3D Cadastral Data Model Based on Conformal Geometry Algebra

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

Development of 3D real estate cadastre data model

Катастар непокретности у Србији се заснива на 2Д катастарским плановима и процедурама које не подржавају недвосмислену регистрацију и приказивање комплексних 3Д ситуација и сложених објеката. Ове потешкоће су посебно изражене у урбаним срединама. Циљ ове докторске дисертације је да истражи на који начин се могу превазићи потешкоће катастра непокретности у Србији када је реч о регистрацији комплексних 3Д ситуација...The real estate cadastre in the Republic of Serbia is based on 2D cadastral maps and procedures that do not support unequivocal registration and visualization of complex 3D property situations and complex objects, especially in urban areas. Тhe aim of this doctoral dissertation is to research how the difficulties of 3D complex situations registration in Serbia can be overcome..