Quasi-Cubic B-Spline Curves by Trigonometric Polynomials

摘要

A class of quasi-cubic B-spline curves by trigonometric polynomials, in short, QC-B-spline curves, is presented in this paper. The QC-B-spline curves retain the main superiority of cubic B-spline curves. The curves can approximate cubic B-spline curves from both sides. The change of a shape parameter will only change two curve segments. With the increase of the value of a shape parameter, the curves approach a corresponding control point. Without solving system of equations and letting shape parameter be special value, the curves can also interpolate the corresponding control point locally. Thus, the given curves unify the representation of the curves for interpolating and approximating the control polygon. With the shape parameters and control points chosen properly, the introduced curves can represent conic and some transcendental curves exactly. As an application, some special segments of a C2 continuous blending curve can be jointed.