Linear precision for parametric patches |
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Authors: | Luis David Garcia-Puente Frank Sottile |
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Institution: | (1) 25 Windmill Lane, Ringwood, Hampshire, United Kingdom, BH24 2DQ |
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Abstract: | 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 Krasauskas’
toric patches, which we show is equivalent to a certain rational map on
\mathbb C\mathbb Pd{\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. |
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Keywords: | |
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