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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 ex- tensions of interpolating α-B-spline based on the new B-splines and the singular blending technique. The advantage of the ex- tensions is that they have global and local shape parameters. Furthermore, we also investigate their applications in data in- terpolation and polygonal shape deformation.