带有给定切线多边形的扩展的四次广义Ball闭曲线

给出了一个含有参数λ的五次多项式基函数,是四次广义Ball曲线基础函数的扩展;分析了此基函数的性质,基于该组基函数定义了带有形状参数的多项式曲线.曲线不仅具有四次广义Ball曲线的特性,而且具有形状的可调性.当λ=0时,曲线退化为四次广义Ball曲线.还讨论了两段曲线C1连续拼接的条件.描述了一种与给定多边形相切的扩展的四次广义Ball闭曲线的算法.在算法中,所有的扩展的四次广义Ball闭曲线的控制点可以通过对多边形的顶点简单计算产生.所构造的曲线对多边形具有保形性,曲线可以局部修改.最后给出了1个算例,实例表明:定义的曲线的形状是随着λ的不同取值而发生变化.

Extension of the Close Quartic Generalized Ball Curves with Given Tangent Polygon

A class of polynomial basis function of 5th degree with shape control parameter λ was presented.It was extension of basis function of quartic generalized Ball curve.Properties of this new basis were analyzed and the corresponding polynomial curve with a shape paramete λ was defined.This curve not only inherited the outstanding properties of quartic generalized Ball curve,but also was adjustable in shape.This curve converged to quartic generalized Ball curve when λ=0.The C1-continuity condition of two-piece of curves was also discussed.An algorithm for constructing an extension of the close quartic generalized Ball curves which were tangent to the given polygon was described.The control points of an extension of the close quartic generalized Ball curves to be constructed were computed simply by the vertices of the given polygon.The constructed curves were shape-preserving to the polygon.The local modification to the extension of the close quartic Generalized Ball curves could be completed by simply adjusting the corresponding control parameters.One example was given,examples illustrated the variation of curve shapes with different values of λ.