摘要
插值曲线的形状控制和应变能的控制可部分地通过对插值函数的二阶导数的控制而实现．文献［１］中利用对分母为线性的有理三次插值样条的二阶导数的控制，将插值曲线的凸性控制和应变能的控制结合起来，给出了将插值函数的二阶导数约束于给定区间的算法及其实现的条件．但在某些情况下，这种约束控制不易实现．利用分母为线性的有理三次插值样条和仅基于函数值的有理三次插值样条构造了一种加权有理三次插值样条，由于这种有理三次插值样条中含有新的参数，给约束控制带来了方便．文中给出了将插值函数的二阶导数约束于给定区间的算法及其实现的条件．最后给出了数值例子．
Controlling the convexity and strain energy of interpolating curve can be carried out by controlling the second\|order derivative of the interpolating function. In literature, algorithm for rational cubic spline with linear denominator has been developed to control the convexity and strain energy of the interpolating curve, but it does not work in some cases. This paper introduces the weighted rational cubic spline with linear denominator for solving such kind of constraints, the sufficient and necessary conditions for controlling the convexity and strain energy of the interpolating curve are derived, and some examples are given.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2000年第1期48-52,共5页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金!(19872041)
关键词
有理插值
加权插值
形状控制
曲线设计
样条插值
rational interpolation, weighted interpolation, constrained interpolation, convexity preserving, shape control
