The Four Intersection-and-Difference Model for Line-Line Topological Relations

The description of line-line topological relations is still an unsolved issue although much effort has been done. The problem is involved in many practical applications such as spatial query, spatial analysis and cartographic generalization. To develop a sound and effective approach to describe line-line relations, it is first necessary to define the topology of an individual line, i.e., local topology. The concept of connective degree is used for the identification of topological differences in the geometric structure of a line. The general topological definition of a line is given, i.e., endpoints set and interior point set. This definition can be applied to the embedded spaces of different dimensions, whether co-dimension is equal to or larger than zero. On this basis, a generic model called the 4 intersection-and-difference is set up for the description of basic line-line topological relations, upon which a conceptual neighborhood graph is built with consideration of topological distance, it is concluded that the proposed model can represent the property of topological changes, and basic relations between line segments in IR^1 and IR^2.

对线线的描述拓扑的关系尽管许多努力被做了，仍然是一个未解决的问题。这个问题涉及象空间质问，空间分析和制图综合那样的许多实际应用。开发一条健全、有效的途径描述线线关系，它是第一必要排队定义一个个人的拓扑学，即，本地拓扑学。连接的度的概念在一根线的几何结构被用于拓扑的差别的鉴定。一根线的一般拓扑的定义被给，即，端点集合和内部点设定。这个定义能被用于不同尺寸的嵌入的空格，合作尺寸是否等于或比零大。在这个基础上，打电话给 4 intersection-and-difference 的一个通用模型为对基本线线的描述被建立拓扑的关系，一张概念的邻居图与拓扑的距离的考虑在之上被造。建议模型能在 /R^1 和 /R^2 代表在线片断之间的拓扑的变化，和基本关系的性质，这被结束。