Non-uniform B-spline curves with multiple shape parameters

We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence. These curves not only have the many valued properties of the usual non-uniform B-spline curves, but also are shape adjustable under fixed control polygons. Our method is based on the degree elevation of B-spline curves, where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform B-spline. We also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms, which are indispensable from the user's perspective.