Abstract: Two classes of six degree polynomial basis functions with two shape control
parameters λ and μ are presented. They are extensions of quartic Bernstein basis functions.
Properties of these two bases are analyzed and the corresponding polynomial curves with two
parameters λ and μ are defined accordingly. These curves not only inherit the outstanding
properties of quartic Bézier curve, but also can be adjusted in shape by changing the value of λ
and μ without the changing of control points. The parameters have obvious geometric meaning.
When λ =μ =0, the curve degenerates to four degree Bézier curve. Experiments show that the
method given in this paper is intuitive, effective and easy to control.

Key words: curve design, quartic Bézier curve, shape parameters