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Register a new userSome geometrical aspects of control points for toric patches
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We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a Bezier curve or patch. In particular, we establish a generalization of Birchs 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 Krasauskass toric patches, and include Bezier and tensor product patches as important special cases.
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