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

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.