A matrix method for degree-raising of B-spline curves

A new identity is proved that represents thekth order B-splines as linear combinations of the (k+1) th order B-splines. A new method for degree-raising of B-spline curves is presented based on the identity. The new method can be used for all kinds of B-spline curves, that is, both uniform and arbitrarily nonuniform B-spline curves. When used for degree-raising of a segment of a uniform B-spline curve of degreek−1, it can help obtain a segment of curve of degreek that is still a uniform B-spline curve without raising the multiplicity of any knot. The method for degree-raising of Bezier curves can be regarded as the special case of the new method presented. Moreover, the conventional theory for degree-raising, whose shortcoming has been found, is discussed.