• 信息技术 •

多维统一GIS构建与实现的几何代数方法

1. 南京师范大学虚拟地理环境教育部重点实验室, 南京210023
• 收稿日期:2012-08-07 修回日期:2013-02-10 出版日期:2013-05-10 发布日期:2013-05-10
• 作者简介:袁林旺(1973- ),男,江苏海安人,博士,教授,博士生导师,主要研究方向为GIS理论与方法。E-mail:yuanlinwang@njnu.edu.cn
• 基金资助:

国家自然科学基金项目(4117130);国家科技支撑项目(2012BAH35B02);江苏省自然科学基金项目(BK2012454)

Geometric algebra-based construction and implementation methods for multidimension-unified GIS

YUAN Linwang, YU Zhaoyuan, LUO Wen, YI Lin, LÜ Guonian

1. Key Laboratory of VGE, Ministry of Education, Nanjing Normal University, Nanjing 210023, China
• Received:2012-08-07 Revised:2013-02-10 Online:2013-05-10 Published:2013-05-10

Abstract: High dimensional data analysis ability,computation complexity and extensibility have become the handicap of existing GIS.There still exist problems such as lack of unification in spatio-temporal expression and high dimensional extention in present spatio-temporal GIS.Geometric algebra(GA)theory,featuring multidimension unification and coordinate-free properties,is introduced to construct the multidimension-unified GIS.The GA method can connect different geometric and algebra systems,and provide rigorous and elegant foundation for expression,modeling and analysis in GIS.The layer structure of multidimension-unified GIS based on GA is proposed.With the help of the outer and inner product expressions,and the consistance of the geometric dimensions and the Grassmann dimensions in object expression in GA,adaptive expression methods that integrate the dimensional structure and geometric relations are defined.The GA operators are extended and constructed for multidimensional GIS analysis.And the computational model,which have intrinsic characteristic and clear structure,are constructed with these operators.And then,a multidimension-unified analysis framework that can support complex geo-computation is discussed.The implementation methods of multidimension-unified GIS based on GA, including key technologies such as multidimension-unified GIS data models,spatio-temporal indexes and analysis methods are also studied.Finally,the prototype system is implemented and demonstrated as case studies.This work shows that GA provides a new mathematical tool to the development of GIS characterized as multidimension unified expression and computation.It is equipped with possible development of multidimension-unified GIS based on GA and suggests a possible way to avoid leakage of existing spatio-temporal GIS.