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Surfaces with Rational Chord Length Parameterization

  • Bohumír Bastl
  • Bert Jüttler
  • Miroslav Lávička
  • Zbyněk Šír
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6130)

Abstract

We consider a rational triangular Bézier surface of degree n and study conditions under which it is rationally parameterized by chord lengths (RCL surface) with respect to the reference circle. The distinguishing property of these surfaces is that the ratios of the three distances of a point to the three vertices of an arbitrary triangle inscribed to the reference circle and the ratios of the distances of the parameter point to the three vertices of the corresponding domain triangle are identical. This RCL property, which extends an observation from [10,13] about rational curves parameterized by chord lengths, was firstly observed in the surface case for patches on spheres in [2]. In the present paper, we analyze the entire family of RCL surfaces, provide their general parameterization and thoroughly investigate their properties.

Keywords

Chord Length Subdivision Scheme Geometric Design Rational Curf Vertex Triangle 
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 2010

Authors and Affiliations

  • Bohumír Bastl
    • 1
  • Bert Jüttler
    • 2
  • Miroslav Lávička
    • 1
  • Zbyněk Šír
    • 1
  1. 1.Faculty of Applied Sciences, Department of MathematicsUniversity of West BohemiaPlzeňCzech Republic
  2. 2.Institute of Applied GeometryJohannes Kepler University of LinzLinzAustria

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