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Parameterization of Star-Shaped Volumes Using Green’s Functions

  • Jiazhi Xia
  • Ying He
  • Shuchu Han
  • Chi-Wing Fu
  • Feng Luo
  • Xianfeng Gu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6130)

Abstract

Parameterizations have a wide range of applications in computer graphics, geometric design and many other fields of science and engineering. Although surface parameterizations have been widely studied and are well developed, little research exists on the volumetric data due to the intrinsic difficulties in extending surface parameterization algorithms to volumetric domain. In this paper, we present a technique for parameterizing star-shaped volumes using the Green’s functions. We first show that the Green’s function on the star shape has a unique critical point. Then we prove that the Green’s functions can induce a diffeomorphism between two star-shaped volumes. We develop algorithms to parameterize star shapes to simple domains such as balls and star-shaped polycubes, and also demonstrate the volume parameterization applications: volumetric morphing, anisotropic solid texture transfer and GPU-based volumetric computation.

Keywords

Integration Curve Volume Parameterization Tetrahedral Mesh Ball Parameterization Volumetric Parameterization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jiazhi Xia
    • 1
  • Ying He
    • 1
  • Shuchu Han
    • 1
  • Chi-Wing Fu
    • 1
  • Feng Luo
    • 2
  • Xianfeng Gu
    • 3
  1. 1.School of Computer EngineeringNanyang Technological UniversitySingapore
  2. 2.Department of MathematicsRutgers UniversityUSA
  3. 3.Department of Computer ScienceStony Brook UniversityUSA

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