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ISPRS Int. J. Geo-Inf. 2016, 5(2), 20; doi:10.3390/ijgi5020020

3D Cadastral Data Model Based on Conformal Geometry Algebra

1
School of Environmental Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221008, China
2
Bureau of Land and Resources of Xuzhou, Xuzhou 221006, China
*
Author to whom correspondence should be addressed.
Academic Editors: François Anton and Wolfgang Kainz
Received: 3 October 2015 / Revised: 15 January 2016 / Accepted: 5 February 2016 / Published: 19 February 2016
(This article belongs to the Special Issue Multi-Dimensional Spatial Data Modeling)
View Full-Text   |   Download PDF [6809 KB, uploaded 19 February 2016]   |  

Abstract

Three-dimensional (3D) cadastral data models that are based on Euclidean geometry (EG) are incapable of providing a unified representation of geometry and topological relations for 3D spatial units in a cadastral database. This lack of unification causes problems such as complex expression structure and inefficiency in the updating of 3D cadastral objects. The inability of current cadastral data models to express cadastral objects in a unified manner can be attributed to the different expressions of dimensional objects. Because the hierarchical Grassmann structure corresponds to the hierarchical structure of dimensions in conformal geometric algebra (CGA), geometric objects in different dimensions can be constructed by outer products in a unified expression form, which enables the direct extension of two-dimensional (2D) spatial representations to 3D spatial representations. The multivector structure in CGA can be employed to organize and store different dimensional objects in a multidimensional and unified manner. With the advantages of CGA in multidimensional expressions, a new 3D cadastral data model that is based on CGA is proposed in this paper. The geometries and topological relations of 3D spatial units can be represented in a unified form within the multivector structure. Detailed methods for 3D cadastral data model design based on CGA and data organization in CGA are introduced. The new cadastral data model is tested and analyzed with experimental data. The results indicate that the geometry and topological relations of 3D cadastral objects can be represented in a multidimensional manner with an intuitive topological structure and a unified dimensional expression. View Full-Text
Keywords: data model; CGA; 3D cadastre; outer production; topological relation data model; CGA; 3D cadastre; outer production; topological relation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Zhang, J.-Y.; Yin, P.-C.; Li, G.; Gu, H.-H.; Zhao, H.; Fu, J.-C. 3D Cadastral Data Model Based on Conformal Geometry Algebra. ISPRS Int. J. Geo-Inf. 2016, 5, 20.

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