An automatic sorting approach of surface bundle based on the shared space curve

The construction of the property right volume is an important prerequisite for data management and topology maintenance in 3D cadastre, and the automatic sorting approach of patches is important to construction of the smallest solid. When property right volumes as true 3D objects are constructed, not only ideal situations that closed patches are discrete planes, but also general conditions that property right boundaries are surfaces should be taken into account. So, firstly, conceptual descriptions of boundary surfaces and mathematical expressions of both the shared curve and the cutting plane are proposed based on theory of point-set topology. Secondly, obeying the principle of topological consistency, an automatic sorting approach and corresponding restrictions are put forward by detailed processes about local interpolation of the surface, calculation of the feature polyline, sorting of the cutting plane bundle. Particularly, this paper emphasizes on the method to obtain the feature polyline of the cutting plane taking triangulation interpolation of the surface in Google SketchUp for example. It is hoped that what is discussed in this paper could provide some references for constructing the smallest solid closed by discrete surface patches applied in urban space utilization cases such as 3D cadastre.