闾国年, 袁林旺, 俞肇元, 罗文, 周良辰, 闫振军. 几何代数在地理信息高维空间表达中的应用[J]. 武汉大学学报 ( 信息科学版), 2020, 45(9): 1328-1333. DOI: 10.13203/j.whugis20200080
引用本文: 闾国年, 袁林旺, 俞肇元, 罗文, 周良辰, 闫振军. 几何代数在地理信息高维空间表达中的应用[J]. 武汉大学学报 ( 信息科学版), 2020, 45(9): 1328-1333. DOI: 10.13203/j.whugis20200080
LÜ Guonian, YUAN Linwang, YU Zhaoyuan, LUO Wen, ZHOU Liangchen, YAN Zhenjun. Role of Geometric Algebra in High Dimensional Space Representation of Geographic Information[J]. Geomatics and Information Science of Wuhan University, 2020, 45(9): 1328-1333. DOI: 10.13203/j.whugis20200080
Citation: LÜ Guonian, YUAN Linwang, YU Zhaoyuan, LUO Wen, ZHOU Liangchen, YAN Zhenjun. Role of Geometric Algebra in High Dimensional Space Representation of Geographic Information[J]. Geomatics and Information Science of Wuhan University, 2020, 45(9): 1328-1333. DOI: 10.13203/j.whugis20200080

几何代数在地理信息高维空间表达中的应用

Role of Geometric Algebra in High Dimensional Space Representation of Geographic Information

  • 摘要: 以欧氏几何为基础的信息框架对地理信息科学的发展起着重要作用。然而,由于欧氏空间对地理信息系统(geographic information system,GIS)中地理对象和现象的表达依赖于坐标系统以及对象具体坐标,使得基于欧氏空间的地理对象表达、计算和分析难以形成多维统一的运算规则和运算框架,增加了GIS算法的复杂度,降低了GIS分析效率。几何代数是一种以维度运算为基础的结合代数,在几何代数中,空间被定义为向量集合间的运算,空间维数直接由运算法则确定,可实现高维几何计算和分析的统一。基于几何代数统一的计算与分析框架对现有GIS进行构造,能够更好地对高维对象进行表达与分析,提升对复杂地理对象与动态地理现象的表达、时空多尺度分析以及不同尺度地理模型耦合集成的能力,有助于奠定GIS向实时动态、虚实融合、全视角、全要素、全内容表达的全息地图方向发展的理论基础。

     

    Abstract: Geographic information space is a high-dimensional space combining virtual and real. Geographic information system (GIS) based on European geometry plays an important role in the development of geographic information science. However, because the expression of GIS geographic objects and phenomena in European-style space depends on object coordinates and the adopted coordinate system, it is difficult for the expression, calculation and analysis of geographic objects to form a multi-dimensional unified operation rule and framework, which increases the algorithm's complexity and reduces the efficiency of algorithm analysis. Geometric algebra is a kind of combination algebra based on dimensional operation. Space can be defined as the operation between vector sets. The dimension of space is directly determined by the algorithm, which realizes the unification of high-dimensional geometric calculation and analysis. Based on the unified calculation and analysis framework of geometric algebra, GIS can better express and analyze high-dimensional objects, and then improve the ability of expressing complex geographical objects and dynamic geographical phenomena, analyzing spatiotemporal multi-scale objects and integration of different scale geographical models. This lays the theoretical foundation for the development of GIS towards holographic maps with real-time dynamics, virtual-real fusion, full perspective, full elements and full content expression.

     

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