多粒度时空对象空间关系的统一表达与计算
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摘要
空间关系表达了空间数据的相互约束,在空间查询语言、数据检索及空间分析中具有重要作用。当前关于空间关系的研究,多基于简单地理对象,或者只对某一种空间关系进行独立的算法设计,难以满足多粒度对象多种空间关系的统一表达与计算。为此,本文利用几何代数运算的对象无关性和维度无关性,构建简单对象空间关系计算算子,并将其推广到多粒度对象,实现全空间地理信息系统框架下多粒度对象三种空间关系的一体化表达与计算。最后,以三角网求交算法为例,证明了算法的可行性,为全空间GIS中空间关系的表达和计算提供了借鉴。
Spatial relationships play an important role in spatial query language, data retrieval and spatial analysis. However, the current research of spatial relations are hard to realize the unified expression and calculation of spatio-temporal objects of multi-granularity. In this paper, the spatial relationships computing operators of the simple objects are designed based on the type-independence and dimension-independence characteristics of GA operators. The operators are then generalized to spatio-temporal objects of multigranularity by the union operator. Lastly, we realized the unified expression and calculation of three kinds of spatial relationships for the spatio-temporal objects of multi-granularity under the framework of pan-spatial GIS.The triangulation intersection algorithm is raised as an example to prove the reliability of our methods. Our research also provides the reference for expression and calculation of spatial relationships in pan-spatial GIS.
Spatial relationships play an important role in spatial query language, data retrieval and spatial analysis. However, the current research of spatial relations are hard to realize the unified expression and calculation of spatio-temporal objects of multi-granularity. In this paper, the spatial relationships computing operators of the simple objects are designed based on the type-independence and dimension-independence characteristics of GA operators. The operators are then generalized to spatio-temporal objects of multigranularity by the union operator. Lastly, we realized the unified expression and calculation of three kinds of spatial relationships for the spatio-temporal objects of multi-granularity under the framework of pan-spatial GIS.The triangulation intersection algorithm is raised as an example to prove the reliability of our methods. Our research also provides the reference for expression and calculation of spatial relationships in pan-spatial GIS.
引文
[1]廖楚江,杜清运.GIS空间关系描述模型研究综述[J].测绘科学,2004,29(4):79-82.[Liao C J.Review on models of the description of GIS spatial relationship[J].Science of Surveying and Mapping,2004,29(4):79-82.]
[2]Egenhofer M J,Herring J R.Categorizing binary topological relationships between regions,lines and points in geographic data bases[A].In:A Framework for the Definition of Topological Relationships and An Approach to Spatial Reasoning within this Framework[C].Santa Barbara,CA,199l:1-28.
[3]Clementini E,Di F P,Oostemm P V.A small set of formal topologica I relationships suitable for end-user interaction.In:D.Abel and B.C.Ooi(eds).Advances in Spatial Databases[C].New York:Springer-Verlag,1993:277-295.
[4]陈军,赵仁亮.GIS空间关系的基本问题与研究进展[J].测绘学报,1999,28(2):95-102.[Chen J,Zhao R L.Spatial relations in GIS:A survey on its key issues and research progress[J].Acta Geodaetica et Cartographica Sinica,1999,28(2):95-102.]
[5]廖士中,石纯一.拓扑关系的闭球模型及复合表的推导[J].软件学报,1997(12):894-900.[Liao S Z,Shi C Y.Closed ball model and composition table derivation for topological relations[J].Journal of Software,1997,12:894-900.]
[6]邓敏,李志林,陈晓勇.GIS空间目标的广义Hausdorff距离模型[C]//中国测绘学会第八次全国会员代表大会暨2005年综合性学术年会论文集,2005:641-645.[Deng M,Li Z L,Chen X Y.A generalized Hausdorff distance model for spatial objects in GIS[C].Geomatics and Information Science of Wuhan University,2005:641-645.]
