Transaction rules for updating surfaces in 3D GIS

Three-dimensional surface models representing the terrain and the outer hull of objects such as buildings and bridges support important 3D GIS applications, for example telecommunication planning and noise emission simulation. Updates of surface models often introduce errors which violate basic assumptions of users and their applications. The notion of geometric-topological consistency covers many of these assumptions. It guarantees that objects do not penetrate mutually or that objects completely cover other objects. Assuring that updates do not violate geometric-topological consistency constitutes a major challenge for 3D GIS which has not been satisfactorily met so far. This article presents a solution which is based on efficient transaction rules for updating 3D surface models. We show that these rules are safe (consistency is preserved by any rule application) and complete (any consistent surface model can be generated by successive rule applications). For both properties rigorous mathematic proofs are given.