Topology of surfaces modelling bridges and tunnels in 3D-GIS

Bridges and tunnels are semantically meaningful objects in Geographical Information Systems (GIS), playing an important role in terms of reachability between locations. From a topological point of view, bridges and tunnels on surfaces are captured by the notion of a handle. In this paper, we extend an existing axiomatic characterization of 3D surfaces, which guarantees consistency between geometry and topology, to the case of handles. Furthermore, we present a method which verifies the occurrence of handles in surfaces, thereby contributing to the semantic-topological consistency in GIS. We close the gap between the global topological definition of handles in surfaces and the local definition of semantical handle objects in GIS – tunnels, bridges, arcades. Our method bases on a classification of cycles in two types. We give an efficient algorithm for discriminating both using standard methods from graph theory. This classification in addition contributes to the correctness of editing operations in GIS.

Research highlights
► Extend an existing axiomatic characterization of surfaces embedded in 3D space without handles to handles, enabling the modeling of bridges and tunnels.
► Topological specification of handle objects contributing to semantical-topological consistency (conditions to distinguish handle objects from non-handle objects topologically).
► Provide an efficient method to differentiate between Jordan and handle cycles.
► Specify conditions which avoid that editing operations on surfaces fail due to handles.