[7]李阳东,韩震,童小华.一种顾及多粒度的时空数据模型[C]//2009国际信息技术与应用论坛论文集(下),2009.[Spatio-temporal data model of multi-granularity[C].2009 International Forum on Information Technology and Applications,2009.]
[8]华一新.全空间信息系统的核心问题和关键技术[J].测绘科学技术学报,2016,33(4):331-335.[Hua Y X,The core problems and key technologies of pan-spatial information system[J].Journal of Geomatics Science and Technology,2016,33(4):331-335.]
[9]周成虎.全空间地理信息系统展望[J].地理科学进展,2015,34(2):129-131.[Zhou C H,Prospects on pan-spatial information system[J].Progress in Geography,2015,34(2):129-131.]
[10]Yu Z,Luo W,Yuan L,et al.Geometric algebra model for geometry-oriented topological relation computation[J].Transactions in GIS,2015,20(2):259-279.
[11]Yuan L,Yu Z,Luo W,et al.Multidimensional-unified topological relations computation:A hierarchical geometric algebra-based approach[J].International Journal of Geographical Information Science,2014,28(12):2435-2455.
[12]景黎.空间区域拓扑、度量关系结合方法的研究[D].长春:吉林大学,2007.[Jing L.Research on the combination method of topological relations and metric relations of spatial regions[D].Changchun:Jilin University,2007.]
[13]袁林旺,俞肇元,罗文,等.多维统一GIS构建与实现的几何代数方法[J].地理研究,2013,32(5):974-983.[Yuan L W,Yu Z Y,Luo W,et al.Geometric-algebra based construction and implementation methods for multi-dimension-unified GIS[J].Geographical Rsearch,2013,32(5):974-983.]
[14]Yuan L W,Yu Z Y,Luo W,et al.A 3D GIS spatial data model based on conformal geometric algebra[J].Science China Earth Sciences,2011,54(1):101-112.
[15]宗真.基于几何代数的空间关系表达与计算模型研究[D].南京:南京师范大学,2013.[Zong Z.Study on the expression and calculation models of spatial relation based on geometry and algebra[D].Nanjing:Nanjing Normal University,2013.]
[16]罗文.基于几何代数的GIS计算模型研究[J].测绘学报,2014,43(9):990-990.[Luo W.The Study on GIS computational model based on geometric algebra[J].Acta Geodaetica et Cartographica Sinaca,2014,43(9):990-990.]
[17]Eduardoe R.Operaciones de Cómputo Gráfico en el Espacio Geométrico Conforme 5D usando GPU[D].Venezuela:Universidad Simón Bolívar,2011.
[18]宗真,袁林旺,罗文,等.三角网求交的共形几何代数算法[J].测绘学报,2014,43(2):200-207.[Zong Z,Yuan L W,Luo W,et al.Triangulation intersection algorithm based on conformal geometric algebra[J].Acta Geodaetica et Cartographica Sunica,2014,43(2):200-207.]
[19]王建超.基于CGA的多维统一曲面求交算法及其应用研究[D].南京:南京师范大学,2012.[Wang J C.Multi-dimensional unified surface intersection algorithm and its application research based on the CGA[D].Nanjing:Nanjing Normal University,2012.]
[2]Egenhofer M J,Herring J R.Categorizing binary topological relationships between regions,lines and points in geographic data bases[A].In:A Framework for the Definition of Topological Relationships and An Approach to Spatial Reasoning within this Framework[C].Santa Barbara,CA,199l:1-28.
[3]Clementini E,Di F P,Oostemm P V.A small set of formal topologica I relationships suitable for end-user interaction.In:D.Abel and B.C.Ooi(eds).Advances in Spatial Databases[C].New York:Springer-Verlag,1993:277-295.
[4]陈军,赵仁亮.GIS空间关系的基本问题与研究进展[J].测绘学报,1999,28(2):95-102.[Chen J,Zhao R L.Spatial relations in GIS:A survey on its key issues and research progress[J].Acta Geodaetica et Cartographica Sinica,1999,28(2):95-102.]
