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Applications of a Fruitful Relation between a Dupin Cyclide and a Right Circular Cone

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Book cover Geometric Modelling

Part of the book series: Computing Supplement ((COMPUTING,volume 13))

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Abstract

A powerful way of handling a Dupin cyclide is presented. It is based on the concept of inversion, which yields a fruitful relation between the symmetric Dupin horn cyclide, from which all other Dupin cyclides may be obtained by offsetting, and a right circular cone. This relation has two important applications. First, it is used for constructing rational rectangular and triangular Bézier patches on the cyclide. Second, it allows to establish an approximative isometry between cyclide and cone patches, a useful result e.g. for scattered data interpolation techniques on Dupin cyclides.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, D-80290, München, Germany

    G. Albrecht

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  1. G. Albrecht
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Arizona State University, Tempe, AZ, USA

    Gerald Farin

  2. Institut für Informatik und angewandte Grafik, Universität Bern, Bern, Switzerland

    Hanspeter Bieri

  3. Fachbereich Maschinenbau, Universität Kaiserslautern, Kaiserslautern, Germany

    Guido Brunnett

  4. Pixar Animation Studios, Richmond, CA, USA

    Tony De Rose

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© 1998 Springer-Verlag Wien

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Albrecht, G. (1998). Applications of a Fruitful Relation between a Dupin Cyclide and a Right Circular Cone. In: Farin, G., Bieri, H., Brunnett, G., De Rose, T. (eds) Geometric Modelling. Computing Supplement, vol 13. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6444-0_1

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  • DOI: https://doi.org/10.1007/978-3-7091-6444-0_1

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83207-3

  • Online ISBN: 978-3-7091-6444-0

  • eBook Packages: Springer Book Archive

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