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 Bezier 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 Bezier curve. Experiments show that the method given in this paper is intuitive, effective and easy to control.%给出了两组带两个形状参数λ,μ的六次多项式基函数,它们是四次Bernstein基函数的扩展.分析了这两组基函数的性质,基于这两组基分别定义了带形状参数的两类多项式曲线,两类曲线具有与四次Bézier曲线类似的性质,且在控制顶点不变的情况下,可通过改变形状参数的值实现对曲线形状的调整.参数λ,μ具有明显的几何意义.当λ=μ=0时,均退化为四次Bézier曲线.实例表明,论文所采用的方法控制灵活,方便有效.
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