TOPOLOGICAL RELATIONSHIPS IN R³ FOR 3D CADASTRE

Abstract. 3D cadastre is necessary for accurately representing real-world parcels that not only exist on land but also above and below ground. The ability to cater to the physical and legal attributes of these 3D parcels is important as it affects the Rights, Restrictions and Responsibilities (RRRs). Tasks such as modification and analysis of 3D parcels also require topological information in addition to the geometrical properties of a 3D parcel. Topological properties describe the connectivity information between objects. In terms of the 3D cadastre, the intrinsic topology is used to ensure the spatial objects that make up a 3D solid are valid, while extrinsic topology is used to determine adjacent 3D solids or overlapping parcels. This paper attempted to define topological relationships in 3D space specifically for the use of 3D cadastre. 3D to 3D solid and 2D to 2D surface topological interactions were defined and proved using the Dimensionally Extended Nine Intersection Model (DE-9IM). The “meet (touches)” and “overlaps” topological relationships were found to be the main topological relationship used in the 3D cadastre.