摘要
在给定端点及其切矢方向的条件下,通过在相邻两节点之间插入一个中间节点,研究三次Hermite插值曲线的优化问题.如果以与曲率有关的二阶导数为目标,证明插入节点与不插入节点的情形是一样的,体现三次Hermite插值曲线的一种特性.如果以与挠率有关的三阶导数为目标,给出优化三次Hermite曲线的计算公式,从而提出一种新的曲线构造方法.实例表明了方法的有效性.
Given .some points and their tangent vectors, this paper studies the problem of the optimization of cubic Hermite interpolation curves. According to the objective of second--order derivative related to curvatures, it is proved that there is no difference whether we insert a knot or not. And it presents a characteristic of cubic Hermite interpolation curves. According to the objective of third--order derivative related to torsions, the formula to calculate the cubic optimized Hermite interpolation curves is given. And then we propose a new method to construct curves. The results show the effectiveness of this method.
出处
《计算技术与自动化》
2009年第4期68-71,共4页
Computing Technology and Automation
基金
国家自然科学基金项目(10871208)
湖南省自然科学基金项目(08JJ3009)
关键词
三次Hermite插值
能量优化
曲线表示
计算机辅助几何设计
cubic hermite interpolation
energy optimization
the representation of curves
computer aided geometric design
