A class of general quartic spline curves with shape parameters

Abstract

With a support on four consecutive subintervals, a class of general quartic splines are presented for a non-uniform knot vector. The splines have C 2 continuity at simple knots and include the cubic non-uniform B-spline as a special case. Based on the given splines, piecewise quartic spline curves with three local shape parameters are given. The given spline curves can be C 2 ∩ G 3 continuous by fixing some values of the curveʼs parameters. Without solving a linear system, the spline curves can also be used to interpolate sets of points with C 2 continuity. The effects of varying the three shape parameters on the shape of the quartic spline curves are determined and illustrated.