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Unified Expression Frame of Geodetic Stations Based on Conformal Geometric Algebra

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Advances in Computer Graphics (CGI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 13002))

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Abstract

Global geodetic stations are the basis for the study of International Terrestrial Reference Frame (ITRF) and crustal plate motion. This paper has collected a total of 288 global geodetic stations calculated by four spatial geodetic technologies. Because different types of geodetic stations use different spatial references, the data of different types of stations can only be used after necessary spatial conversion. And with the motion of the Earth’s crust, conversion methods and formulas are constantly being revised. The complexity and dynamics of spatial conversion have greatly hindered the integrated application of different global geodetic stations. This paper proposes a unified expression frame for global geodetic stations. Based on the theory of conformal geometric algebra, the motion operator that uniformly expresses translation, rotation, and scaling in the form of versor product is introduced. From the perspective of the unified expression and calculation of the operator, a unified expression frame and ITRF conversion method for different reference frames of the geodetic station are constructed. The experimental case shows that the ITRF conversion method based on the unified motion operator reduces the complexity of the reference frame conversion, which provides a certain reference for the unified expression and analysis of different frame conversion and crustal plate motion.

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References

  1. Yuan, L., Yu, Z., Luo, W., et al: Geometric algebra for multidimension-unified geographical information system. Adv. Appl. Clifford Algebras. 23(2), 497–518 (2013). https://doi.org/10.1007/s00006-012-0375-z

  2. Hua, Y.: The core problems and key technologies of Pan-Spatial information system. J. Geo. Sci. Tech. 33(4), 331–335 (2016). https://doi.org/10.3969/j.issn.1673-6338.2016.04.001

  3. Crespi, M., Mazzoni, A., Colosimo, G.: Global and local reference frames. Rendiconti Lincei 26(1), 25–31 (2015). https://doi.org/10.1007/s12210-015-0435-0

    Article  Google Scholar 

  4. Altamimi, Z., Collilieux, X., Métivier, L.: ITRF2008: an improved solution of the international terrestrial reference frame. J. Geod. 85(8), 457–473 (2011). https://doi.org/10.1007/s00190-011-0444-4

    Article  Google Scholar 

  5. Böckmann, S., Artz, T., Nothnagel, A.: VLBI terrestrial reference frame contributions to ITRF2008. J. Geod. 84(3), 201–219 (2010). https://doi.org/10.1007/s00190-009-0357-7

    Article  Google Scholar 

  6. Liu, J., Wei, N., Shi, C.: Status and prospects of the international terrestrial reference frame (ITRF). Chinese J. Nat. 35(4), 243–250 (2013). https://doi.org/10.3969/j.issn.0253-9608.2013.04.002

  7. Wang, J.: Correlations among parameters in seven-parameter transformation model. J. Geod. Geadyn. 27(2), 43–46 (2007). https://doi.org/10.14075/j.jgg.2007.02.008

  8. Liu, L., Cheng, Y.: On transform between ITRFS. J. Geod. Geodyn 30(2), 141–143 (2010). https://doi.org/10.14075/j.jgg.2010.02.003

    Article  Google Scholar 

  9. Yuan, L., Yu, Z., Wen, L., et al.: Multidimensional-unified topological relations computation: a hierarchical geometric algebra-based approach. Int. J. Geogr. Inf. Sci. 28(11–12), 2435–2455 (2014). https://doi.org/10.1080/13658816.2014.929136

    Article  Google Scholar 

  10. Yuan, L., Yu, Z., Chen, S., et al.: CAUSTA: clifford algebra-based unified spatio-temporal Analysis. Trans. GIS 14(s1), 59–83 (2010). https://doi.org/10.1111/j.1467-9671.2010.01221.x

    Article  Google Scholar 

  11. Li, H.: Conformal geometric algebra–a new frame for computational geometry. J. Comput. -Aided Des. Comput. Graph. 17(11), 2383–2393 (2005). https://doi.org/10.1016/j.molcatb.2005.02.001

    Article  Google Scholar 

  12. Dorst, L., Daniel, F., Stephen, M.: Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry. Morgan Kaufmann Publishers, San Francisco (2007)

    Google Scholar 

  13. Wareham, R., Cameron, J., Lasenby, J.: Applications of conformal geometric algebra in computer vision and graphics. In: Li, H., Olver, P.J., Sommer, G. (eds.) GIAE/IWMM -2004. LNCS, vol. 3519, pp. 329–349. Springer, Heidelberg (2005). https://doi.org/10.1007/11499251_24

    Chapter  MATH  Google Scholar 

  14. Bayro-Corrochano, E., Scheuermann, G.: Geometric Algebra Computing. Springer, London (2010)

    Book  Google Scholar 

  15. Li, H.: Conformal geometric algebra for motion and shape description. J. Comput. -Aided Des. Comput. Graph. 18(7), 895–901 (2006). https://doi.org/10.1016/S1004-4132(06)60027-3

