曲线设计中形状控制的加权有理插值方法

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，给出了将插函数的二阶导数约束于给定区间的算法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任值样条了一种加权有理三次插值样条，由于这种有理三次插

Shape Control in Curve Design by Weighted Rational Interpolation

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.