Abstract: Spatial direction relation theory affects design, development and application of GIS, which is given a high recognition by International GIS and related academia, so it is important to research on the models. When the scale changes, uncertainty of special data is variable accordingly, which impacts description of spatial relations. This paper develops models to describe cardinal directions，considering uncertainty variety of spatial data because of scale change, and determine critical values between cardinal directions to remedy 9-intersection matrix. The model partitions the direction relations with smooth transition regions, which accords with percipience on direction concept description.

摘要： 空间方向关系理论直接影响着GIS系统的设计、开发和应用,因而受到国际GIS及相关学术界的高度重视,因此进行其模型的研究意义重大。当空间尺度发生变化时，空间数据的不确定性随之变化，从而影响到空间关系的准确描述。本文考虑了由尺度变化带来的空间数据不确定性变化，在投影模型中添加了扩展不确定度的参数，对多尺度下顾及不确定性的空间方向关系进行形式化描述，来适应多尺度性带来的空间数据不确定性变化，同时还能判定方向间的临界值，可以弥补9元交方向矩阵等模型的缺陷。该模型使得方向关系的划分上有个平滑的过渡区，在方向概念的表达上更符合人的认知。