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

  • Michael Bartoň
  • Bert Jüttler
  • Wenping Wang
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

rational rotation-minimizing frame Möbius transformations Pythagorean-hodograph curve 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Michael Bartoň
    • 1
  • Bert Jüttler
    • 2
  • Wenping Wang
    • 3
  1. 1.Technion - Israel Institute of TechnologyHaifaIsrael
  2. 2.Institute of Applied GeometryJohannes Kepler UniversityLinzAustria
  3. 3.Dept. of Computer ScienceUniversity of HongkongChina

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