参数曲面片的线性精度
Linear precision for parametric patches
摘要：
我们给出了一个精确的数学公式的参数补丁和线性精度的概念，并建立其基本性质。我们将线性精度与特定线性投影的几何形状联系起来，给出了面片具有线性精度的必要（且相当限制性）条件。主要的焦点是Krasauskas的复曲面片的线性精度，我们证明了它等价于CP^d上的某个有理映射是一个双有理同构。最后，我们建立了复曲面片的线性精度与代数统计中离散指数族的最大似然度之间的联系，并说明了如何用迭代比例拟合来计算复曲面片。
英文摘要：
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 CP^d being a birational isomorphism. Lastly, we establish the connection between linear presision 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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