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Geometric Algebra for Multidimension-Unified Geographical Information System

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Abstract

Traditional Euclidean geometry-based Geographical Information System (GIS) is not multidimensional unification with weak ability to object expression and analysis of high dimensions. Geometric algebra (GA) can connect different geometric and algebra systems, and provide rigorous and elegant foundation for expression, modeling and analysis in GIS. This paper proposes the implementation methods for system construction and key components of multidimension-unified GIS. Based on such properties as multidimension-unified and coordinate-free of GA, data models, data indexes, and data analysis algorithms for multidimensional vector data, raster and vector field data are developed. This study indicates that GA provides a new mathematical tool for the development of GIS characterized as multidimension-unified expression and computation. For the development of geographical analysis methods, it can represent multidimensional spatio-temporal changes conveniently.

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Authors and Affiliations

  1. Key Laboratory of Virtual Geographic Environment, Ministry of Education & Jiangsu Provincial Key Laboratory for NSLSCS, XianLin Campus of Nanjing Normal University, No. 1 Wenyuan Road, Nanjing, China

    Linwang Yuan

  2. Key Laboratory of Virtual Geographic Environment, Ministry of Education, XianLin Campus of Nanjing Normal University, No. 1 Wenyuan Road, Nanjing, China

    Zhaoyuan Yu, Wen Luo, Lin Yi & Guonian Lü

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  1. Linwang Yuan
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  2. Zhaoyuan Yu
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  3. Wen Luo
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  4. Lin Yi
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  5. Guonian Lü
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Correspondence to Linwang Yuan.

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Yuan, L., Yu, Z., Luo, W. et al. Geometric Algebra for Multidimension-Unified Geographical Information System. Adv. Appl. Clifford Algebras 23, 497–518 (2013). https://doi.org/10.1007/s00006-012-0375-z

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  • DOI: https://doi.org/10.1007/s00006-012-0375-z

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