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Zbl 1193.65018
Garcia-Puente, Luis David; Sottile, Frank
Linear precision for parametric patches. (English)
[J] Adv. Comput. Math. 33, No. 2, 191-214 (2010). ISSN 1019-7168; ISSN 1572-9044/e

Summary: We give a precise mathematical formulation for the notions of a parametric patch and linear precision, and establish their elementary properties. We relate linear precision to the geometry of a particular linear projection, giving necessary (and quite restrictive) conditions for a patch to possess linear precision. A main focus is on linear precision for {\it R. Krasauskas}' toric patches [Adv. Comput. Math. 17, No.~1--2, 89--113 (2002; Zbl 0997.65027)], which we show is equivalent to a certain rational map on ${\mathbb C}{\mathbb P}^d$ being a birational isomorphism. Lastly, we establish the connection between linear precision for toric surface patches and maximum likelihood degree for discrete exponential families in algebraic statistics, and show how iterative proportional fitting may be used to compute toric patches.

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

Keywords: tensor product Bézier surfaces; triangular Bézier surface patches; barycentric coordinates; iterative proportional fitting

Citations: Zbl 0997.65027

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