Universal Rational Parametrizations and Spline Curves on Toric Surfaces

Rimvydas Krasauskas () and Margarita Kazakevičiūté ()
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Rimvydas Krasauskas: Vilnius University
Margarita Kazakevičiūté: Vilnius University

A chapter in Computational Methods for Algebraic Spline Surfaces, 2005, pp 213-231 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-27157-4_15

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DOI: 10.1007/3-540-27157-0_15

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