Bézier curves with shape parameter

Abstract

In this paper, Bezier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bezier curves with shape parameter. The Bezier basis curves with shape parameter have most properties of Bernstein basis and the Bezier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase of the shape parameter, the Bezier curves with shape parameter approximate to the control polygon. In the last, the Bezier surface with shape parameter is also constructed and it has most properties of Bezier surface.