Topological information are the most important kind of qualitative spatial information. Current formalisms for the topological aspect of space focus on relations between regions or properties of regions. This work provides a qualitative model for representing the topological internal structure of complex regions, which could be of multiple pieces and or have holes and islands to any finite level. We propose a layered graph model for representing the internal structure of complex plane regions, where each node represents the closure of a connected component of the interior or the exterior of a complex region. The model provides a complete representation in the sense that the (global) nine-intersections between the interiors, the boundaries, and the exteriors of two complex regions can be determined by the (local) RCC8 topological relations between the associated simple regions. Moreover, this graph model has an inherent hierarchy which could be exploited for map generalization.
The Worboys-Bofakos tree model is perhaps the most related one to ours. Suppose @math is a bounded region that has a finite representation. In @cite_13 , each region @math is represented as a tree, where the root node represents, in our terms, the generalized region of @math , and each non-root node represents a simple region. If @math is a child node of @math , then @math is contained in @math . All child nodes of @math form a composite region (called a in @cite_13 ), which may separate @math into pieces.
@cite_13
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This study aims to model an appropriate set of 2-dimensional spatial objects (i.e. areas) embedded in R2 with the usual metric and topology. The set of objects to be modelled is an extension of the set of 2-dimensional objects which can be represented within the vector-based data model. The model aims to capture explicitly some important topological properties of the spatial objects, e.g. connectedness and region inclusion. The construction discussed in this paper is capable of representing a large class of areal objects, including objects with holes which have islands (to any finite level). It has the virtue of being canonical, in the sense that any appropriate areal object has a unique representation in this model. The paper describes the model by specifying the areal objects under consideration and providing their representation. It also defines a set of operations and discusses algorithms for their implementation.