Abstract: Two classes of blending functions with multiple shape parameters are presented in this paper. They are the extension of uniform cubic B-spline basic functions. Based on the given blending functions, the piecewise polynomial curves with shape parameters are defined. These curves inherit the most properties of uniform cubic B-spline curves with GC1 or GC2 continuity. The position and the length of tangent vector at the end points of curve segments can be independently controlled by changing the values of the shape parameters. These curves can be adjusted totally or locally and interpolated by any given control points.

Key words: uniform cubic B-spline, blending function, position parameter of end point, tangent vector, interpolation