A class of general quartic spline curves with shape parameters (Q543837)

A general method to generate quartic splines with a non-uniform knot vector from four consecutive subintervals (i.e., four control points) are presented. The splines have \(C^{2}\) continuity at simple knots and include the cubic non-unifrom B-spline as a special case. Piecewise quartic spline curves with three local parameters based on the given splines, which have \(C^2 \cap G^3\) continuity, are presented. The spline curves can be used as interpolate sets of \(C^2\) continuous points without solving a linear system. The effects of local adjustments via three shape parameters on the shape of the quartic spline curves are illustrated.