Deriving Topological Relationships Between Simple Regions with Holes

Topological relationships between objects in space are of great importance in many disciplines. Due to the lack of local topological information between components, i.e. faces, in the model of topological relationships between complex regions, recently, localized topological relationships have been defined for complex regions based on the relationships between simple regions with holes. However, unlike for simple regions, topological relationships between simple region with holes are not widely implemented. Therefore, in this paper, we propose an approach to derive topological relationships between simple regions with holes based on well known topological relationships between the simple regions as their components. This will allow localized topological predicates between complex regions to be implemented using only topological relationships between simple regions. Furthermore, localized topological predicates between complex regions can be used to implement topological relationships between complex regions. Therefore, this work allows topological relationships between complex regions to be implemented using only topological relationships between simple regions.