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G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions

  • Bohumír Bastl
  • Miroslav Lávička
  • Zbyněk Šír
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6920)

Abstract

It was recently proved in [27] that all rational hypocycloids and epicycloids are Pythagorean hodograph curves, i.e., rational curves with rational offsets. In this paper, we extend the discussion to a more general class of curves represented by trigonometric polynomial support functions. We show that these curves are offsets to translated convolutions of scaled and rotated hypocycloids and epicycloids. Using this result, we formulate a new and very simple G 2 Hermite interpolation algorithm based on solving a small system of linear equations. The efficiency of the designed method is then presented on several examples. In particular, we show how to approximate general trochoids, which, as we prove, are not Pythagorean hodograph curves in general.

Keywords

Support Function Medial Axis Algebraic Curf Geometric Design Rational Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bohumír Bastl
    • 1
  • Miroslav Lávička
    • 1
  • Zbyněk Šír
    • 1
  1. 1.Faculty of Applied Sciences, Department of MathematicsUniversity of West BohemiaPlzeňCzech Republic

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