An algorithm to construct 3D triangles with circular edges

Bertrand Belbis, Lionel Garnier, Sebti Foufou

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

Abstract

Dupin cyclides are non-spherical algebraic surfaces of degree 4, discovered by the French mathematician Pierre-Charles Dupin at the beginning of the 19th century. A Dupin cyclide has one parametric equation, two implicit equations, and a set of circular lines of curvature. It can be defined as the image of a torus, a cone of revolution, or a cylinder of revolution by an inversion. A torus has two families of circles: meridians and parallels. A ring torus has an additional third family, called Villarceau circles. As the image, by an inversion, of a circle is a circle or a straight line, there are three families of circles onto a Dupin cyclide too. The goal of this paper is to construct, onto a Dupin cyclide, 3D triangles with circular edges defined as a meridian arc, a parallel arc, and an arc of a Villarceau circle.

Original languageEnglish (US)
Title of host publicationProceedings - 5th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2009
PublisherIEEE Computer Society
Pages16-21
Number of pages6
ISBN (Print)9780769539591
DOIs
StatePublished - 2009

Publication series

NameProceedings - 5th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2009

Keywords

  • 3D triangles
  • Circular edges
  • Dupin cyclides
  • Rational biquadratic Bézier surfaces

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Vision and Pattern Recognition
  • Signal Processing

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