Describing and computing model of the topological relation in spherical surface quaternary triangular mesh

Spherical surface QTM (Quaternary Triangular Mesh) is one of an efficient tool to deal with the global data because of its advantages of multi-resolution and hierarchy. Based on characters of spherical surface QTM, set muti-operators and Euler-number of symmetric difference were presented to describing and computing model of the topological relation in spherical surface QTM. In this model, the topological invariant (empty or not empty) of the result of the intersection, difference, difference by and symmetric difference between two spatial objects are used to partially distinguish their five traditional topological relation, and then the Euler number of the result of symmetric difference between two spatial objects is introduced to confirm the other three topological relations of disconnected/disjoin, contain/overlap, and contained by/overlaped by which the traditional methods can t distinguish.