Asymptotic Iterative Approximation of Intellectualized Periodic Interpolating Spline and its Application

Abstract. This paper presents an efficient and sufficient algorithm to approximate general interpolating Spline curve which goes through the given set of design-data points by using asymptotic iterative B-spline curves. Firstly, the given set is considered as the control points of a B-spline, to create the initial approximate curve, then the iterative grade is built based on the error between the initial approximate curve and given set, it is used to generate an iterative function sequence to approximate the interpolating function of the cover. New algorithms and approaches are successfully employed to create realistic and flexible geometry models for the centerline of yarns in woven fabrics. The algorithm described on this paper will be generalized to wide range for general 2D and 3D geometry and computer graphics with regard to curves and surfaces, especially for complex geometrical models on CAD and CAM.