YUAN LW et al: A 3D GIS spatial data model based on conformal geometric algebra


by YUAN LinWang, YU ZhaoYuan, LUO Wen, ZHOU LiangChen & LÜ GuoNian
Key Laboratory of VGE, Ministry of Education, Nanjing Normal University, Nanjing 210046, China
Published in: Sci China Earth Sci, 2011, 54: 101–112, doi: 10.1007/s11430-010-4130-9
Received: August 18, 2010; accepted November 2, 2010

Abstract
We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are constructed and expressed by the inner and outer operators. This expression combined geometrics of different dimensions and metric relations. We present the structure of the framework, data structure design, and the data storage, editing and updating mechanisms of the proposed 3D GIS data model. 3D GIS geometric and topological analyses are performed by CGA metric, geometric and topological operators using an object-oriented approach. Demonstrations with 3D residence district data suggest that our 3D data model expresses effectively geometric objects in different dimensions, which supports computation of both geometric and topological relations. The clear and effective expression and computation structure has the potential to support complex 3D GIS analysis, and spatio-temporal analysis.

Keywords
conformal geometric algebra, 3D data model, 3D measurement, 3D spatial relation

Source: Email by co-author Yu Zhaoyuan (yuzhaoyuan_at_163.com), 16 Dec. 2010, 15:21

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