Conversion of biquadratic rational Bézier surfaces into patches of particular Dupin cyclides: The torus and the double sphere

Lionel Garnier, Bertrand Belbis, Sebti Foufou

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

Abstract

Toruses and double spheres are particular cases of Dupin cyclides. In this paper, we study the conversion of rational biquadratic Bézier surfaces into Dupin cyclide patches. We give the conditions that the Bézier surface should satisfy to be convertible, and present a new conversion algorithm to construct the torus or double sphere patch corresponding to a given Bézier surface, some conversion examples are illustrated and commented.

Original languageEnglish (US)
Title of host publication17th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, WSCG'2009 - In Co-operation with EUROGRAPHICS, Full Papers Proceedings
Pages101-107
Number of pages7
StatePublished - 2009
Event17th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, WSCG'2009 - Plzen, Czech Republic
Duration: Feb 2 2009Feb 5 2009

Publication series

Name17th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, WSCG'2009 - In Co-operation with EUROGRAPHICS, Full Papers Proceedings

Other

Other17th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, WSCG'2009
CountryCzech Republic
CityPlzen
Period2/2/092/5/09

Keywords

  • Rational biquadratic Bézier surfaces
  • Torus and Dupin cyclides surfaces

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition

Cite this

Garnier, L., Belbis, B., & Foufou, S. (2009). Conversion of biquadratic rational Bézier surfaces into patches of particular Dupin cyclides: The torus and the double sphere. In 17th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, WSCG'2009 - In Co-operation with EUROGRAPHICS, Full Papers Proceedings (pp. 101-107). (17th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, WSCG'2009 - In Co-operation with EUROGRAPHICS, Full Papers Proceedings).