【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.更多还原

【Abstract】 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.更多还原