The representation and judgment of binary topological relations between regions and lines in three dimensional space

Representing and reasoning about the topological relationships has attracted many discussions in the GIS field, several formalized descriptive model was proposed. As GIS is developing towards 3D (three dimensional), one of the most difficult problems is spatial analysis, especially the topology analysis. This article aims to provide a simple solution to the issue of judging the topological relation between a line and a connected region without holes in 3D space based on the DE-9IM (Dimensionally Extended 9-Intersection Model). We will discuss how to use the DE-9IM to describe the binary topological relations between regions and lines in 3D. A set of possible existing topological relations between a line and a region in three-dimensional space will be given out, and the algorithm of judging the topological relations mentioned above will be explored in detail.