C^2连续约束下三次Bézier扩展曲线的延拓

Extensions of cubic Bézier Expansion curve with C^2 constraint

给出了带有2个参数的四次多项式基函数,是三次Bernstein基函数的扩展;分析了这组基函数的性质,并定义了相应带有形状参数的多项式曲线,讨论了参数对曲线端点曲率的影响,此类曲线不仅具有三次Bézier曲线的特性,而且由于带有形状参数,从而曲线更加灵活;基于C2连续讨论了在能量最小意义下的曲线延拓问题,通过极小化方法确定参数的选取;实例表明文中的算法是有效的。

A class of polynomial basis functions of 4th degree with two shape control parameters is presented. It is an extension of cubic Bernstein basis functions. Properties of the basis functions are analyzed and the corresponding polynomial curve with two shape parameters is defined. And the influence of the parameters on the end curvatures is discussed. The curve not only inherits the outstanding properties of the cubic Bézier curve, but it is also adjustable in shape parameters. The problem of curve extension with least energy is discussed based on C^2 continuity. Some examples illustrate the algorithm is useful for the curve design.