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Piecewise Rational Parametrizations of Canal Surfaces

  • Conference paper
Mathematical Methods for Curves and Surfaces (MMCS 2012)

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

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Abstract

Canal surfaces, as envelopes of one-parameter families of spheres, correspond to curves in Minkowski space. We show that the continuity properties of a canal surface are inherited from the continuity properties of the associated curve, i.e., two curves joined with G 1 or G 2 continuity in Minkowski space correspond to two canal surfaces joined with the same level of continuity.We also describe an algorithm for minimal bi-degree rational parametrizations of patches on canal surfaces, and show how this can be used to parametrize piecewise rational corner and edge blends.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, SINTEF ICT, Forskningsveien 1, 0373, Oslo, Norway

    Heidi E. I. Dahl

Authors
  1. Heidi E. I. Dahl
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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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Dahl, H.E.I. (2014). Piecewise Rational Parametrizations of Canal Surfaces. 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-54382-1_6

  • 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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