G1-blend between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides

Lionel Garnier, Sebti Foufou, Yohan Fougerolle

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    In this article, we present a method to perform G1- continuous blends between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. These blends are patches delimited by four lines of curvature. They allow to avoid parameterization problems that may occur when parametric surfaces are used. Rational quadratic B'ezier curves are used to approximate the principal circles of the Dupin cyclide blends and thus a complex 3D problem is now reduced to a simpler 2D problem. We present the necessary conditions to be satisfied to create the blending patches and illustrate our approach by a number of superellipsoid/plane and superellipsoid/sphere blending examples.

    Original languageEnglish (US)
    Title of host publicationSITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems
    Pages435-442
    Number of pages8
    DOIs
    StatePublished - Dec 1 2008
    Event4th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2008 - Bali, Indonesia
    Duration: Nov 30 2008Dec 3 2008

    Other

    Other4th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2008
    CountryIndonesia
    CityBali
    Period11/30/0812/3/08

    Fingerprint

    Parameterization

    ASJC Scopus subject areas

    • Computer Networks and Communications
    • Software

    Cite this

    Garnier, L., Foufou, S., & Fougerolle, Y. (2008). G1-blend between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. In SITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems (pp. 435-442). [4725838] https://doi.org/10.1109/SITIS.2008.73

    G1-blend between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. / Garnier, Lionel; Foufou, Sebti; Fougerolle, Yohan.

    SITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems. 2008. p. 435-442 4725838.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Garnier, L, Foufou, S & Fougerolle, Y 2008, G1-blend between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. in SITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems., 4725838, pp. 435-442, 4th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2008, Bali, Indonesia, 11/30/08. https://doi.org/10.1109/SITIS.2008.73
    Garnier L, Foufou S, Fougerolle Y. G1-blend between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. In SITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems. 2008. p. 435-442. 4725838 https://doi.org/10.1109/SITIS.2008.73
    Garnier, Lionel ; Foufou, Sebti ; Fougerolle, Yohan. / G1-blend between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. SITIS 2008 - Proceedings of the 4th International Conference on Signal Image Technology and Internet Based Systems. 2008. pp. 435-442
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