Parameterization of star-shaped volumes using Green's functions

Jiazhi Xia, Ying He, Shuchu Han, Chi Wing Fu, Feng Luo, Xianfeng Gu

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

23 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationAdvances in Geometric Modeling and Processing - 6th International Conference, GMP 2010, Proceedings
Pages219-235
Number of pages17
DOIs
StatePublished - 2010
Event6th International Conference on Advances in Geometric Modeling and Processing, GMP 2010 - Castro Urdiales, Spain
Duration: Jun 16 2010Jun 18 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6130 LNCS

Other

Other6th International Conference on Advances in Geometric Modeling and Processing, GMP 2010
Country/TerritorySpain
CityCastro Urdiales
Period6/16/106/18/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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