Obtaining implicit equations of supercyclides and definition of elliptic supercyclides

Sebti Foufou, Lionel Garnier

Research output: Contribution to journalArticlepeer-review


The use of Dupin cyclides and supercyclides in CAGD applications has been the subject of many publications in the last decade. Dupin cyclides are low degree algebraic surfaces having both parametric and implicit representations. In this paper, we aim to give the necessary expansions to derive implicit equations of supercyclides in the affine as well as in the projective space, starting from equations of the Dupin cyclide and the transformation matrix. We introduce a particular subfamily of supercyclides, called elliptic supercyclides, and show how to use them for the blending of elliptic quadratic primitives. We also show how one can convert an elliptic supercyclide into a set of rational biquadratic Bézier patches.

Original languageEnglish (US)
Pages (from-to)123-144
Number of pages22
JournalMachine Graphics and Vision
Issue number2
StatePublished - 2005


  • Dupin cyclides
  • Projective and affine geometry
  • Supercyclides

ASJC Scopus subject areas

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

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