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Unified Spatial Intersection Algorithms Based on Conformal Geometric Algebra

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Listed:
  • Feng Zhang
  • Xiaomin Jiang
  • Xiaoyi Zhang
  • Yingzhi Wang
  • Zhenhong Du
  • Renyi Liu

Abstract

Conformal Geometric Algebra has been introduced into geographic information science as a mathematical theory because of its advantages in terms of uniform multidimensional representation and computation. The traditional intersection computation between two geometric objects of different types is not unified. In this study, we propose algorithms based on Conformal Geometric Algebra to determine the spatial relationships between geographic objects in a unified manner. The unified representation and intersection computation can be realized for geometric objects of different dimensions. Different basic judgment rules are provided for different simple geometries. The algorithms are designed and implemented using MapReduce to improve the efficiency of the algorithms. From the results of several experiments we provide, the correctness and effectiveness of the algorithms can be verified.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:7412373
    DOI: 10.1155/2016/7412373
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    Cited by:

    1. 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.

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