Dupin cyclide blends between non-natural quadrics of revolution and concrete shape modeling applications

Lionel Garnier, Hichem Barki, Sebti Foufou

Research output: Contribution to journalArticlepeer-review


In this work, we focus on the blending of two quadrics of revolution by two patches of Dupin cyclides. We propose an algorithm for the blending of non-natural quadrics of revolution by decomposing the blending operation into two complementary sub-blendings, each of which is a Dupin cyclide-based blending between one of the two quadrics and a circular cylinder, thus enabling the direct computation of the two Dupin cyclide patches and offering better flexibility for shape composition. Our approach uses rational quadric Bézier curves to model the relevant arcs of the principal circles of Dupin cyclides. It is quite general and we have successfully used it for the blending of several non-natural surfaces of revolution, such as paraboloids, hyperboloids, tori, catenaries, and pseudospheres. Two complete examples of 3D shape modeling, representing a satellite antenna and a hippocampus are presented to show how quadrics and Dupin cyclide patches can be combined to model concrete objects.

Original languageEnglish (US)
Pages (from-to)31-41
Number of pages11
JournalComputers and Graphics (Pergamon)
Issue number1
StatePublished - Aug 2014


  • Algebraic surfaces
  • Blending
  • Dupin cyclides
  • Quadrics of revolution

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • General Engineering
  • Human-Computer Interaction
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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