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.

Landscape pattern change (LPC) can provide comprehensive insight into the effects of mining activities on regional ecosystems. This paper examined the impact of coal mining on LPC of Peixian mining area, China. An analysis of LPC was conducted based on GIS-RS technology from 1994 to 2014. The influence of coal mining on the LPC was studied quantitatively from the perspective of life cycle. The following conclusions were drawn: 1) The LPC of the study area changed significantly during the study period. Landscape type index showed a rising trend in fluctuation, and landscape fractal characteristics tended to be simplified and regularized. 2) Landscape indices of cultivated land and waterlogged subsidence zones were highly correlated with annual coal production, and the correlation coefficients were -0.634, -0.748 and 0.991, respectively. 3) The abrupt changes of largest patch index (LPI) and aggregation index (AI) of cultivated land occurred in 1999 and 2001, respectively. The LPI of waterlogged subsidence zones had a sustained upward trend since 1995, but the AI had a significant rising trend in 1997-2006 and 2011-2013. These results could provide useful guidance on sustainable land use planning and restoring the damaged landscape for underground coal mining areas.

The application of a 3-D topology to cadasters is becoming increasingly important as 3-D cadasters continue to develop and cadastral data applications increase. This study discusses spatial topological relations related to 3-D cadasters, the geometric objects used in 3-D cadastral spatial modelling, and the characteristics of the spatial data. The characteristics of the topological relations for a 3-D cadaster are summarized, and a classification method is proposed. Research on the classification of topological spatial relations in 3-D cadasters provides guidance for the analysis and computation of the topological spatial relations, changing of cadastral parcels, and topological consistency in cadastral spatial data.