Toric曲面的渐进迭代逼近  

Progressive Iterative Approximation of Toric Surfaces

作　　者：段卓 彭兴璇[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2023年第12期5166-5174,共9页Advances in Applied Mathematics

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。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.

关 键 词：Toric曲面 渐进迭代逼近(PIA) 数据拟合 BÉZIER曲面 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]