四面体格网模型的三维拓扑关系计算
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摘要
四面体格网(TEN)模型是一种重要的空间数据构模方法,侧重于三维空间对象内部的表达,但是存在着数据量大、计算速度慢的问题。三维拓扑关系是三维GIS的重要研究内容,为此,该文提出了面向TEN的三维拓扑关系计算方法。基于点集拓扑学理论,将TEN分解为内部、边界和外部3个集合,并使用9交模型描述了TEN/TEN的8种拓扑关系;设计了面向TEN的三维拓扑关系计算流程,详细阐述了面向TEN的三维拓扑关系计算的核心算法;基于提出的三维拓扑关系算法,设计了面向TEN的拓扑关系计算实验。实验结果表明:该文提出的面向TEN的三维拓扑关系计算方法,能够满足TEN之间拓扑关系计算的需求。
As an important spatial data model,tetrahedron network(TEN)model has advantage in representation of the interior of 3Dobjects and disadvantage in large volume of data and slow computation speed.Because 3Dtopological relationship calculation was the focus of 3DGIS,a topological relationship calculation algorithm for TEN model was proposed in this paper.TEN was divided into three sets including interior set,boundary set and exterior set based on point set theory.Eight topological relationships were expressed based on 9IM(nine intersection model).Flow chart of 3Dtopological relationship calculation method for TEN model was given and the core algorithms were described in detail.A prototype system was developed and topological relationship calculation results were showed.From the topological relationship calculation results,we can conclude that the proposed algorithm can calculate topological relationship between TEN.
As an important spatial data model,tetrahedron network(TEN)model has advantage in representation of the interior of 3Dobjects and disadvantage in large volume of data and slow computation speed.Because 3Dtopological relationship calculation was the focus of 3DGIS,a topological relationship calculation algorithm for TEN model was proposed in this paper.TEN was divided into three sets including interior set,boundary set and exterior set based on point set theory.Eight topological relationships were expressed based on 9IM(nine intersection model).Flow chart of 3Dtopological relationship calculation method for TEN model was given and the core algorithms were described in detail.A prototype system was developed and topological relationship calculation results were showed.From the topological relationship calculation results,we can conclude that the proposed algorithm can calculate topological relationship between TEN.
引文
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[15]曹雪峰.复杂体目标之间三维拓扑关系描述模型[J].地理与地理信息科学,2013,29(1):12-16.(CAO Xuefeng.A point neighborhood model descirption of three dimensional topological relationships between complex volume objects[J].Geography and Geo-Information Science,2013,29(1):12-16.)
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[17]杜世宏,秦其明,王桥.空间关系及其应用[J].地学前缘,2006,13(3):69-80.(DU Shihong,QIN Qiming,WANG Qiao.The spatial relations in GIS and their applications[J].Earth Science Frontiers,2006,13(3):69-80.)
[18]THEOBALD D M.Topology revisited:representing spatial relations[J].International Journal of Geographical Information Science,2001,15(8):689-705.
[19]邓敏,刘文宝,黄杏元,等.空间目标的拓扑关系及其GIS应用分析[J].中国图象图形学报,2006,12(11):1743-1749.(DENG Min,LIU Wenbao,HUANG Xingyuan,et al.Modeling topological relations of spatial objects and its applications in GIS[J].Journal of Image and Graphics,2006,12(11):1743-1749.)
[20]史文中,吴立新,李清泉,等.三维空间信息系统模型与算法[M].北京:电子工业出版社,2007.(SHI Wenzhong,WU Lixin,LI Qingquan,et al.Models and algorithums for three dimensional spatial information system[M].Beijing:Publishing House of Electronics Industry,2007.)
[2]MOLENAAR M.A formal data structure for 3Dvector maps[C]//Proceedings of EGIS′90.[S.l.]:[s.n.],1990:770-781.
[3]LOSA A,CERVELLE B.3Dtopological modeling and visualization for 3D GIS[J].Computers&Graphics,1999,23(4):469-478.
[4]PILOUK M,TEMPFLI K,MOLENAAR M.A tetrahedron-based 3Dvector data model for geo-Information[C]//AGDM′94 Spatial Data Modelling and Query Languages for 2Dand 3D Applications.Delft:Netherlands Geodetic Commission,1994:129-140.
