| 基于离散点和法矢的曲线重构算法 |
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| 引用本文： | 郭明阳,李崇君.基于离散点和法矢的曲线重构算法[J].数学研究及应用,2020,40(1):87-100. |
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| 作者姓名： | 郭明阳 李崇君 |
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| 作者单位： | 大连理工大学数学科学学院, 辽宁 大连 116024,大连理工大学数学科学学院, 辽宁 大连 116024 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11871137; 11572081)，辽宁省高等学校创新人才支持计划(Grant No.LCR2018001). |
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| 摘 要： | This paper presents a curve reconstruction algorithm based on discrete data points and normal vectors using B-splines.The proposed algorithm has been improved in three steps:parameterization of the discrete data points with tangent vectors,the B-spline knot vector determination by the selected dominant points based on normal vectors,and the determination of the weight to balancing the two errors of the data points and normal vectors in fitting model.Therefore,we transform the B-spline fitting problem into three sub-problems,and can obtain the B-spline curve adaptively.Compared with the usual fitting method which is based on dominant points selected only by data points,the B-spline curves reconstructed by our approach can retain better geometric shape of the original curves when the given data set contains high strength noises.
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| 关 键 词： | curve recons truction curve fit ting normal vector SPLINE dominant point |
| 收稿时间： | 2019/6/17 0:00:00 |
| 修稿时间： | 2019/10/26 0:00:00 |
Curve Reconstruction Algorithm Based on Discrete Data Points and Normal Vectors |
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| Mingyao GUO and Chongjun LI.Curve Reconstruction Algorithm Based on Discrete Data Points and Normal Vectors[J].Journal of Mathematical Research with Applications,2020,40(1):87-100. |
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| Authors: | Mingyao GUO and Chongjun LI |
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| Institution: | Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China and Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: | This paper presents a curve reconstruction algorithm based on discrete data points and normal vectors using B-splines. The proposed algorithm has been improved in three steps: parameterization of the discrete data points with tangent vectors, the B-spline knot vector determination by the selected dominant points based on normal vectors, and the determination of the weight to balancing the two errors of the data points and normal vectors in fitting model. Therefore, we transform the B-spline fitting problem into three sub-problems, and can obtain the B-spline curve adaptively. Compared with the usual fitting method which is based on dominant points selected only by data points, the B-spline curves reconstructed by our approach can retain better geometric shape of the original curves when the given data set contains high strength noises. |
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| Keywords: | curve reconstruction curve fitting normal vector B-spline dominant point |
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