Splitting Ratios: Metric Details of Topological Line-Line Relations
Splitting Ratios: Metric Details of Topological Line-Line Relations
复制标题
分裂比：拓扑线-线关系的度量细节
DOI：
10.3210/fst.26.9
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
M. Egenhofer
中科院分区：
文献类型：
--
作者：
K. A. Nedas;M. Egenhofer
在地理领域内，一类重要的问题依赖于线形式的几何抽象，例如，交通网络和运动轨迹通常在这样的广义几何水平上被感知或建模。为了支持查询和计算比较，通常需要多分辨率模型来引导用户从较粗糙到较精细的细节。在这样的设置中，拓扑属性是粗略的空间信息，而度量细化提供更精细的细节。9相交区分了两条线之间的33种拓扑关系。本文开发了一个模型，通过分割比，这是标准化的长度和面积的交叉点的值，捕捉度量细节的线-线的关系。这些比率适用于9-交集的非空值，从而提供拓扑属性的细化。三个这样的分裂比率全面细化33个拓扑关系中的30个：一个用于公共路径的长度，一个用于通过交叉点划分线，另一个用于由具有两个或更多公共组件的两条线包围的区域。对于其余三种关系--不相交、相交和相等--不可能基于公共部分进行进一步的度量细化。分裂比被集成到一个紧凑的表示详细的拓扑关系，从而解决任意复杂的线-线关系的拓扑和度量特性。
Within the geographic domain, an important class of problems relies on geometric abstractions in the form of lines where, for instance, transportation networks and trajectories of movements are typically perceived or modeled at such a generalized geometric level. To support querying and computational comparisons, oftentimes multi-resolution models are needed to guide users from coarser to finer details. Within such a setting topological properties are coarse spatial information, whereas metric refinements offer finer details. The 9-intersection distinguishes 33 topological relations between two lines. This paper develops a model that captures metric details for line-line relations through splitting ratios, which are normalized values of lengths and areas of intersections. These ratios apply to the 9-intersection’s nonempty values, thereby providing refinements of topological properties. Three such splitting ratios comprehensively refine 30 of the 33 topological relations: one for the lengths of common paths, one for the partitioning of lines through intersections, and another one for the areas enclosed by two lines with two or more common components. For the remaining three relations—disjoint, meet, and equal—no further metric refinements based on common parts are possible. The splitting ratios are integrated into a compact representation of detailed topological relations, thereby addressing topological and metric properties of arbitrarily complex line-line relations.