An error reduced and uniform parameter approximation in fitting of B-spline curves to data points

Abstract: Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or uniform parameter values are assumed for the points. Tangents are assumed at the data points, corresponding to the property used in cardinal splines, for shape preserving and visually pleasing fit. Control points of piecewise continuous cubic bezier curves, meeting the boundary conditions of cardinal spline segments, are used for b-spline curve in corresponding coordinate planes. Approximation using error computed in the least square sense, based on a fraction of data points, is also presented.