[5]WU L.Topological relations embodied in a generalized tri-prism(GTP)model for a 3D geoscience modeling system[J].Computers&Geosciences,2004,30(4):405-418.
[6]EGENHOFER M,Franzosa R D.Point-set topological spatial relations[J].International Journal of Geographical Information Systems,1991,5(2):161-174.
[7]EGENHOFER M,HERRING J.Categorizing binary topological relations between regions,lines,and points in geographic databases[R].[S.l.]:NCGIA Technical Report,1994:1-28.
[8]CLEMENTINI E,DI FELICE P.A model for representing topological relationships between complex geometric features in spatial databases[J].Information Sciences,1996,90(1):121-136.
[9]CHEN J,LI C,LI Z,et al.A Voronoi-based 9-intersection model for spatial relations[J].International Journal of Geographical Information Science,2001,15(3):201-220.
[10]邓敏,张雪松,林宗坚.拓扑关系形式化描述的Euler示性数模型[J].武汉大学学报(信息科学版),2004,29(10):872-876.(DENG Min,ZHANG Xuesong,LIN Zongjian.Modeling topological relations based on euler characteristics[J].Geomatics and Information Science of Wuhan University,2004,29(10):872-876.)
[11]郭甲腾,吴立新.栅格空间中三维地学实体拓扑关系表达的K6N9-I模型[J].地理与地理信息科学,2008,24(1):6-9.(GUO Jiateng,WU Lixin.K6N9-I model:a topological relation representation model for three dimensional geo-entities in raster space[J].Geography and Geo-Information Science,2008,24(1):6-9.)
[12]BEN H,BOOCHS F,CRUZ C,et al.From quantitative spatial operator to qualitative spatial relation using constructive solid geometry,logic rules and optimized9-IM model:a semantic based approach[C]//Computer Science and Automation Engineering(CSAE).Washington DC,USA:IEEE,2012:453-458.
[13]ZHANG J,QIN X.Topological analysis between bodies with holes[J].International Journal of Computer Science and Network Security,2008,8(5):167-174.
[14]沈敬伟,温永宁,闾国年,等.体/体拓扑关系计算研究[J].测绘科学,2012,37(4):120-122.(SHEN Jingwei,WEN Yongning,LV Guonian,et al.Calculation of topological relationships between bodies[J].Science of Surveying and Mapping,2012,37(4):120-122.)
[15]曹雪峰.复杂体目标之间三维拓扑关系描述模型[J].地理与地理信息科学,2013,29(1):12-16.(CAO Xuefeng.A point neighborhood model descirption of three dimensional topological relationships between complex volume objects[J].Geography and Geo-Information Science,2013,29(1):12-16.)
[16]狄爽.三维带洞体拓扑关系表达[D].济南:山东师范大学,2015.(DI Shuang.The expression of topological relations between 3d objects with holes[D].Jinan:Shandong Normal University,2015.)
[17]杜世宏,秦其明,王桥.空间关系及其应用[J].地学前缘,2006,13(3):69-80.(DU Shihong,QIN Qiming,WANG Qiao.The spatial relations in GIS and their applications[J].Earth Science Frontiers,2006,13(3):69-80.)
[18]THEOBALD D M.Topology revisited:representing spatial relations[J].International Journal of Geographical Information Science,2001,15(8):689-705.
[19]邓敏,刘文宝,黄杏元,等.空间目标的拓扑关系及其GIS应用分析[J].中国图象图形学报,2006,12(11):1743-1749.(DENG Min,LIU Wenbao,HUANG Xingyuan,et al.Modeling topological relations of spatial objects and its applications in GIS[J].Journal of Image and Graphics,2006,12(11):1743-1749.)
[20]史文中,吴立新,李清泉,等.三维空间信息系统模型与算法[M].北京:电子工业出版社,2007.(SHI Wenzhong,WU Lixin,LI Qingquan,et al.Models and algorithums for three dimensional spatial information system[M].Beijing:Publishing House of Electronics Industry,2007.)
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