Asymptotic Iterative Approximation of Intellectualized Periodic Interpolating Spline and its Application

Abstract

This \u00a0paper \u00a0presents \u00a0an \u00a0efficient \u00a0and \u00a0sufficient \u00a0algorithm \u00a0to \u00a0approximate \u00a0general \u00a0interpolating 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 \u00a0the \u00a0centerline \u00a0of \u00a0yarns \u00a0in \u00a0woven \u00a0fabrics. \u00a0The \u00a0algorithm \u00a0described \u00a0on \u00a0this \u00a0paper \u00a0will \u00a0be \u00a0generalized \u00a0to wide \u00a0range \u00a0for \u00a0general \u00a02D \u00a0and \u00a03D \u00a0geometry \u00a0and \u00a0computer \u00a0graphics \u00a0with \u00a0regard \u00a0to \u00a0curves \u00a0and \u00a0surfaces, especially for complex geometrical models on CAD and CAM. \u00a0