Iterative construction of Dupin cyclides characteristic circles using non-stationary Iterated Function Systems (IFS)

Lucie Druoton 1 Lionel Garnier 2 Rémi Langevin 3
1 MGSI
IMB - Institut de Mathématiques de Bourgogne [Dijon], Le2i - Laboratoire Electronique, Informatique et Image [UMR6303]
Abstract : A Dupin cyclide can be defined, in two different ways, as the envelope of an one-parameter family of oriented spheres. Each family of spheres can be seen as a conic in the space of spheres. In this paper, we propose an algorithm to compute a characteristic circle of a Dupin cyclide from a point and the tangent at this point in the space of spheres. Then, we propose iterative algorithms (in the space of spheres) to compute (in 3D space) some characteristic circles of a Dupin cyclide which blends two particular canal surfaces. As a singular point of a Dupin cyclide is a point at infinity in the space of spheres, we use the massic points defined by J.C. Fiorot. As we subdivide conic arcs, these algorithms are better than the previous algorithms developed by Garnier and Gentil.
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Journal articles
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-00785315
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Submitted on : Tuesday, February 5, 2013 - 7:12:04 PM
Last modification on : Wednesday, September 12, 2018 - 1:26:08 AM

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  • HAL Id : hal-00785315, version 1

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Lucie Druoton, Lionel Garnier, Rémi Langevin. Iterative construction of Dupin cyclides characteristic circles using non-stationary Iterated Function Systems (IFS). Computer-Aided Design, Elsevier, 2012, http://www.elsevier.com/locate/cad. ⟨hal-00785315⟩

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