameIEEE Visualization 2004 - Proceedings, VIS 2004

Other

OtherIEEE Visualization 2004 - Proceedings, VIS 2004
Country/TerritoryUnited States
CityAustin, TX
Period10/10/0410/15/04

Keywords

  • Computational geometry and object modeling
  • Curve, surface, solid, and object representations
  • Surface parameterization

ASJC Scopus subject areas

  • Engineering(all)

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