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基于共形几何代数的空间几何相似性研究。

Study on Spatial Geometric Similarity Based on Conformal Geometric Algebra.

机构信息

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.

出版信息

Int J Environ Res Public Health. 2022 Aug 30;19(17):10807. doi: 10.3390/ijerph191710807.

DOI:10.3390/ijerph191710807
PMID:36078512
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9518588/
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.

摘要

空间几何相似性研究在空间数据检索中起着重要作用。许多研究人员已经研究了空间几何相似性，这对于空间分析和数据检索非常有用。然而，他们中的大多数人都专注于同一类型的对象。支持不同类型对象的空间几何相似性计算的方法很少，尚未建立系统的理论指标，也没有全面的空间几何相似性计算模型。在本研究中，我们对基于共形几何代数（CGA）的空间几何相似性计算进行了分析，CGA 在空间对象的测量信息的定量计算和空间对象拓扑关系的定性判断方面具有一定的优势。首先，我们开发了一个统一的空间几何场景表达模型，集成了对象的形状和它们之间的空间关系。然后，我们建立了各种地理环境下的空间几何相似性计算模型，为空间几何相似性研究提供了一种新方法。最后，通过案例研究验证了计算模型。空间几何相似性的研究对空间数据检索具有科学意义和实际价值。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/912fd6fdb0ce/ijerph-19-10807-g020.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/cb6b416d58e4/ijerph-19-10807-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/51d6fdd949af/ijerph-19-10807-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/e632cdd089df/ijerph-19-10807-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/c840f2d5c867/ijerph-19-10807-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/5eee079b3c64/ijerph-19-10807-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/b38e62b09ec0/ijerph-19-10807-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/1d51a9d9eb63/ijerph-19-10807-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/fd4a20473ed7/ijerph-19-10807-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/4e655f1d0cae/ijerph-19-10807-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/6e5eda1d5de5/ijerph-19-10807-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/0c8a6d1da0be/ijerph-19-10807-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/ab257cfabdc0/ijerph-19-10807-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/bfe1b642d02a/ijerph-19-10807-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/e22826752d02/ijerph-19-10807-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/b4b46f87a3b5/ijerph-19-10807-g015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/f053544a796e/ijerph-19-10807-g016.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/b453611cbfbb/ijerph-19-10807-g017.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/2fc231cffa32/ijerph-19-10807-g018.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/3958c7896c27/ijerph-19-10807-g019.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/912fd6fdb0ce/ijerph-19-10807-g020.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/cb6b416d58e4/ijerph-19-10807-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/51d6fdd949af/ijerph-19-10807-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/e632cdd089df/ijerph-19-10807-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/c840f2d5c867/ijerph-19-10807-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/5eee079b3c64/ijerph-19-10807-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/b38e62b09ec0/ijerph-19-10807-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/1d51a9d9eb63/ijerph-19-10807-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/fd4a20473ed7/ijerph-19-10807-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/4e655f1d0cae/ijerph-19-10807-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/6e5eda1d5de5/ijerph-19-10807-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/0c8a6d1da0be/ijerph-19-10807-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/ab257cfabdc0/ijerph-19-10807-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/bfe1b642d02a/ijerph-19-10807-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/e22826752d02/ijerph-19-10807-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/b4b46f87a3b5/ijerph-19-10807-g015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/f053544a796e/ijerph-19-10807-g016.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/b453611cbfbb/ijerph-19-10807-g017.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/2fc231cffa32/ijerph-19-10807-g018.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/3958c7896c27/ijerph-19-10807-g019.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e60e/9518588/912fd6fdb0ce/ijerph-19-10807-g020.jpg

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本文引用的文献

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