| B-spline流形的几何结构 |
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| 引用本文： | 李春辉,孙华飞,张士诚. B-spline流形的几何结构[J]. 北京理工大学学报, 2011, 31(1): 113-116 |
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| 作者姓名： | 李春辉 孙华飞 张士诚 |
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| 作者单位： | 李春辉,孙华飞,Li Chun-hui,SUN Hua-fei(北京理工大学理学院,北京,100081);张士诚,ZHANG Shi-cheng(北京理工大学理学院,北京,100081;徐州师范大学数学科学学院,江苏,徐州,221116) |
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| 摘 要： | 给出了由B-spline方程构成的B-spline流形的几何结构.通过B-spline流形的定义,得到B-spline流形是±1平坦的,同时,还给出了B-spline流形的曲率张量和二维B-spline流形的高斯曲率.给出算例,验证文中二维B-spline流形的高斯曲率.
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| 关 键 词： | B-spline流形 曲率张量 高斯曲率 |
| 收稿时间： | 2010-03-26 |
The Geometric Structure of the B-Spline Manifolds |
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| LI Chun-hui,SUN Hua-fei and ZHANG Shi-cheng. The Geometric Structure of the B-Spline Manifolds[J]. Journal of Beijing Institute of Technology(Natural Science Edition), 2011, 31(1): 113-116 |
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| Authors: | LI Chun-hui SUN Hua-fei ZHANG Shi-cheng |
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| Affiliation: | School of Science, Beijing Institute of Technology, Beijing 100081, China;School of Science, Beijing Institute of Technology, Beijing 100081, China;School of Science, Beijing Institute of Technology, Beijing 100081, China; School of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu 221116, China |
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| Abstract: | In the present paper, the geometric structure of the B-spline manifolds, which consists of all the B-spline functions, is given. From the definition of the B-spline manifolds of all the B-spline functions, it can be seen that the B-spline manifolds are ±1-flat. Moreover, the curvature tensor and the Gaussian curvature for two dimensional B-spline manifolds are obtained. At last, an example illustrates the validity of the Gaussian curvature obtained in this paper. |
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| Keywords: | B-spline manifold curvature tensor Gaussian curvature |
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