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Zbl pre05682099
Craciun, Gheorghe; Garc{\'\i}a-Puente, Luis David; Sottile, Frank
Some geometrical aspects of control points for toric patches. (English)
[A] Daehlen, Morten (ed.) et al., Mathematical methods for curves and surfaces. 7th international conference, MMCS 2008, Tønsberg, Norway, June 26--July 1, 2008. Revised selected papers. Berlin: Springer. Lecture Notes in Computer Science 5862, 111-135 (2010). ISBN 978-3-642-11619-3/pbk

Summary: We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a Bézier curve or patch. In particular, we establish a generalization of Birch's Theorem and use it to deduce sufficient conditions on the control points for a patch to be injective. We also explain a way that the control points influence the shape via degenerations to regular control polytopes. The natural objects of this investigation are irrational patches, which are a generalization of Krasauskas's toric patches, and include Bézier and tensor product patches as important special cases.

MSC 2000:: *65D17 Computer aided design (modeling of curves and surfaces)
65D18 Computer graphics and computational geometry

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