A class of general quartic spline curves with shape parameters

With a support on four consecutive subintervals, a class of general quartic splines are presented for a non-uniform knot vector. The splines have C2C2 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 C2∩G3C2∩G3 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 C2C2 continuity. The effects of varying the three shape parameters on the shape of the quartic spline curves are determined and illustrated.

Research highlights
► A general explicit formula of quartic splines with C2C2 continuity.
► Quartic spline with a support on four consecutive subintervals.
► C2∩G3C2∩G3 continuous quartic spline curves.
► C2C2 continuous quartic local interpolation curves.
► Quartic spline curves with three local shape parameters.