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Study on Spatial Geometric Similarity Based on Conformal Geometric Algebra

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  • Xiaomin Jiang

    (School of Civil Engineering & Architecture, Zhejiang University of Science & Technology, 318 Liuhe Road, Hangzhou 310023, China
    Center of Urban and Rural Development, Zhejiang University of Science & Technology, 318 Liuhe Road, Hangzhou 310023, China)

  • Yangfei Huang

    (School of Civil Engineering & Architecture, Zhejiang University of Science & Technology, 318 Liuhe Road, Hangzhou 310023, China
    Center of Urban and Rural Development, Zhejiang University of Science & Technology, 318 Liuhe Road, Hangzhou 310023, China)

  • Feng Zhang

    (Zhejiang Provincial Key Laboratory of Geographic Information Science, Zhejiang University, 148 Tianmushan Road, Hangzhou 310028, China
    School of Earth Sciences, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China)

Abstract

The study of spatial geometric similarity plays a significant role in spatial data retrieval. Many researchers have examined spatial geometric similarity, which is useful for spatial analysis and data retrieval. However, the majority of them focused on objects of the same type. Methods to support the spatial geometric similarity computation for different types of objects are rare, a systematic theory index has not been developed yet, and there has not been a comprehensive computational model of spatial geometric similarity. In this study, we conducted an analysis of the spatial geometric similarity computation based on conformal geometric algebra (CGA), which has certain advantages in the quantitative computation of the measurement information of spatial objects and the qualitative judgment of the topological relations of spatial objects. First, we developed a unified expression model for spatial geometric scenes, integrating shapes of objects and spatial relations between them. Then, we established a model for the spatial geometric similarity computation under various geographical circumstances to provide a novel approach for spatial geometric similarity research. Finally, the computation model was verified through a case study. The study of spatial geometric similarity sheds light on spatial data retrieval, which has scientific significance and practical value.

Suggested Citation

  • Xiaomin Jiang & Yangfei Huang & Feng Zhang, 2022. "Study on Spatial Geometric Similarity Based on Conformal Geometric Algebra," IJERPH, MDPI, vol. 19(17), pages 1-22, August.
    • Handle: RePEc:gam:jijerp:v:19:y:2022:i:17:p:10807-:d:901739
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    References listed on IDEAS

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    1. Feng Zhang & Xiaomin Jiang & Xiaoyi Zhang & Yingzhi Wang & Zhenhong Du & Renyi Liu, 2016. "Unified Spatial Intersection Algorithms Based on Conformal Geometric Algebra," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-10, November.
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