Construction of 3D triangles on Dupin cyclides

Bertrand Belbis, Lionel Garnier, Sebti Foufou

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This paper considers the conversion of the parametric Bézier surfaces, classically used in CAD-CAM, into patched of a class of non-spherical degree 4 algebraic surfaces called Dupin cyclides, and the definition of 3D triangle with circular edges on Dupin cyclides. Dupin cyclides was 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. The authors use the properties of these surfaces to prove that three families of circles (meridian arcs, parallel arcs, and Villarceau circles) can be computed on every Dupin cyclide. A geometric algorithm to compute these circles so that they define the edges of a 3D triangle on the Dupin cyclide is presented. Examples of conversions and 3D triangles are also presented to illustrate the proposed algorithms.

Original languageEnglish (US)
Title of host publicationIntelligent Computer Vision and Image Processing
Subtitle of host publicationInnovation, Application, and Design
PublisherIGI Global
Pages113-127
Number of pages15
ISBN (Electronic)9781466639096
ISBN (Print)9781466639072
DOIs
StatePublished - Apr 30 2013

ASJC Scopus subject areas

  • Computer Science(all)

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    Belbis, B., Garnier, L., & Foufou, S. (2013). Construction of 3D triangles on Dupin cyclides. In Intelligent Computer Vision and Image Processing: Innovation, Application, and Design (pp. 113-127). IGI Global. https://doi.org/10.4018/978-1-4666-3906-5.ch009