[5]廖士中,石纯一.拓扑关系的闭球模型及复合表的推导[J].软件学报,1997(12):894-900.[Liao S Z,Shi C Y.Closed ball model and composition table derivation for topological relations[J].Journal of Software,1997,12:894-900.]
[6]邓敏,李志林,陈晓勇.GIS空间目标的广义Hausdorff距离模型[C]//中国测绘学会第八次全国会员代表大会暨2005年综合性学术年会论文集,2005:641-645.[Deng M,Li Z L,Chen X Y.A generalized Hausdorff distance model for spatial objects in GIS[C].Geomatics and Information Science of Wuhan University,2005:641-645.]
[7]李阳东,韩震,童小华.一种顾及多粒度的时空数据模型[C]//2009国际信息技术与应用论坛论文集(下),2009.[Spatio-temporal data model of multi-granularity[C].2009 International Forum on Information Technology and Applications,2009.]
[8]华一新.全空间信息系统的核心问题和关键技术[J].测绘科学技术学报,2016,33(4):331-335.[Hua Y X,The core problems and key technologies of pan-spatial information system[J].Journal of Geomatics Science and Technology,2016,33(4):331-335.]
[9]周成虎.全空间地理信息系统展望[J].地理科学进展,2015,34(2):129-131.[Zhou C H,Prospects on pan-spatial information system[J].Progress in Geography,2015,34(2):129-131.]
[10]Yu Z,Luo W,Yuan L,et al.Geometric algebra model for geometry-oriented topological relation computation[J].Transactions in GIS,2015,20(2):259-279.
[11]Yuan L,Yu Z,Luo W,et al.Multidimensional-unified topological relations computation:A hierarchical geometric algebra-based approach[J].International Journal of Geographical Information Science,2014,28(12):2435-2455.
[12]景黎.空间区域拓扑、度量关系结合方法的研究[D].长春:吉林大学,2007.[Jing L.Research on the combination method of topological relations and metric relations of spatial regions[D].Changchun:Jilin University,2007.]
[13]袁林旺,俞肇元,罗文,等.多维统一GIS构建与实现的几何代数方法[J].地理研究,2013,32(5):974-983.[Yuan L W,Yu Z Y,Luo W,et al.Geometric-algebra based construction and implementation methods for multi-dimension-unified GIS[J].Geographical Rsearch,2013,32(5):974-983.]
[14]Yuan L W,Yu Z Y,Luo W,et al.A 3D GIS spatial data model based on conformal geometric algebra[J].Science China Earth Sciences,2011,54(1):101-112.
[15]宗真.基于几何代数的空间关系表达与计算模型研究[D].南京:南京师范大学,2013.[Zong Z.Study on the expression and calculation models of spatial relation based on geometry and algebra[D].Nanjing:Nanjing Normal University,2013.]
[16]罗文.基于几何代数的GIS计算模型研究[J].测绘学报,2014,43(9):990-990.[Luo W.The Study on GIS computational model based on geometric algebra[J].Acta Geodaetica et Cartographica Sinaca,2014,43(9):990-990.]
[17]Eduardoe R.Operaciones de Cómputo Gráfico en el Espacio Geométrico Conforme 5D usando GPU[D].Venezuela:Universidad Simón Bolívar,2011.
[18]宗真,袁林旺,罗文,等.三角网求交的共形几何代数算法[J].测绘学报,2014,43(2):200-207.[Zong Z,Yuan L W,Luo W,et al.Triangulation intersection algorithm based on conformal geometric algebra[J].Acta Geodaetica et Cartographica Sunica,2014,43(2):200-207.]
[19]王建超.基于CGA的多维统一曲面求交算法及其应用研究[D].南京:南京师范大学,2012.[Wang J C.Multi-dimensional unified surface intersection algorithm and its application research based on the CGA[D].Nanjing:Nanjing Normal University,2012.]