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.
Highlights
Due to an increasing demand for land use in urban areas, the future direction of urban development involves extending the current land use to higher spaces and the underground
Euclidean Geometry (EG)-based cadastral data models organize, store and represent geometry according to their topological relations, which are contained in 3D cadastral objects in a cadastral database
We introduce the theory of conformal geometric algebra (CGA) to 3D cadastral data modeling to solve problems with spatial representations that are encountered in the extension from a 2D cadastre to a 3D cadastre
Summary
Due to an increasing demand for land use in urban areas, the future direction of urban development involves extending the current land use to higher spaces and the underground. A 3D cadastral data model focuses on methods to organize, store and represent spatial representations for 3D cadastral objects in a cadastral database. Because land ownership boundaries and rights should be accurately defined in a cadastral registration, a large percentage of cadastral data models represent the structures of 3D spatial units by describing topological relations among composed elements [7,8,9]. The majority of existing data representation models of traditional 3D cadastres are topological-based [7]. EG-based cadastral data models organize, store and represent geometry according to their topological relations, which are contained in 3D cadastral objects in a cadastral database. How to store and represent spatial representations efficiently for 3D cadastral objects in a database remains a challenge in 3D cadastre development [15]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
