复杂面实体拓扑关系的精细化模型
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摘要
简单空间对象经过特定组合可形成复杂空间实体。现有的拓扑关系模型对复杂边界间的复杂交互的表达能力不足,很难精确地对复杂空间面实体间拓扑关系的不同形式进行区分。顾及复杂空间面实体间的交互细节,本文对其拓扑关系进行精细化建模。首先引入线面实体间拓扑关系的元拓扑关系,进而利用元拓扑关系与重叠面积对简单面实体间的边界交集进行精细化描述,对洞边界遍历定义和洞中面与洞关系的定义,实现对复杂空间面实体的拓扑关系进行精确地区分与表达,最后对复杂面实体边界交集的5种基础拓扑关系描述模型进行归纳总结。通过5种基础拓扑关系描述模型的叠加,实现对复杂面实体各子部分之间关系细节的精细化表达。
For complex planar objects, which are composed of simple spatial objects, the existent models of topological relations may not be able to describe some topological attributes of complex objects well. Taking the topological content between complex objects into account, this paper presents a model of basic topological relations between line/planar objects, and then in which the basic topological relations and the concept of overlapping area are leveraged to describe the topological relations of simple planar objects. The definition of traversing of hole's boundary and planar with a hole are used to describe the topological relations between complex planar objects. Finally, the five basic topological relationship description modes of complex planar objects are summarized to realize description of the details of topological relations between partitions of complex planar objects.
For complex planar objects, which are composed of simple spatial objects, the existent models of topological relations may not be able to describe some topological attributes of complex objects well. Taking the topological content between complex objects into account, this paper presents a model of basic topological relations between line/planar objects, and then in which the basic topological relations and the concept of overlapping area are leveraged to describe the topological relations of simple planar objects. The definition of traversing of hole's boundary and planar with a hole are used to describe the topological relations between complex planar objects. Finally, the five basic topological relationship description modes of complex planar objects are summarized to realize description of the details of topological relations between partitions of complex planar objects.
引文
[1]陈占龙,冯齐奇,吴信才.复合面状对象拓扑关系的表达模型[J].测绘学报,2015,44(4):438-444,452.DOI:10.11947/j.AGCS.2015.20130708.CHEN Zhanlong,FENG Qiqi,WU Xincai.Representation model of topological relations between complex planar objects[J].Acta Geodaetica et Cartographica Sinica,2015,44(4):438-444,452.DOI:10.11947/j.AGCS.2015.20130708.
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[3]周晓光,陈斐,陈军.引入结点度的线/面拓扑关系细分方法与应用[J].测绘学报,2015,44(4):445-452.DOI:10.11947/j.AGCS.2015.20140138.ZHOU Xiaoguang,CHEN Fei,CHEN Jun.A node-degree based line/polygon topological relationship refinement model and its application[J].Acta Geodaetica et Cartographica Sinica,2015,44(4):445-452.DOI:10.11947/j.AGCS.2015.20140138.
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[12]邓敏,李志林,李光强.简单面目标与带孔洞面目标间拓扑关系的层次表达方法[J].测绘学报,2008,37(3):330-337.DOI:10.3321/j.issn:1001-1595.2008.03.011.DENG Min,LI Zhilin,LI Guangqiang.A hierarchical approach to topological relations between a simple area and an area with holes[J].Acta Geodaetica et Cartographica Sinica,2008,37(3):330-337.DOI:10.3321/j.issn:1001-1595.2008.03.011.
[13]唐雪华,秦昆,孟令奎.基于拓扑参考的定性方向关系矩阵描述模型[J].测绘学报,2014,43(4):396-403.DOI:10.13485/j.cnki.11-2089.2014.0059.TANG Xuehua,QIN kung,MENG Lingkui.A qualitative matrix model of direction-relation based on topological refer-ence[J]Acta Geodaetica et Cartographica Sinica,2014,43(4):396-403.DOI:10.13485/j.cnki.11-2089.2014.0059.
[14]吴华意,刘波,李大军,等.空间对象拓扑关系研究综述[J].武汉大学学报(信息科学版),2014,39(11):1269-1276.WU Huayi,LIU Bo,LI Dajun,et al.Topological relations of spatial objects:a review[J].Geomatics And Information Science of Wuhan University,2014,39(11):1269-1276.
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[16]吴长彬,闾国年.空间拓扑关系若干问题研究现状的评析[J].地球信息科学学报,2010,12(4):524-531.WU Changbin,LGuonian.Spatial topological relationships:an overview and analysis[J].Geo-Information Science,2010,12(4):524-531.
