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Bilinear Clifford-Bézier Patches on Isotropic Cyclides

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Book cover Mathematical Methods for Curves and Surfaces (MMCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8177))

Abstract

We study Bézier-like formulas with weights in geometric algebra for parametrizing a special class of rational surfaces in isotropic 3-space. These formulas are useful for constructing isotropic-Möbius invariant surfaces that are dual to rational offset surfaces in euclidean 3-space. Our focus is on bilinear Clifford-Bézier patches. We derive their implicitization formula and characterize them as patches on special quartic surfaces called isotropic cyclides. Finally we present one modeling application with rational surfaces admitting rational offsets.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko g. 24, 03225, Vilnius, Lithuania

    Rimvydas Krasauskas, Severinas Zubė & Salvatore Cacciola

Authors
  1. Rimvydas Krasauskas
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  2. Severinas Zubė
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  3. Salvatore Cacciola
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Editor information

Editors and Affiliations

  1. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  2. DMA, University of Oslo, P.O.Box 1053, 0316, Blindern, Oslo, Norway

    Tom Lyche

  3. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  4. University of Oslo, Norway

    Knut Mørken

  5. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry L. Schumaker

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Krasauskas, R., Zubė, S., Cacciola, S. (2014). Bilinear Clifford-Bézier Patches on Isotropic Cyclides. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2012. Lecture Notes in Computer Science, vol 8177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54382-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-54382-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54381-4

  • Online ISBN: 978-3-642-54382-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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