Application of Lodrigues Matrix in Coordinate Transformation of Similar Material Simulation Experiment

Abstract:

In the two-dimensional experiment of similar material simulation, three-dimensional coordinate data obtained by total station should be conversed to the coordinate system which is concerned in the experiment.When using bursa-wolf model to converse coordinate,the three rotation parameters should be linearized,which will affect the accuracy of coordinate conversion if the three rotation parameters are big.In this paper,it is researched that using an antisymmetric matrix which is consist of three separate parameters to substitute for the three rotation parameters,and then the lodrigues matrix is composed from the antisymmetric matrix. Conversion results showed that: By introducing of lodrigues matrix, not only the algorithm becomes simple but also the coordinate transformation precision is improved.

• Periodical: Advanced Materials Research (Volumes 455-456)
• Pages: 204-210
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.455-456.204
• Online since: January 2012
• Authors: Guo Wang, Xi Min Cui, De Bao Yuan, Ya Hui Qiu, Jin Lin Yang, Xiao Guo Guan
• Keywords: Coordinate Transformation, Linear Model, Lodrigues Matrix, Similar Material Simulation Experiment

References

[1] ZENG Wenxian，TAO Benzao. Non-Linear Adjustment Model of Three-Dimensional Coordinate Transformation[J]. Geomatics and Information Science of Wuhan University，2003, 28(5): 566-568.

[2] Yang Fan, Li Guangyun, Wang Li, Yu Ying. A method of least squre iterative coordinate transformation based on Lodrigues matrix[J]. Geotechnical Investigation & Surveying, 2010(9): 80-84.

[3] ZENG Huai'en, HUANG Shengxiang. A Kind of Direct Search Method Adapted to Solution of 3D Coordinate Transformation Parameters[J]. Geomatics and Information Science of Wuhan University, 2008, 33(11): 1118-1121.

[4] YAO Jili, HAN Baomin, YANG Yuanxi. Applications of Lodrigues Matrix in 3D Coordinate Transformation[J]. Geomatics and Information Science of Wuhan University, 2006, 31(12): 1094-1096.

[5] Cui Ximin, Peng Xiaozhan, Liu Wenlong. Surveying Course [M]. BeiJing:  Coal Industry Press, (2009).

[6] YANG Fan, LI Guangyun, WANG Li. Research on the Methods of Calculating 3D Coordinate Transformtion Parameters[J]. Bulletin OF SURVEYING AND MAPPING, 2010, 6: 5-7.

[7] YU Zhi-lu, YAO Ji-li, LV Chang-guang. The direct-solution of spatial-resection based on Lodriguez matrix[J]. ENGINEERING OF SURVEYING AND MAPPING, 2005, 2(14): 50-52.

[8] Xie Mingyu, Yao Yibin. A NEW METHOD FOR SOLUTION OF SEVEN-PARAMETER TRANSFORMATION BETWEEN 3D AND 2D SPACES[J]. JOURNAL OF GEODESY AND GEODYNAMICS , 2008 , 2 8(02): 104-109.

[9] SHI Yimin, ZHU Ziyang, SONG Shujun. Coordinate Transformation Between New Forms of Geodetic Coordinate Systems[J]. JOURNAL OF TONGJI UNIVERSITY(NATURAL SCIENCE), 2008, 36(07): 977-980.

[10] CUI Ximin, XU Jialin, Miao Xiexing, ZHAO Yingli, JIN Riping. Modeling Experiment for the Rock Movement in Fully Mechanized Sub-level Caving and Slice Mining at Lu'an Coal Field[J]. JOURNAL OF EXPERIMENTAL MECHANICS, 1999, 14(3): 402-406.

[11] WANG Guangxing, HE Wei. A New Method for Detemination of Transformation Parameter between 2D Space and 3D Space[J]. Bulletin OF SURVEYING AND MAPPING, 2005, 5: 42-45.

[12] LIU Renzhao, DUAN Wengui, ZHANG Yutang. STUDY on Close Computation of Parameters of Bursa Transformation Model[J]. Resources Environment& Engineering, 2010, 24(4): 416-423.

[13] Wang Jiexian. CORRELATIONS AMONG PARAMETERS IN SEVEN-PARAMETER TRANSFORMATION MODEL[J]. JOURNAL OF GEODESY AND GEODYNAMICS, 2007, 2(27): 43-46.

[14] Tian FengRui, Hua XiangHong, Liu JinBiao, Zhou Bo. An Improved ICP Algorithm Based on Rodrigues Matrix[J]. Urban Geotechnical Investigation&Surveying, 2010, 5: 90-97.

[15] Guo Wang; Xi-min Cui; De-bao Yuan; Hai-wei Liu; Jing-jing Jin. Research on automatic extraction of roadside line from vehicle-borne Lidar point cloud data [C]. Proceedings of 2010 International Conference on Management Science, 2010, 163-166.

[16] REN Xiao-peng, LI Zhi-qiang, LV Xi-fu. Similar Material Simulation Experiment at Longma Coal Mine[J]. Coal Technology, 2007, 26(8): 136-138.

[17] WANG Luo-feng, JIANG Fu-xing, YU Zheng-xing. Similar material simulation experiment on destressing effects of the deep thick coal seam with high burst liability after mining upper and lower protective seams[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(3): 442-446.

[18] Liu Deqian, Jing Zhengquan, Feng Haiying, Zhao Pengyan. Study on the Pressure of Overlying Rock in Mining of Deep Buried Coal Seam by Similar Material Simulation Experiment[J]. MINING R&D, 2010, 30(1): 29-32.

[19] YANG Fan, KONG Xiaoyong, CHENG Guangran, JIANG Hao, YANG Wentuo. Application on digital camera and T3 theodolite in similar material model test[J]. Journal of Liaoning Technical University(Natural Science), 2010, 29(4): 579-581.

[20] XIA Lifu, LI Jingchun, HU Youjian, SUN Hua. Test and Precision Analysis of Ranging Performance of Reflectorless Total Station[J]. GEOSPATIAL INFORMATION, 2008, 6(2): 133-135.

[21] SUN Guang-jun, GUO Ying-zhong. Theory of Error Offset in the Simulation Experiment of Equivalent Materials[J]. G Zhongzhou coal, 2009, 164: 11-13.