Three parameters extension of easily spliced Bézier curves

This article studies Bézier curves with shape parameters. Firstly, three of group of polynomial basis function with three shape parameters 𝛂, 𝛃, 𝛄 were presented. It is referred to as the second, third and fourth order αβγ-B basis functions. Then, the geometry meaning of the shape parameters are analyzed. Basis on the basis function three kinds of Bézier curves were constructed, which have the basic properties of Bézier curve. The shape of the curve has more flexible expression, and can be local or whole modified by the introduction of three shape parameters. And the composite curves which consist of the this curves can achieve 𝐆 𝟐 continuity when the control points of curves satisfy the 𝐆 𝟏 continuity conditions of Bézier curve. Finally, the practicability of the method is proved by the curve modeling design.