    Article  Google Scholar 

  16. Zou, L., Lasenby, J., He, Z.: Pattern analysis of conformal array based on geometric algebra. IET Microwaves Antennas Propag. 5(10), 1210–1218 (2011). https://doi.org/10.1049/iet-map.2010.0588

    Article  Google Scholar 

  17. Zou, L., Lasenby, J., He, Z.: Polarisation diversity of conformal arrays based on geometric algebra via convex optimization. Iet. Radar Sonar Navig. 6(6), 417–424 (2012). https://doi.org/10.1049/iet-rsn.2011.0293

    Article  Google Scholar 

  18. Fan, Y., Liu, W., Shi, G., et al.: A research on method based on the foundation of the theory of rotation matrix described by the CGA [C]. In: The 9th Member Congress of China Photographic Society and the Academic Annual Conference, pp. 307–311. Beijing (2014)

    Google Scholar 

  19. Li, H.: Conformal geometric algebra and algebraic manipulations of geometric invariants. J. Comput.-Aided Des. Comput. Graph. 18(7), 902–911 (2006). https://doi.org/10.1016/S1005-8885(07)60042-9

    Article  Google Scholar 

  20. Vince, J.: Geometric Algebra for Computer Graphics. Springer, London (2008)

    Book  Google Scholar 

  21. Perwass, C.: Geometric Algebra with Applications in Engineering. Springer, Berlin Heidelberg (2009)

    MATH  Google Scholar 

  22. Yuan, L., Lv, G., Yu, Z., et al.: Multidimensional Unified GIS Based on Geometric Algebra: Theory, Algorithm. Application. Science Press, Beijing (2012)

    Google Scholar 

  23. Cheng, Y.: Brief introduction of ITRF2008 frame. J. Geod. Geodyn. 32(1), 47–50 (2012). https://doi.org/10.14075/j.jgg.2012.01.011

    Article  Google Scholar 

  24. Liu, L., Cheng, Y.: Research on some problems of coordinate frame transformation. GNSS World of China 001, 20–24 (2010). https://doi.org/10.13442/j.gnss.2010.01.014

    Article  Google Scholar 

  25. Peng, X., Gao, J., et al.: Research of the coordinate conversion between WGS84 and CGCS200. J. Geod. Geodyn. 35(2), 119–221 (2015). https://doi.org/10.14075/j.jgg.2015.02.010

    Article  Google Scholar 

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Acknowledgment

This work was supported by National Natural Science Fundation for Distinguished Young Scholar (Grant No. 41625004), National Natural Science Foundation of China (Grant No. 42001325, 41976186, 41971404, 42001320).

Author information

Authors and Affiliations

  1. School of Geography, Nanjing Normal University, Nanjing, 210023, China

    Zhenjun Yan, Zhaoyuan Yu, Yun Wang, Wen Luo, Hong Gao & Linwang Yuan

  2. Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing, 210023, China

    Zhaoyuan Yu, Wen Luo & Linwang Yuan

  3. Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing, 210023, China

    Zhaoyuan Yu, Wen Luo & Linwang Yuan

  4. College of Geographic Science, Nantong University, Nantong, 226019, China

    Jiyi Zhang

Authors
  1. Zhenjun Yan
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  2. Zhaoyuan Yu
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  3. Yun Wang
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  4. Wen Luo
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  5. Jiyi Zhang
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  6. Hong Gao
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  7. Linwang Yuan
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Corresponding author

Correspondence to Wen Luo .

Editor information

Editors and Affiliations

  1. University of Geneva, Carouge, Switzerland

    Nadia Magnenat-Thalmann

  2. University of Minnesota, Minneapolis, MN, USA

    Victoria Interrante

  3. EPFL, Lausanne, Switzerland

    Daniel Thalmann

  4. University of Crete, Heraklion, Crete, Greece

    George Papagiannakis

  5. Shanghai Jiao Tong University, Shanghai, China

    Bin Sheng

  6. University of Sydney, Sydney, NSW, Australia

    Jinman Kim

  7. University of Calgary, Calgary, AB, Canada

    Marina Gavrilova

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Yan, Z. et al. (2021). Unified Expression Frame of Geodetic Stations Based on Conformal Geometric Algebra. In: Magnenat-Thalmann, N., et al. Advances in Computer Graphics. CGI 2021. Lecture Notes in Computer Science(), vol 13002. Springer, Cham. https://doi.org/10.1007/978-3-030-89029-2_51

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  • DOI: https://doi.org/10.1007/978-3-030-89029-2_51

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89028-5

  • Online ISBN: 978-3-030-89029-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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