Wide-Ranging Families of Subdivision Schemes for Fitting Data

Abstract

In this paper, we present wide-ranging families of subdivision schemes for fitting data to subdivision models. These schemes are
constructed by fitting multivariate polynomial functions of any degree to different types of data by least squares techniques. Moreover, we also present the closed analytic expressions of the families of schemes for fitting data in 2 and 3 dimensional spaces. The schemes for fitting 3D data are non-tensor product schemes. Furthermore, it is straightforward by using our framework to construct schemes for fitting data in higher dimensional spaces. The performance of such schemes is demonstrated on examples of curves and surfaces.