球面四元三角网的基本拓扑关系描述和计算

Describing and Computing Model of the Topological Relation in Spherical Surface Quaternary Triangular Mesh

球面四元三角网具有多分辨率和层次组织的特性,已成为目前研究球面问题的有效方法之一。本文在此基础上,利用引入集合多算子和对称差的欧拉数,给出描述和计算球面栅格拓扑关系的四元组模型。该模型利用两空间目标间的交(∩)、差(\)、被差(/)和对称差(Δ)的内容是否为空来初步区分相离/相接、交叉、相等、包含/覆盖、被包含/被覆盖这五对拓扑关系。然后通过引入对称差的欧拉数来进一步区分传统模型难以区分的相离/相接、包含/覆盖和被包含/被覆盖这三对拓扑关系。

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.