| 限制在光滑参数曲线上的C1曲面插值 |
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| 引用本文： | 周正华,罗卫民. 限制在光滑参数曲线上的C1曲面插值[J]. 兰州理工大学学报, 2006, 32(6): 96-99 |
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| 作者姓名： | 周正华 罗卫民 |
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| 作者单位： | 中国计量学院,理学院,浙江,杭州,310018;西安邮电学院,应用数理系,陕西,西安,710061;西安邮电学院,应用数理系,陕西,西安,710061 |
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| 基金项目： | 陕西省自然科学基金 , 陕西省教育厅资助项目 |
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| 摘 要： | 给出了一种限制在光滑参数曲线上的C1曲面插值方法.首先通过曲线参数化,建立从曲线到实参数轴的一个一一映射,将限制在曲线上的曲面插值问题转化为实参数轴上的一元插值问题,然后采用范数极小的方法给出参数轴上的一元C1插值函数,再将此插值函数映射到原曲线上即得到限制在参数曲线上的插值函数.理论推导和图形实例显示表明该方法具有逼近效果好的优点.
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| 关 键 词： | 参数曲线 曲面插值 极小范数 |
| 文章编号： | 1673-5196(2006)06-0096-04 |
| 收稿时间： | 2005-10-27 |
| 修稿时间： | 2005-10-27 |
C1 surface interpolation restricted to smooth parametric curve |
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| ZHOU Zheng-hua,LUO Wei-min. C1 surface interpolation restricted to smooth parametric curve[J]. Journal of Lanzhou University of Technology, 2006, 32(6): 96-99 |
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| Authors: | ZHOU Zheng-hua LUO Wei-min |
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| Abstract: | An approach to resolve the problem of C^1 surface interpolation restricted to a smooth parametric curve was given. Through curve parametrizing, an one-to-one map from the curve onto real parametric axis was set up and the problem of surface interpolation restricted to curve was transformed to one-dimensional interpolation on the real parametric axis. Then, an one-dimensional C^1 interpolation function was given by using the method of minimum norm. Finally, the required interpolating function restricted to the parametric curve could be obtained by mapping the one-dimensional function onto the original parametric curve. Theoretical deduction and graphical illustration showed that such an approach was effective to produce good approximation result. |
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| Keywords: | parametric curve surface interpolation minimum norm |
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