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.

Key words: Surface modeling, Two-level fitting, Multivariate multiquadric quasi-interpolation, CSRBF-based networks, Shape-preserving model