| 有理三次PH曲线的G1 Hermite插值 |
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| 引用本文： | 潘俊.有理三次PH曲线的G1 Hermite插值[J].复旦学报(自然科学版),2007,46(2):184-191. |
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| 作者姓名： | 潘俊 |
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| 作者单位： | 复旦大学,数学科学学院,上海,200433 |
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| 基金项目： | 国家自然科学基金资助项目(10125102) |
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| 摘 要： | 探讨了有理PH曲线的G1 Hermite插值问题,运用复数表达将问题转化为包含5个复代数方程的方程组,通过求解这个方程组,得到结论:当插值条件形成凸多边形时,插值问题有2个解,其中之一为多项式解;而当插值条件形成非凸多边形时,只有切方向满足一定条件时,插值问题才有一个解.而对于后一种情况,总可以通过加点的方式细分原逼近曲线,进而得到由两段有理三次PH曲线G1拼接而成的4组样条插值曲线.
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| 关 键 词： | PH曲线 有理参数曲线 G1 Hermite插值 NURBS 有理三次PH样条曲线 |
| 文章编号： | 0427-7104（2007）02-0184-08 |
| 修稿时间： | 2006-03-07 |
G1 Hermite Interpolation by Rational Pythagorean Hodograph Cubics |
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| PAN Jun.G1 Hermite Interpolation by Rational Pythagorean Hodograph Cubics[J].Journal of Fudan University(Natural Science),2007,46(2):184-191. |
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| Authors: | PAN Jun |
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| Institution: | School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
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| Abstract: | The G1 Hermite interpolation by Rational Pythagorean Hodograph Cubics is discussed.By means of complex representation the problem is transformed to a system of complex equations with 5 complex algebraic equations.By solving this system,the following results are obtained.There are 2 solutions(especially one is a polynomial solution),when the conditions form a convex polygon.And with the concave polygon conditions,there is no solution unless the tangents satisfy some special conditions.But four solutions constituted with two G1 PH rational cubic segments always can be got by means of adding points between the former extreme points. |
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| Keywords: | PH curves rational curves G1 Hermite interpolation NURBS rational cubic PH spline curves |
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