Approximation to clothoid in same length via G1 quintic Pythogrean Hodograph splines(用G1 5次PH曲线等弧长逼近clothoid曲线)
PH曲线是弧长为多项式的Bézier曲线，其等距线可用有理多项式表示.由clothoid曲线端点的G1 Hermite插值条件，构造对应等弧长的最佳G1 5次PH插值曲线，以此作为逼近.利用微分几何中的Frenet-Serret公式和经典的Taylor展开式，推导该逼近方式的误差、等距线误差和曲率误差.最后，给出在误差范围内，将clothoid曲线转化为等弧长G1 5次PH样条及等距线生成的算法....
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2012-01-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2012.01.006 |
| _version_ | 1797236078620442624 |
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| author | ZHENGZhi-hao(郑志浩) |
| author_facet | ZHENGZhi-hao(郑志浩) |
| author_sort | ZHENGZhi-hao(郑志浩) |
| collection | DOAJ |
| description | PH曲线是弧长为多项式的Bézier曲线，其等距线可用有理多项式表示.由clothoid曲线端点的G1 Hermite插值条件，构造对应等弧长的最佳G1 5次PH插值曲线，以此作为逼近.利用微分几何中的Frenet-Serret公式和经典的Taylor展开式，推导该逼近方式的误差、等距线误差和曲率误差.最后，给出在误差范围内，将clothoid曲线转化为等弧长G1 5次PH样条及等距线生成的算法. |
| first_indexed | 2024-04-24T16:58:08Z |
| format | Article |
| id | doaj.art-e314d1585d194e8d9f38f08de11f1f24 |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:58:08Z |
| publishDate | 2012-01-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-e314d1585d194e8d9f38f08de11f1f242024-03-29T01:58:30ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972012-01-01391202610.3785/j.issn.1008-9497.2012.01.006Approximation to clothoid in same length via G1 quintic Pythogrean Hodograph splines(用G1 5次PH曲线等弧长逼近clothoid曲线)ZHENGZhi-hao(郑志浩)0Department of Mathematics, Zhejiang University, Hangzhou 310027, China(浙江大学数学系，浙江 杭州 310027)PH曲线是弧长为多项式的Bézier曲线，其等距线可用有理多项式表示.由clothoid曲线端点的G1 Hermite插值条件，构造对应等弧长的最佳G1 5次PH插值曲线，以此作为逼近.利用微分几何中的Frenet-Serret公式和经典的Taylor展开式，推导该逼近方式的误差、等距线误差和曲率误差.最后，给出在误差范围内，将clothoid曲线转化为等弧长G1 5次PH样条及等距线生成的算法.https://doi.org/10.3785/j.issn.1008-9497.2012.01.006clothoid曲线5次ph曲线等距线frenet-serret公式taylor展开误差样条 |
| spellingShingle | ZHENGZhi-hao(郑志浩) Approximation to clothoid in same length via G1 quintic Pythogrean Hodograph splines(用G1 5次PH曲线等弧长逼近clothoid曲线) Zhejiang Daxue xuebao. Lixue ban clothoid曲线 5次ph曲线 等距线 frenet-serret公式 taylor展开 误差 样条 |
| title | Approximation to clothoid in same length via G1 quintic Pythogrean Hodograph splines(用G1 5次PH曲线等弧长逼近clothoid曲线) |
| title_full | Approximation to clothoid in same length via G1 quintic Pythogrean Hodograph splines(用G1 5次PH曲线等弧长逼近clothoid曲线) |
| title_fullStr | Approximation to clothoid in same length via G1 quintic Pythogrean Hodograph splines(用G1 5次PH曲线等弧长逼近clothoid曲线) |
| title_full_unstemmed | Approximation to clothoid in same length via G1 quintic Pythogrean Hodograph splines(用G1 5次PH曲线等弧长逼近clothoid曲线) |
| title_short | Approximation to clothoid in same length via G1 quintic Pythogrean Hodograph splines(用G1 5次PH曲线等弧长逼近clothoid曲线) |
| title_sort | approximation to clothoid in same length via g1 quintic pythogrean hodograph splines 用g1 5次ph曲线等弧长逼近clothoid曲线 |
| topic | clothoid曲线 5次ph曲线 等距线 frenet-serret公式 taylor展开 误差 样条 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2012.01.006 |
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