Toric曲面的渐进迭代逼近
Progressive Iterative Approximation of Toric Surfaces
摘要: 渐进迭代逼近(PIA)是一种直观有效的数据拟合方法。当给定数据点的参数域为不规则的凸多边形时，需要对参数域剖分来用多片曲面拟合，然后考虑相邻曲面片的拼接。Toric曲面是Bézier曲面的推广，它的参数域可以调整为任意凸多边形。使用Toric曲面做渐进迭代逼近即可以保留渐进迭代逼近的优点，也可以整体对数据点进行拟合，无需考虑曲面的重构与拼接。本篇文章定义了一种对凸多边形上的参数点进行字典排序的方法。并实现了一种用Toric曲面做渐进迭代逼近的算法。我们还用具体的数值例子证明方法有效。
Abstract: Progressive iterative approximation (PIA) is an intuitive and effective data fitting method. When the parameter domain of a given data point is an irregular convex polygon, the parameter domain needs to be partitioned to be fitted by a multi-piece surface. Then we consider the stitching of adja-cent surface patches. Toric surfaces are a generalization of Bézier surfaces whose parametric do-main can be adjusted to any convex polygon. Using Toric surface for progressive iterative approxi-mation can not only retain the advantages of progressive iterative approximation, but also fit the data points as a whole, without considering the reconstruction and splicing of the surface. This pa-per defines a lexicographic method for sorting the points of a convex polygon. A progressive itera-tive approximation algorithm using Toric surfaces is also implemented. We also use specific nu-merical examples to prove that the method is effective.
文章引用：段卓, 彭兴璇. Toric曲面的渐进迭代逼近[J]. 应用数学进展, 2023, 12(12): 5166-5174. https://doi.org/10.12677/AAM.2023.1212507

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