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International Conference on Mathematical Methods for Curves and Surfaces

MMCS 2008: Mathematical Methods for Curves and Surfaces pp 15–25Cite as

Construction of Rational Curves with Rational Rotation-Minimizing Frames via Möbius Transformations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5862))

Abstract

We show that Möbius transformations preserve the rotation-minimizing frames which are associated with space curves. In addition, these transformations are known to preserve the class of rational Pythagorean-hodograph curves and rational frames. Based on these observations we derive an algorithm for G 1 Hermite interpolation by rational Pythagorean-hodograph curves with rational rotation-minimizing frames.

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Author information

Authors and Affiliations

  1. Technion - Israel Institute of Technology, Haifa, Israel

    Michael Bartoň

  2. Institute of Applied Geometry, Johannes Kepler University, Linz, Austria

    Bert Jüttler

  3. Dept. of Computer Science, University of Hongkong, China

    Wenping Wang

Authors
  1. Michael Bartoň
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  2. Bert Jüttler
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  3. Wenping Wang
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Norway

    Morten Dæhlen  & Tom Lyche  & 

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

    Michael Floater

  3. INSA de Rennes, Rennes, France

    Jean-Louis Merrien

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

    Knut Mørken

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

    Larry L. Schumaker

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Bartoň, M., Jüttler, B., Wang, W. (2010). Construction of Rational Curves with Rational Rotation-Minimizing Frames via Möbius Transformations. In: Dæhlen, M., Floater, M., Lyche, T., Merrien, JL., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2008. Lecture Notes in Computer Science, vol 5862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11620-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-11620-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11619-3

  • Online ISBN: 978-3-642-11620-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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