[17]郭庆胜,杜晓初,刘浩.空间拓扑关系定量描述与抽象方法研究[J].测绘学报,2005,34(2):123-128.DOI:10.3321/j.issn:1001-1595.2005.02.006.GUO Qingsheng,DU Xiaochu,LIU Hao.Research on quantitative representation and abstraction of spatial topological relation between two regions[J].Acta Geodaetica et Cartographica Sinica,2005,34(2):123-128.DOI:10.3321/j.issn:1001-1595.2005.02.006.
[18]郭庆胜,刘小利,陈宇箭.线与线之间的空间拓扑关系组合推理[J].武汉大学学报(信息科学版),2006,31(1):39-42.GUO Qingsheng,LIU Xiaoli,CHEN Yujian.Combinational reasoning of topological spatial relations between two lines[J].Geomatics and Information Science of Wuhan University,2006,31(1):39-42.
[19]吴长彬,闾国年.复杂线-线对象的拓扑关系描述与计算方法[J].地球信息科学学报,2014,16(6):839-845.WU Changbin,LGuonian.Representation and Calculation method of topological relationships for complex line objects[J].Journal of Geo-Information Science,2014,16(6):839-845.
[20]GALTON A.Modes of overlap[J].Journal of Visual Languages&Computing,1998,9(1):61-79.
[21]CLEMENTINI E,DI FELICE P.Topological invariants for lines[J].IEEE Transactions on Knowledge and Data Engineering,1998,10(1):38-54.
[22]EGENHOFER M J,FRANZOSA R D.On the equivalence of topological relations[J].International Journal of Geographical Information Systems,1995,9(2):133-152.
[23]AKTOUF Z,BERTRAND G,PERROTON L.A threedimensional holes closing algorithm[J].Pattern Recognition Letters,2002,23(5):523-531.
[24]EGENHOFER M J.A reference system for topological relations between compound spatial objects[C]∥Proceedings of the 28th International Conference on Conceptual Modeling.Gramado,Brazil:Springer,2009:307-316.
[25]EGENHOFER M J,VASARDANI M.Spatial reasoning with a hole[C]∥Proceedings of the 8th International Conference on Spatial Information Theory.Melbourne,Australia:Springer,2007:303-320.
[2]曹亚妮,吴芳华,王立军,等.基于元拓扑关系的线面空间关系集成表达模型[J].武汉大学学报(信息科学版),2016,41(1):123-130.CAO Yani,WU Fanghua,WANG Lijun,et al.The integrated representation model of line-region spatial relations based on meta-relations[J]Geomatics And Information Science of WuHan University,2016,41(1):123-130.
[3]周晓光,陈斐,陈军.引入结点度的线/面拓扑关系细分方法与应用[J].测绘学报,2015,44(4):445-452.DOI:10.11947/j.AGCS.2015.20140138.ZHOU Xiaoguang,CHEN Fei,CHEN Jun.A node-degree based line/polygon topological relationship refinement model and its application[J].Acta Geodaetica et Cartographica Sinica,2015,44(4):445-452.DOI:10.11947/j.AGCS.2015.20140138.
[4]FRANKLIN W R.Cartographic errors symptomatic of underlying algebra problems[C]∥Proceedings of the International Symposium on Spatial Data Handling.Zurich,Switzerland:[s.n.],1984:190-208.
[5]RANDELL D,CUI Z,COHN A.A spatial logic based on regions and connection[C]∥Proceedings of the 3rd International Conference on Knowledge Representation and Reasoning.Cambridge,MA:[s.n.],1992:165-176.
[6]EGENHOFER M J,CLEMENTINI E,DI FELICE P.Topological relations between regions with holes[J].International Journal of Geographical Information Systems,1994,8(2):128-142.
[7]EGENHOFER M J,VASARDANI M.Spatial reasoning with a hole[C]∥Proceedings of the 8th International Conference on Spatial Information Theory.Melbourne,Australia:Springer.2007:303-320.
[8]KODRATOFF Y,LEMERLE-LOISEL R.Learning complex structural descriptions from examples[J].Computer Vision,Graphics,and Image Processing,1984,27(3):266-290.
[9]EGENHOFER M J.Deriving the composition of binary topological relations[J].Journal of Visual Languages&Computing,1994,5(2):133-149.
[10]刘波,李大军,邹时,等.带孔洞面域间的拓扑关系的组合推理[J].测绘学报,2011,40(2):262-267.LIU Bo,LI Dajun,ZOU Shi,et al.Combinational reasoning of topological relations between regions with holes[J].Acta Geodaetica et Cartographica Sinica,2011,40(2):262-267.
