A generalization of a Bezier-like curve

A new generalization basis called A-Bezier was constructed for the space span 2 {1, , ,..., } n t t t by using systolic array. This basis was based on a Bezier-like cubic curve consisting of two shape parameters which gave more degrees of freedom used in constructing the desired free form spline and surfaces. By fixing the shape parameters to specific values, this basis could be reduced to Wang-Ball basis and could be generalized to the other Bezier-like curve such as Timmer PC curve. The results showed that such basis and curves shared some properties with the Bernstein basis and the Bezier curves in polynomial spaces respectively.