| 曲线设计中形状控制和能量控制的一种方法 |
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| 引用本文： | 段奇,刘爱奎,杜世田,Twizell E H.曲线设计中形状控制和能量控制的一种方法[J].计算机辅助设计与图形学学报,1999,11(6):485-489. |
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| 作者姓名： | 段奇 刘爱奎 杜世田 Twizell E H |
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| 作者单位： | 1. 山东工业大学数理系,济南,250061
2. 英国Brunel大学数学与统计系,伦敦 |
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| 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来实现，通过对父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条件。
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| 关 键 词： | 有理样条 约束插值 保凸插值 形状控制 |
| 修稿时间： | 1998-06-22 |
A METHOD FOR SHAPE CONTROL AND ENERGY CONTROL IN CURVE DESIGN |
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| DUAN Qi,LIU Ai-Kui,DU Shi-Tian,Twizell E H.A METHOD FOR SHAPE CONTROL AND ENERGY CONTROL IN CURVE DESIGN[J].Journal of Computer-Aided Design & Computer Graphics,1999,11(6):485-489. |
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| Authors: | DUAN Qi LIU Ai-Kui DU Shi-Tian Twizell E H |
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| Affiliation: | DUAN Qi;
(Department of Applied Mathematics, Shandong University of Technology, Jinan |
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| Abstract: | Controlling the shape and the strain energy of the interpolating curve can be carried out by controlling the second order derivative of the interpolating function. This paper deals with the convexity control and the strain energy control of the interpolating curves by controlling the second order derivative of the rational cubic spline with linear denominator. The algorithm and the conditions for constraining the second order derivative of the interpolating function to be in the given interval are obtained. |
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| Keywords: | rational spline constrained interpolation convexity interpolation shape control |
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