A Conceptual Framework for Modelling Spatial Relations

Various approaches lie behind the modelling of spatial relations, which is a heterogeneous and interdisciplinary field. In this paper, we introduce a conceptual framework to describe the characteristics of various models and how they relate each other. A first categorization is made among three representation levels: geometric, computational, and user. At the geometric level, spatial objects can be seen as point-sets and relations can be formally defined at the mathematical level. At the computational level, objects are represented as data types and relations are computed via spatial operators. At the user level, objects and relations belong to a context-dependent user ontology. Another way of providing a categorization is following the underlying geometric space that describes the relations: we distinguish among topologic, projective, and metric relations. Then, we consider the cardinality of spatial relations, which is defined as the number of objects that participate in the relation. Another issue is the granularity at which the relation is described, ranging from general descriptions to very detailed ones. We also consider the dimension of the various geometric objects and the embedding space as a fundamental way of categorizing relations

Extension of RCC*-9 to Complex and Three-Dimensional Features and Its Reasoning System

RCC*-9 is a mereotopological qualitative spatial calculus for simple lines and regions. RCC*-9 can be easily expressed in other existing models for topological relations and thus can be viewed as a candidate for being a “bridge” model among various approaches. In this paper, we present a revised and extended version of RCC*-9, which can handle non-simple geometric features, such as multipolygons, multipolylines, and multipoints, and 3D features, such as polyhedrons and lower-dimensional features embedded in ℝ3. We also run experiments to compute RCC*-9 relations among very large random datasets of spatial features to demonstrate the JEPD properties of the calculus and also to compute the composition tables for spatial reasoning with the calculus

Functionality and performance: two important considerations when implementing topology in 3D.

This thesis contributes to the understanding of the use of topology in analysing 3D spatial data, focussing in particular on two aspects of the problem - what binary topological analysis functionality is required in a commercial 3D Geographical Information System (GIS), and how should this functionality be implemented to achieve the most efficient query performance. Topology is defined as the identification of spatial relationships between adjacent or neighbouring objects. The first stage of this research, a review of applications of topology, results in a generic list of requirements for topology in 3D. This was carried out in parallel with a review of topological frameworks and the relationships identified by one of the frameworks, Egenhofer and Herring's 9-Intersection, selected for implementation. Three generic binary relationship queries are identified (Find Objects with a Specific Relationship, Find Intersecting Objects and What Relationship is there Between These Objects) and a mechanism described to allow these to be adapted to specific application terminology. Approaches to the implementation of 3D binary topological queries include the use of data structures and an As-Required calculation, where computational geometry algorithms are run to determine relationships each time the user runs a query. The Three-Dimensional Formal Data Structure (3DFDS) was selected as a representative example of a Boundary-Representation (B- Rep) structure in GIS. Given the number of joins to be traversed when identifying binary relationships from a B-Rep structure, along with the requirement to query additional containment exception tables, an alternate structure, the Simplified Topological Structure (STS), was proposed to improve binary query performance. Binary relationship queries were developed and comparative performance tests carried out against 3DFDS, STS and a Proxy for the As-Required calculation, using a 1.08 million object test dataset. Results show that STS provides a significant performance improvement over 3DFDS. No definitive conclusion could be drawn when comparing STS with the Proxy for the As-Required approach