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Toric Surface Patches

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Abstract

We define a toric surface patch associated with a convex polygon, which has vertices with integer coordinates. This rational surface patch naturally generalizes classical Bézier surfaces. Several features of toric patches are considered: affine invariance, convex hull property, boundary curves, implicit degree and singular points. The method of subdivision into tensor product surfaces is introduced. Fundamentals of a multidimensional variant of this theory are also developed.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 2600, Vilnius, Lithuania

    Rimvydas Krasauskas

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  1. Rimvydas Krasauskas
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Krasauskas, R. Toric Surface Patches. Advances in Computational Mathematics 17, 89–113 (2002). https://doi.org/10.1023/A:1015289823859

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