[11]沈敬伟,周廷刚,朱晓波.面向带洞面状对象间的拓扑关系描述模型[J].测绘学报.2016,45(6):72-730.DOI:10.11947/j.AGCS.2016.20150352.SHEN Jingwei,ZHOU Tinggang,ZHU Xiaobo.Topological relation representation model between regions with holes[J].Acta Geodaetica et Cartographica Sinica,2016,45(6):722-730.DOI:10.11947/j.AGCS.2016.20150352.
[12]邓敏,李志林,李光强.简单面目标与带孔洞面目标间拓扑关系的层次表达方法[J].测绘学报,2008,37(3):330-337.DOI:10.3321/j.issn:1001-1595.2008.03.011.DENG Min,LI Zhilin,LI Guangqiang.A hierarchical approach to topological relations between a simple area and an area with holes[J].Acta Geodaetica et Cartographica Sinica,2008,37(3):330-337.DOI:10.3321/j.issn:1001-1595.2008.03.011.
[13]唐雪华,秦昆,孟令奎.基于拓扑参考的定性方向关系矩阵描述模型[J].测绘学报,2014,43(4):396-403.DOI:10.13485/j.cnki.11-2089.2014.0059.TANG Xuehua,QIN kung,MENG Lingkui.A qualitative matrix model of direction-relation based on topological refer-ence[J]Acta Geodaetica et Cartographica Sinica,2014,43(4):396-403.DOI:10.13485/j.cnki.11-2089.2014.0059.
[14]吴华意,刘波,李大军,等.空间对象拓扑关系研究综述[J].武汉大学学报(信息科学版),2014,39(11):1269-1276.WU Huayi,LIU Bo,LI Dajun,et al.Topological relations of spatial objects:a review[J].Geomatics And Information Science of Wuhan University,2014,39(11):1269-1276.
[15]RODRGUEZ M A,EGENHOFER M J,BLASER A D.Query pre-processing of topological constraints:comparing a composition-based with neighborhood-based approach[C]∥Proceedings of the 8th International Symposium on Advances in Spatial and Temporal Databases.Santorini Island,Greece:Springer,2003:362-379.
[16]吴长彬,闾国年.空间拓扑关系若干问题研究现状的评析[J].地球信息科学学报,2010,12(4):524-531.WU Changbin,LGuonian.Spatial topological relationships:an overview and analysis[J].Geo-Information Science,2010,12(4):524-531.
[17]郭庆胜,杜晓初,刘浩.空间拓扑关系定量描述与抽象方法研究[J].测绘学报,2005,34(2):123-128.DOI:10.3321/j.issn:1001-1595.2005.02.006.GUO Qingsheng,DU Xiaochu,LIU Hao.Research on quantitative representation and abstraction of spatial topological relation between two regions[J].Acta Geodaetica et Cartographica Sinica,2005,34(2):123-128.DOI:10.3321/j.issn:1001-1595.2005.02.006.
[18]郭庆胜,刘小利,陈宇箭.线与线之间的空间拓扑关系组合推理[J].武汉大学学报(信息科学版),2006,31(1):39-42.GUO Qingsheng,LIU Xiaoli,CHEN Yujian.Combinational reasoning of topological spatial relations between two lines[J].Geomatics and Information Science of Wuhan University,2006,31(1):39-42.
[19]吴长彬,闾国年.复杂线-线对象的拓扑关系描述与计算方法[J].地球信息科学学报,2014,16(6):839-845.WU Changbin,LGuonian.Representation and Calculation method of topological relationships for complex line objects[J].Journal of Geo-Information Science,2014,16(6):839-845.
[20]GALTON A.Modes of overlap[J].Journal of Visual Languages&Computing,1998,9(1):61-79.
[21]CLEMENTINI E,DI FELICE P.Topological invariants for lines[J].IEEE Transactions on Knowledge and Data Engineering,1998,10(1):38-54.
[22]EGENHOFER M J,FRANZOSA R D.On the equivalence of topological relations[J].International Journal of Geographical Information Systems,1995,9(2):133-152.
[23]AKTOUF Z,BERTRAND G,PERROTON L.A threedimensional holes closing algorithm[J].Pattern Recognition Letters,2002,23(5):523-531.
[24]EGENHOFER M J.A reference system for topological relations between compound spatial objects[C]∥Proceedings of the 28th International Conference on Conceptual Modeling.Gramado,Brazil:Springer,2009:307-316.
[25]EGENHOFER M J,VASARDANI M.Spatial reasoning with a hole[C]∥Proceedings of the 8th International Conference on Spatial Information Theory.Melbourne,Australia:Springer,2007:303-320.