面向带洞面状对象间的拓扑关系描述模型

Topological Relation Representation Model between Regions with Holes

为研究带洞面状对象间的拓扑关系,提出了一种25IM(25交集模型)。以点集拓扑理论为基础,对带洞面状区域的内部、边界和外部进行定义。分析了9IM(9交集模型)在表达带洞面状对象间拓扑关系方面存在的问题,将带洞面状对象分为内部、外边界、内边界、外边界外部、内边界外部共5部分,提出了一种5×5的矩阵模型,即25IM。基于点集拓扑理论,定义了8条规则来排除不符合逻辑的拓扑关系。基于25IM,对8种基本拓扑关系:相离、相接、重叠、覆盖、包含、相等、被覆盖和被包含,进行细分描述。结果表明,本文提出的25IM能够更为详细地表达带洞面状对象间的拓扑关系。

In order to study the topological relation between regions with holes, a topological relation representation model named 251M（25 intersection model） is proposed. Based on point set theory, interior, boundary and exterior of spatial object are defined. The shortcoming of 91M（9 intersection model） between regions with holes is analyzed. A region with holes can be separated into five parts including interior, outer boundary, inner boundary, exterior outside the outer boundary, and exterior within the inner boundary. Then, 5X5 matrix model named 251M between two regions with holes are defined. Eight rules are defined to exclude the illogical topological relations. Eight basic topological relations, including disjoint, meet, overlaps, covers, contains, equal, coveredby and Inside, are described in detail by using 251M. It can be concluded that the proposed 251M can express the topological relation between regions with holes in more detail.