摘要
给出了一个含有参数λ的四次多项式基函数,它是三次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。曲线不仅具有三次Ball曲线的特性,而且具有形状的可调性和更好的逼近性。参数λ有明确的几何意义:λ越大,曲线越逼近控制多边形;当λ=0时,曲线退化为三次Ball曲线。还讨论了两段曲线C1连续拼接的条件。实例表明,曲线形状随λ的取值不同而发生变化。
A polynomial basis function of 4th degree with shape control parameter λ, is presented. It is extension of basis function of cubic Ball curve. Properties of this new basis are analyzed and the corresponding polynomial curve with a shape parameter λ is defined. This curve not only inherits the outstanding properties of cubic Ball curve, but also is adjustable in shape and fit close to the control polygon. This curve converge to cubic Ball curve when λ=-0. The C^1-continuity condition of two-piece of curves is also discussed. Some examples illustrate the variation curve shapes with different values of λ.
出处
《工程图学学报》
CSCD
北大核心
2008年第1期77-81,共5页
Journal of Engineering Graphics
基金
北京市属市管高等学校人才强教计划资助项目(06PHR315)
