Decomposition of Splines

Abstract

In this paper we discuss decomposition techniques and data reduction strategies with emphasis on piecewise polynomial curves and surfaces. The main idea behind the methods is to transform the object (curve or surface) into a sequence of components in order to analyze the original object in a multiresolutional setting. Data reduction is obtained by only keeping coefficients from each component which give “significant” contributions to the reconstruction of the original. A new method combining decomposition and knot removal is given. We present several examples which show data reduction and the special effect of decomposition.