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作 者:杨当福 刘圣军[1,2] 刘平波[3] 刘新儒[1] Yang Dangfu;Liu Shengjun;Liu Pingbo;Liu Xinru(School of Mathematics and Statistics,Central South University,Changsha 410083,China;State Key Laboratory of High Performance Complex Manufacturing,Central South University,Changsha 410083,China;College of Computer and Information Engineering,Central South University of Forestry and Technology,Changsha 410004,China)
机构地区:[1]中南大学数学与统计学院,长沙410083 [2]中南大学高性能复杂制造国家重点实验室,长沙410083 [3]中南林业科技大学计算机与信息工程学院,长沙410083
出 处:《数学理论与应用》2021年第4期57-76,共20页Mathematical Theory and Applications
基 金:The research is supported by the National Natural Science Foundation of China(Grant No.61572527);the Hunan Science Fund for Distinguished Young Scholars(Grant No.2019JJ20027);the Hunan R&D Program(Grant No.2017NK2383);the Mathematics and Interdisciplinary Sciences Project of Central South University。
摘 要:紧支撑的径向基函数已广泛用于曲面建模方法中以插值或拟合给定数据.合理的紧支撑半径可以避免求解大型稠密线性系统.通常基于CSRBF重建曲面方法不具有保形性,而多元二次拟插值的逼近精度不足.本文引入一种新的高精度保形曲面建模的两级拟合方法.首先使用精度较低的准插值方法构造初始保形模型,然后通过进行基于CSRBF的网络插值方法补偿初始拟合模型与给定数据之间的误差,进而得到精度更高的保形模型.此外,本文还讨论拟插值平滑因子的选择和基于CSRBF网络的支持半径设置,并建立它们之间的经验公式.数值示例说明了本文方法的有效性.Compactly supported radial basis function(CSRBF) has been widely used in surface modeling methods to interpolate or approximate the given data, which avoids solving a large dense linear system with a proper supported radius. The surfaces reconstructed by the CSRBF-based method usually are not shape preserving, while the multivariate multiquadric quasi-interpolation results the lower approximation accuracy. In this paper, we introduce a two-level fitting method to conduct the shape-preserving modelling with a higher accuracy. An initial shape-preserving model is constructed by using the lower accuracy quasi-interpolation, and then a CSRBF-based networks interpolation is performed to compensate the errors between the initial fitting model and the given data, then the higher accuracy shape-preserving model can be obtained. Moreover, we discuss the choice of the smoothing factor in quasi-interpolation and the supported radius in CSRBF-based networks, and an empirical formula between them is constructed. The numerical examples demonstrate the performance of our method.
关 键 词:曲面建模 二级拟合 多元二次拟插值 紧支撑径向基函数网络 保形模型
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