Subdivision schemes for the fair discretization of the spherical motion group

Georg Nawratil*, Helmut Pottmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We present two subdivision schemes for the fair discretization of the spherical motion group. The first one is based on the subdivision of the 600-cell according to the tetrahedral/octahedral subdivision scheme in [S. Schaefer, J. Hakenberg, J. Warren, Smooth subdivision of tetrahedral meshes, in: R. Scopigno, D. Zorin (Eds.), Eurographics Symposium on Geometry Processing, 2004, pp. 151-158]. The second presented subdivision scheme is based on the spherical kinematic mapping. In the first step we discretize an elliptic linear congruence by the icosahedral discretization of the unit sphere. Then the resulting lines of the elliptic three-space are discretized such that the difference in the maximal and minimal elliptic distance between neighboring grid points becomes minimal.

Original languageEnglish (US)
Pages (from-to)574-591
Number of pages18
JournalJournal of Computational and Applied Mathematics
Volume222
Issue number2
DOIs
StatePublished - Dec 15 2008

Keywords

  • 600-cell
  • Discretization
  • Elliptic linear congruence
  • Spherical kinematic mapping
  • Spherical motion group

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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