A New Method for 3D Cadastral Parcel Merging Based on Conformal Geometry Algebra
Jiyi Zhang, Pengcheng Yin et al.
With the development of urbanization, conflicts between the demand for land due to urban expansion and the limitation of land resources contribute to the appearance of complex buildings below and above land surface. Traditional two dimension (2D) cadastre has encountered great challenge in registering overlapping and interlocking constructions in the urban area. There is no doubt that developing three dimension (3D) cadastre could resolve the problems in registering and managing objects with complex structures more efficiently. Much research has been carried out on the development of 3D cadaster in recent years, which is conducive to the implementation of 3D cadastral management. However, since Euclidean geometry lacks consistency in unified representation form for cadastral objects with different dimensions, traditional cadastral data models based on Euclidean geometry represent dimensional cadastral objects in a rather different way. Due to the dimensional isolation characteristics of Euclidean geometry, representation and management of 3D cadastral objects are more complex than 2D cadastral objects, thus hindering implementation of 3D cadastral objects management and updating. In order to represent cadastral objects with different dimensions in a unified multidimensional manner, Conformal Geometry Algebra (CGA) is introduced in this paper. As the hierarchical Grassmann structure corresponding to the hierarchical structure of dimensions in CGA, cadastral objects in different dimensions can be expressed in a unified form with outer product. Different dimensional objects can be organized and stored by the multivector structure in a multidimensional unified way in CGA.
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