Geometric algebra method for multidimensionally-unified GIS computation

Seamless multidimensional handling and coordinate-free characteristics of geometric algebra (GA) provide means to construct multidimensionally-unified GIS computation models. Using the multivector representation for basic geometric objects within GA, we are able to construct adaptable unified geometric-topological structural models of a multidimensional geographical scene. Multidimensional operators found within the geometry, topology and GIS analysis are developed with basic GA operators. A unified computational framework is proposed, it unifies expressions and operation structures, as well as supports the analysis of multidimensional complex scenes. Finally, we illustrate modelling a three-dimensional residential district, which shows that GA-based multidimensionally-unified computation models can effectively represent and analyze complex and multidimensional geographical scenes. The development of the proposed GIS multidimensionally-unified representation, analysis, and modeling enhances current GIS algorithms and geographical models.