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| 一类基于函数值的有理三次样条曲线的形状控制 | |
| 引用本文： | 邓四清,方逵,谢进.一类基于函数值的有理三次样条曲线的形状控制[J].工程图学学报,2007,28(2):89-94. |
| 作者姓名： | 邓四清 方逵 谢进 |
| 作者单位： | 1. 湘南学院数学系,湖南,郴州,423000 2. 湖南师范大学数学与计算机科学学院,湖南,长沙,410081;长沙学院计算机科学与技术系,湖南,长沙,410003 3. 合肥学院数理系,安徽,合肥,230601 |
| 基金项目： | 国家自然科学基金 , 湖南省自然科学基金 , 湖南省教育厅科研项目 , 湖南省长沙市高新技术项目 |
| 摘 要： | 将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题.构造了一种基于函数值的分母为二次的C1连续有理三次插值样条.这种有理三次插值样条中含有调节参数,因而给约束控制带来了方便.给出了将该种插值曲线约束于给定的折线、二次曲线之上、之下或之间的充分条件及将其约束于给定折线之上、之下或之间的充分必要条件. |
| 关 键 词： | 计算机应用 曲线设计 有理插值 三次样条 |
| 文章编号： | 1003-0158（2007）02-0089-06 |
| 收稿时间： | 2006-07-04 |
| 修稿时间： | 2006年7月4日 |
Shape Control of a Rational Cubic Interpolating Spline Based on Function Values |
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| DENG Si-qing,FANG Kui,XIE Jin.Shape Control of a Rational Cubic Interpolating Spline Based on Function Values[J].Journal of Engineering Graphics,2007,28(2):89-94. | |
| Authors: | DENG Si-qing FANG Kui XIE Jin |
| Affiliation: | 1. Department of Mathematics, Xiangnan University, Chenzhou Hunan 423000, China; 2. School of Mathematics and Computer, Hunan Normal University, Changsha Hunan 410081, China; 3. Department of Computer Science and Technology, Changsha University, Changsha Hunan 410003 China; 4. Department of Mathematics and Physics, Hefei University, Hefei Anhui 230601, China |
| Abstract: | To constrain the interpolating curves to be bounded in the given region is an important problem in curve design.A rational cubic interpolating spline based on function values and with quadratic denominators is constructed.The sufficient conditions for the interpolating curves to be above,below or between the given broken lines or piecewise quadratic curves and the sufficient and necessary conditions for the interpolating curves to be above,below or between the given broken lines are derived. |
| Keywords: | computer application curve design rational interpolation cubic spline |
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