Geometric algebra method for multidimensionally-unified GIS computation  

作　　者：YUAN LinWang LüGuoNian LUO Wen YU ZhaoYuan YI Lin SHENG YeHua 

机构地区：[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

出　　处：《Chinese Science Bulletin》2012年第7期802-811,共10页

基　　金：supported by the National Natural Science Foundation of China (41171300, 40730527 and 40801149);the National High Technology R & D Porogram of China (2009AA12Z205)

摘　　要：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 GAbased 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.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 geo- graphical scenes. The development of the proposed GIS multidimensionally-unified representation, analysis, and modeling en- hances current GIS algorithms and geographical models.

关 键 词：地理信息系统 计算几何 多维 代数方法 遗传算法 计算模型 几何拓扑 复杂场景 

分 类 号：O18[理学—数学] P208[理学—基础数学]