Topological Relationship Identification in 3D Cadastre

With the accelerated urbanization process, the trend of three-dimensional land use makes the traditional model of 2D cadastral management encounter challenges, because of insufficiency to express in 3D. Therefore, the 3D cadastre and related concepts have been proposed. The breadth and depth of its research are gradually broadened and refined. Within all the studies, the core concept of the "cadastre" is not changed, the core purpose of which is to "guarantee the legitimate geo-space for the owner of property units", and to ensure that each property unit, whether it is two-dimensional or three-dimensional, is unique, non-overlapping. We can understand the “legitimacy” characteristics from two aspects: 1) The reliability for each property unit itself, that satisfies the definition of property unit, i.e., the property unit should be connected, closed and homogenous; 2) From the space view, a property unit is unique and occupies its space exclusively, and there is no overlap among them. Therefore, in cadastral management work, managers must preserve the inviolability of the legitimate geo-space. In a 2D cadastre system, the main solution to guarantee a unique geo-space for every property unit is topological checking. But in 3D status, the situation managers have to face more complexity than with 2D cases. This is a technology problem, which should be solved with help of computational geometry, topology rules, the Euler–Poincaré formula etc. Some people have done research in these areas such as Verbree and Si(2008), Kazar et al. (2008), Brugman et al. (2011), Thompson and Van Oosterom(2011), and Karki et al. (2011). In this paper, an approach based on a topology construction algorithm is introduced to check the validation of each property unit and among them. In other words, this paper mainly focuses on the topology checking among polyhedra in 3DGIS systems. Firstly, 34 topological relations among property units, which are classified as either correct relations or incorrect relations, are described in a 9-intersection model matrix. As to correct relations, they are sample relations to prove property units’ legitimacy. Conversely, incorrect relations explain their illegality. Secondly, it is elaboratedhow to identify these topological relations, which is the focus of the paper. At the end, an introduction is given regarding the 3D cadastre system in Shenzhen, China