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 corresp...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.展开更多
New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the buil...New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the building blocks of the principal value distribution, involvingspherical harmonics, considered by Horvath and Stein.展开更多
基金supported by National High Technology R & D Program of China (Grant No. 2009AA12Z205)Key Project of National Natural Science Foundation of China (Grant No. 40730527)National Natural Science Foundation of China (Grant No. 41001224)
文摘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.
文摘New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the building blocks of the principal value distribution, involvingspherical harmonics, considered by Horvath and Stein.
