A Spline Approximation of a Large Set of Points

Abstract

This paper presents a spline approximation method for the representation of a large set of points. The representation should be smooth with preserving important shape characteristics given by the points. Because of a large size of the set, the standard spline interpolation cannot be used. The proposed method is based on a least squares minimization of the distances of the points from the spline function subject to the conditions of smoothness of the representation. The spline approximation produces accurate and suitable representation of the points. The proposed approach has been verified on both synthetic and real data sets of points.