Title: From Dupin cyclides to scaled cyclides
Authors: Garnier, Lionel
Foufou, Sebti
Neveu, Marc
Citation: Journal of WSCG. 2003, vol. 11, no. 1-3.
Issue Date: 2003
Publisher: UNION Agency – Science Press
Document type: článek
URI: http://wscg.zcu.cz/wscg2003/Papers_2003/H71.pdf
ISSN: 1213-6972
Keywords: geometrické modelování;Dupinovy cyklidy;supercyklidy;Béziérovy plochy
Keywords in different language: geometric modelling;Dupin cyclides;supercyclides;Bézier surfaces
Abstract: Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. They have a low algebraic degree and have been proposed as a solution to a variety of geometric modeling problems. The circular curvature line’s property facilitates the construction of the cyclide (or the portion of a cyclide) that blends two circular quadric primitives. In this context of blending, the only drawback of cyclides is that they are not suitable for the blending of elliptic quadric primitives. This problem requires the use of non circular curvature blending surfaces. In this paper, we present another formulation of cyclides: Scaled cyclides. A scaled cyclide is the image of a Dupin cyclide under an affine scaling application. These surfaces are well suited for the blending of elliptic quadrics primitives since they have elliptical lines of curvature. We also show how one can convert a scaled cyclide into a set of rational quadric B´ezier patches.
Rights: © UNION Agency – Science Press
Appears in Collections:Volume 11, number 1-3 (2003)

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