中文摘要：

三维空间下不确定性对象拓扑关系是研究三维GIS中不确定性问题的基础。该文将二维平面直线不确定性的思想引入到三维空间，基于二维平面ε-带自旋转构建三维拓展包络体，表达不确定性三维线对象的置信区域。在对不确定性三维线对象进行描述的基础上，对不确定性线-线对象各部分之间的交集程度提出了一种定量化分析方法；通过对交集程度的度量，将三维空间下不确定性线-线拓扑关系用这些度量组成的空间向量表达；结合9I模型确定的参考空间关系向量理论，逐一考察度量化空间关系向量与参考空间关系向量之间的相关度，提出三维空间下不确定性线-线对象之间拓扑关系的描述模型，通过定量化分析方法对其空间拓扑关系进行判别。实验结果表明，该方法具备一定的可行性，可为不确定性问题的探讨提供科学依据。

英文摘要：

Topological relations between uncertain objects in 3D space are the fundamental research of 3D GIS indeterminacy problem. In this paper, the thinking of plane linear uncertainty is introduced into the 3D space. Firstly, inspired by e-band in 2D plane, the extended envelope of ε-band is constructed through the rotation of the 2D buffer area of linear objects in a specific way, and the extended envelope of ε-band is mainly used to express the confidence region of uncertain linear objects in 3D space. Then, based on the description of uncertain linear objects in 3D space, an analysis method is proposed to calculate intersection degrees for all parts of uncertain linear objects, including the interior, exterior and boundary, and the intersection degrees can be quantitatively expressed by some mathematical formulas. By measuring each intersection degree, the topological relations between uncertain linear objects in 3D space are presented by space vectors which are composed of these measures. And combining the theory of specific reference spatial relation vector based on 9-intersection model, the correlation degrees between the metric spatial relation vectors and the reference spatial relation vectors are calculated one by one and a description model is presented for topological relations between uncertain linear objects in 3D space. Finally, to identify the spatial topological relation between linear objects, the experiment is clone by using the quantitative analysis method. The results show the method is practicability to some extent and can provide a scientific basis to the exploration on some uncertain problems.