Topological relations between directed lines and simple geometries  

作　　者：GAO Yong1,ZHANG Yi1,TIAN Yuan1 & WENG JingNong2 1 Institute of Remote Sensing and Geographic Information System,Peking University,Beijing 100871,China 2 Colledge of Software,Beihang University,Beijing 100083,China 

出　　处：《Science China(Technological Sciences)》2008年第S1期91-101,共11页中国科学（技术科学英文版）

基　　金：the National Natural Science Foundation of China (Grant Nos. 40701134 and 40771171);the National Hi-Tech Research and Development Program of China (Grant No. 2007AA12Z216)

摘　　要：Directed lines are fundamental geometric elements to represent directed linear en-tities. The representations of their topological relations are so different from those of simple lines that they cannot be solved exactly with normal methods. In this paper,a new model based on point-set topology is defined to represent the topo-logical relations between directed lines and simple geometries. Through the inter-sections between the start-points,end-points,and interiors of the directed lines and the interiors,boundaries,and exteriors of the simple geometries,this model identifies 5 cases of topological relations between directed lines and points,39 cases of simple lines,and 26 cases of simple polygons. Another 4 cases of simple lines and one case of simple polygons are distinguished if considering the exteri-ors of the directed lines. All possible cases are furthermore grouped into an exclu-sive and complete set containing 11 named predicts. And the conceptual neigh-borhood graph is set up to illustrate their relationship and similarity. This model can provide a basis for natural language description and spatial query language to present the dynamic semantics of directed lines relative to the background fea-tures.Directed lines are fundamental geometric elements to represent directed linear en-tities. The representations of their topological relations are so different from those of simple lines that they cannot be solved exactly with normal methods. In this paper,a new model based on point-set topology is defined to represent the topo-logical relations between directed lines and simple geometries. Through the inter-sections between the start-points,end-points,and interiors of the directed lines and the interiors,boundaries,and exteriors of the simple geometries,this model identifies 5 cases of topological relations between directed lines and points,39 cases of simple lines,and 26 cases of simple polygons. Another 4 cases of simple lines and one case of simple polygons are distinguished if considering the exteri-ors of the directed lines. All possible cases are furthermore grouped into an exclu-sive and complete set containing 11 named predicts. And the conceptual neigh-borhood graph is set up to illustrate their relationship and similarity. This model can provide a basis for natural language description and spatial query language to present the dynamic semantics of directed lines relative to the background fea-tures.

关 键 词：TOPOLOGICAL RELATION directed line SIMPLE geometry INTERSECTION model 

分 类 号：P208[天文地球—地图制图学与地理信息工程]