三次Bezier曲线的一种双参数扩展及应用

Two parameters extension of cubic Bezier curve and its applications

对三次Bernstein基函数进行扩展,给出了含有双参数λμ的一组四次多项式基函数,基于该组基定义了带双参数的多项式曲线。该曲线不仅具有三次Bezier曲线的诸多特性,而且具有更加灵活的形状可调性。参数λμ的几何意义非常明显:在控制顶点不变的情况下,λμ分别起到了对曲线相对于控制多边形两内顶点的推拉作用,当λ=μ时,曲线退化为三次Bezier曲线的单参数扩展情形。重点讨论了在不改变控制点位置的情况下如何实现两曲线间的C1拼接。

A set of quartic polynomial basis function with two parameters is presented.It is an extension of the cubic Bernstein basis function.Based on these basis functions, the polynomial curve with two parameters is defined.The curve inherits many properties of cubic Bezier curve.Its shape can be adjusted more easily.Parameters λ,μ have specific geometric significance.When control points are fixed,parameters λ,μ have the function of pushing or dragging curve.When λ=μ the quartic curve degenerates to the polynomial curve with a shape parameter.The focus of this paper is discussing how to realize C1-continuity built-up of two-piece of curves,