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Universal Rational Parametrizations and Spline Curves on Toric Surfaces

In: Computational Methods for Algebraic Spline Surfaces

Author

Listed:
  • Rimvydas Krasauskas

    (Vilnius University)

  • Margarita Kazakevičiūté

    (Vilnius University)

Abstract

Recently a constructive description of all rational parametrizations for toric surfaces was described in terms of the universal rational parametrizations (URP). We give an elementary introduction to this theory from the Geometric Modelling point of view: toric surfaces are defined via homogeneous coordinates; projections, singular cases, and non-canonical real structures are described; the URP theorem is explained. A theory of rational C 1 spline curves with certain interpolation properties on toric surfaces is developed. Applications for smooth blending of natural quadrics are sketched.

Suggested Citation

  • Rimvydas Krasauskas & Margarita Kazakevičiūté, 2005. "Universal Rational Parametrizations and Spline Curves on Toric Surfaces," Springer Books, in: Computational Methods for Algebraic Spline Surfaces, pages 213-231, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27157-4_15
    DOI: 10.1007/3-540-27157-0_15
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