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Universal Rational Parametrizations and Spline Curves on Toric Surfaces

  • Rimvydas Krasauskas
  • Margarita Kazakevičiūté

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.

Keywords

Toric Variety Spline Curve Toric Surface Hirzebruch Surface Canal Surface 
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 2005

Authors and Affiliations

  • Rimvydas Krasauskas
    • 1
  • Margarita Kazakevičiūté
    • 1
  1. 1.Vilnius UniversityVilniusLithuania

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