Extended Cubic Uniform B-spline and α-B-spline

Spline curve and surface play an important role in CAD and computer graphics. In this paper, we propose several extensions of cubic uniform B-spline. Then, we present the extensions of interpolating α-B-spline based on the new B-splines and the singular blending technique. The advantage of the extensions is that they have global and local shape parameters. Furthermore, we also investigate their applications in data interpolation and polygonal shape deformation.