Geometric algebra method for multidimensionally-unified GIS computation |
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| Authors: | LinWang Yuan GuoNian Lü Wen Luo ZhaoYuan Yu Lin Yi YeHua Sheng |
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| Institution: | 1 Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing 210046, China; 2 Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex System, Nanjing Normal University, Nanjing 210046, China |
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| Abstract: | 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. |
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| Keywords: | geometric algebra GIS multidimensionally-unified representation multidimensionally-unified computation |
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