| Applications of Lodrigues Matrix in 3D Coordinate Transformation |
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| 引用本文： | YAO Jili XU Yufei XIAO Wei. Applications of Lodrigues Matrix in 3D Coordinate Transformation[J]. 地球空间信息科学学报, 2007, 10(3): 173-176. DOI: 10.1007/s11806-007-0070-8 |
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| 作者姓名： | YAO Jili XU Yufei XIAO Wei |
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| 作者单位： | School of Architecture Engineering Shandong University of Technology，12 Zhangzhou Road Zibo 255049 China |
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| 摘 要： | Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: ① the traditional rotation angles θ , φ ,ψ are substituted with a , b, c which are three re-spective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.
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| 关 键 词： | 坐标 三维转换 Lodrigues矩阵 线性模型 转化方程 |
| 文章编号： | 1009-5020（2007）03-173-04 |
| 收稿时间： | 2007-06-11 |
| 修稿时间： | 2007-06-11 |
Applications of Lodrigues matrix in 3D coordinate transformation |
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| Yao Jili,Xu Yufei,Xiao Wei. Applications of Lodrigues matrix in 3D coordinate transformation[J]. Geo-Spatial Information Science, 2007, 10(3): 173-176. DOI: 10.1007/s11806-007-0070-8 |
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| Authors: | Yao Jili Xu Yufei Xiao Wei |
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| Affiliation: | (1) School of Architecture Engineering, Shandong University of Technology, 12 Zhangzhou Road, Zibo, 255049, China |
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| Abstract: | Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: the traditional ➀ rotation angles θ, φ, ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ➁ directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ➂ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick. |
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| Keywords: | 3D transformation linear model transformation equation Lodrigues matrix |
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