Cubic polynomial curves with a shape parameter

Abstract: A class of cubic polynomial blending functions with a shape parameter is presented. It is an extension of cubic uniform B-spline basis functions. Piecewise polynomial curves with a shape parameter are constructed from these blending functions. The generated curves have second geometric continuity for any fixed shape parameter and have the same terminal properties as the cubic uniform B-spline curves. If the value of the shape parameter is changed, the approaching degree of the curves to their control polygon is adjusted accordingly and the curves are manipulated to approximate the cubic uniform B-spline curve from its both sides. In comparison with the existing results, the degree of blending functions is lower and the domain of the shape parameter is larger in this paper. A new method using cubic polynomial curves with a shape parameter is also proposed to solve interpolation problem without solving global systems of equations. Finally some computing examples of the curve design are also given.