Topological relationships calculation for 3D curves data set based on monotone chains

Topological relations are research focus in 3D GIS. Constructing nodes and arcs from curves, building the topological relations of these primitives with their parent geometry and other geometries, and forming the topological graph, are the basis of the calculation of topological relationship. The formal description and smallest set of topological relationships of 3D curves are given. The line segments intersection algorithm computational geometry and the traditional line segments intersection algorithm in GIS are discussed, and a new algorithm based on the monotone chains are proposed to building the topological graph. The method of curves splitting and intersection algorithm of curves are analyzed. Topological graph is constructed based on the label of the topological primitives. Then, a comparison between the monotone chains method and the tradition algorithm is listed. Some experiments are carried out to testify the algorithm performance.