基于凸凹理论的三维地质体空间关系模型研究
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摘要
目前的三维地质体空间关系模型表达能力较弱,限制了其在空间分析、查询等方面的应用。三维模型的应用与发展迫切需要一种新的底层分解与理论建模解决此类问题。该文基于凸凹理论重新对地质体进行结构定义与空间关系建模,提出了内凸体、外凸体、内缘体、外缘体等构造,并在此基础上建立了三维地质体R7×7空间关系模型,将地质体间空间关系表达能力理论上扩充至249种,实际能够表达40余种空间关系;给出了包容、镶嵌、部分镶嵌等关系的定义并对其进行了模型表达;针对不同应用,给出了R7×7模型的变换模型R(5×5 3×3)等。为能够表达地质体交集的边界长度、交面面积、地质体体积、外缘体体积、镶嵌体积等地质空间重要关系,基于凸凹理论建立了地质体度量关系模型,是矿区地质体拓扑关系查询、空间分析推理等应用的基础模型。给出了模型与地质体模糊理论的相契性分析,二者模型能够相辅相成,相互借鉴使用。
Because of the weak expressive ability of spatial relational models,the application of 3 Dgeological bodies in spatial analysis and query is restricted.The application and development of 3 Dmodels urgently need a new underlying decomposition and theoretical modeling to solve such problems.Based on convex concave theory,the structural definition and spatial relationship model of geological bodies is reestablished.In this paper,the structures of inner convex body,outer convex body,inner edge,body edge are put forward,and a three-dimensional geological body spatial relationship model R7×7 is established based on convex body theory.The model extends the spatial relationship expression ability between geological bodies to 249 kinds in theory.R7×7 can express more than 40 kinds of spatial relations in application.This paper gives the definition of the relationship between inclusion,mosaic,partial mosaic and so on.For different applications,the transformation model of the R7×7,such as R(5×5,3×3),is given.The transformation model ignores external relations and is suitable for fast modeling and expression of geological bodies.In order to express the important relation of geological space,such as boundary length,surface area,volume of geological body,volume of outer edge body and mosaic volume,the relationship model of geological body measurement is built on the basis of convex and concave theory.The model in this paper is a basic model for the application of topological relations,geological analysis,reasoning and so on.Finally,the corresponding analysis of the model and the geological body fuzzy theory is given.The model proposed in this paper can be applied to the fuzzy geological body better.
Because of the weak expressive ability of spatial relational models,the application of 3 Dgeological bodies in spatial analysis and query is restricted.The application and development of 3 Dmodels urgently need a new underlying decomposition and theoretical modeling to solve such problems.Based on convex concave theory,the structural definition and spatial relationship model of geological bodies is reestablished.In this paper,the structures of inner convex body,outer convex body,inner edge,body edge are put forward,and a three-dimensional geological body spatial relationship model R7×7 is established based on convex body theory.The model extends the spatial relationship expression ability between geological bodies to 249 kinds in theory.R7×7 can express more than 40 kinds of spatial relations in application.This paper gives the definition of the relationship between inclusion,mosaic,partial mosaic and so on.For different applications,the transformation model of the R7×7,such as R(5×5,3×3),is given.The transformation model ignores external relations and is suitable for fast modeling and expression of geological bodies.In order to express the important relation of geological space,such as boundary length,surface area,volume of geological body,volume of outer edge body and mosaic volume,the relationship model of geological body measurement is built on the basis of convex and concave theory.The model in this paper is a basic model for the application of topological relations,geological analysis,reasoning and so on.Finally,the corresponding analysis of the model and the geological body fuzzy theory is given.The model proposed in this paper can be applied to the fuzzy geological body better.
引文
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[16]翁正平.复杂地质体三维模型快速构建及更新技术研究[D].武汉:中国地质大学,2013.26-30.
[17]刘瑜,龚咏喜,张晶,等.地理空间中的空间关系表达和推理[J].地理与地理信息科学,2007,23(5):1-3.
[18]邓小龙,李丽慧,陈宇箭,等.基于三维激光扫描技术的复杂三维地质体建模方法[J].工程地质学报,2017,25(1):209-212.
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[20]邓敏.空间分析[M].长沙:测绘出版社,2015.25-29.
[21]贺涛,孙在宏,吴长彬,等.基于等宽ε-带的三维线-线对象不确定性拓扑关系描述与判别方法[J].地理与地理信息科学,2017,33(1):23-26.
[22] ZONG Z,YUAN L W.Triangulation intersection algorithm based on conformal geometric algebra[J].Acta Geodaetica et Cartographica Sinica,2014,43(2):200-207.
[2]郭薇,陈军.基于点集拓扑学的三维拓扑空间关系形式化描述[J].测绘学报,1997,26(2):122-125.
[3] GOODCHILD M.Geomatics and Geographic Information Science[M].Wuhan:Wuhan Technical University of Surveying and Mapping Press,1998.304-311.
[4]闫浩文,郭仁忠.基于Voronoi图的空间方向关系形式化描述模型[J].武汉大学学报(信息科学版),2003,28(4):468-471.
[5]陈军.Voronoi空间数据模型[M].北京:测绘出版社,2002.55
[6]邓敏,李成名,刘晓丽.论GIS空间关系描述中存在的几个基本问题[J].中国工程科学,2013,15(5):20-24.
[7]卢浩,王少华,钟耳顺,等.一种面向大规模空间数据的拓扑关系检查算法[J].地理与地理信息科学,2014,30(5):17-20.
[8]刘新,刘文宝,李成名.三维体目标间拓扑关系与方向关系的混合推理[J].武汉大学学报(信息科学版),2010,35(1):74-78.
[9]李成名,郭沛沛,殷勇,等.一种顾及空间关系约束的线化简算法[J].测绘学报,2017,46(4):498-501.
[10] DENG M,LIU W B,FENG X Z.Generic model of topological relations between spatial regions in GIS[J].Acta Geodaetica et Cartographica Sinica,2005,34(1):85-90.
[11]侯晓琳,杨博.基于pillargrid三维地质体表面模型提取算法[J].计算机工程与应用,2017,53(11):1-4.
[12]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.
[13] HAN H,YANG C.Evolution of Jobs-housing spatial relationship in Beijing metropolitan area:A job accessibility perspective[J].Chinese Geographical Science,2015,25(3):375-388.
[14]王芳.空间方向关系推理及多种空间关系结合推理的研究[D].吉林:吉林大学,2012.70-71.
[15]杜世宏.空间关系模糊描述及组合推理的理论和方法研究[D].北京:中国科学院研究生院,2004.23-25.
[16]翁正平.复杂地质体三维模型快速构建及更新技术研究[D].武汉:中国地质大学,2013.26-30.
[17]刘瑜,龚咏喜,张晶,等.地理空间中的空间关系表达和推理[J].地理与地理信息科学,2007,23(5):1-3.
[18]邓小龙,李丽慧,陈宇箭,等.基于三维激光扫描技术的复杂三维地质体建模方法[J].工程地质学报,2017,25(1):209-212.
[19]马林兵,曹小曙.空间关系的动态性和模糊性描述[J].地理与地理信息科学,2006,22(6):1-3.
[20]邓敏.空间分析[M].长沙:测绘出版社,2015.25-29.
[21]贺涛,孙在宏,吴长彬,等.基于等宽ε-带的三维线-线对象不确定性拓扑关系描述与判别方法[J].地理与地理信息科学,2017,33(1):23-26.
[22] ZONG Z,YUAN L W.Triangulation intersection algorithm based on conformal geometric algebra[J].Acta Geodaetica et Cartographica Sinica,2014,43(2):200-207.