Classification of topological relations between spatial objects in two‐dimensional space within the dimensionally extended 9‐intersection model

As an important topological relation model, the dimensionally extended 9‐intersection model (DE‐9IM) has been widely used as a basis for standards of queries in spatial databases. However, the negative conditions for the specification of the topological relations within the DE‐9IM have not been studied. The specification of the topological relations is closely related to the definition of the spatial objects and the topological relation models. The interior, boundary, and exterior of the spatial objects, including the point, line, and region, are defined. Within the framework of the DE‐9IM, 43 negative conditions are proposed to eliminate impossible topological relations. Configurations of region/region, region/line, line/line, region/point, line/point, and point/point relations are drawn. The mutual exclusion of the negative conditions is discussed, and the topological relations within the framework of 9IM and DE‐9IM are compared. The results show that: (1) impossible topological relations between spatial objects can be eliminated by the application of 43 negative conditions; and (2) 12 relations between two regions, 31 relations between a region and a line, 47 relations between two lines, three relations between a region and a point, three relations between a line and a point, and two relations between two points can be distinguished by the DE‐9IM.     

不确定线-面拓扑关系的描述与判别

不确定线状目标和面状目标之间拓扑关系的描述是空间信息处理过程中经常面对的问题。在对不确定线状目标和面状目标进行描述的基础上,对不确定线状目标与面状目标各组成部分之间的相交程度进行了定量表达,通过计算这些度量组成的空间向量与9-交集模型确定的空间关系向量之间的相关度,提出了一种不确定线状目标和面状目标之间拓扑关系的描述模型,通过定量的方法来对其空间拓扑关系进行判别。     

Topological relations between a directed line and a directed region

Representing the topological relations between directed spatial objects has gained increasing attention in recent years. Although topological relations between directed lines and other types of spatial objects, such as regions and bodies, have been widely investigated, few studies have focused on the topological relations between directed lines and directed regions. This research focuses on the representation and application of directed line–directed region (DLDR) topological relations, and may contribute to spatial querying and spatial analyses related to directed spatial objects or time‐varying objects. Compared with other topological relation models, a DLDR model that considers the starting and ending points of the directed line and the front and back faces of directed regions is proposed in this research to describe the topological relations between directed lines and directed regions. DLDR topological relations are presented, the completeness of the 111 DLDR topological relations is proved, and the topological relations based on the 9‐intersection model (9IM), 9⁺‐intersection model (9⁺‐IM), and DLDR model are compared. The formalism of the DLDR model and the corresponding geometric interpretations of the 111 DLDR topological relations are presented, seven propositions are stated to prove the completeness of the 111 DLDR topological relations, and the case study shows that more detailed topological relation information can be obtained based on the DLDR model.     

Fuzzy topological relations between fuzzy spatial objects

Fuzziness is an internal property of spatial objects.How to model fuzziness of a spatial object is a main task of next generation GIS.This paper proposes basic fuzzy spatial object types based on fuzzy topology.These object types are the natural extension of current nonfuzzy spatial object types.A fuzzy cell complex structure is defined for modeling fuzzy regions,lines and points.Furthermore,fuzzy topological relations between these fuzzy spatial objects are formalized based on the 9intersection approach.This model can be implemented for GIS applications due to its scientific theory basis.     

基于拓扑约束的方向关系定性描述模型

针对原有方向关系矩阵模型对于参考目标MBR区域的方向描述缺陷问题,本文将拓扑约束引入方向关系定性描述,构建基于拓扑参考的方向关系定性描述模型,实现了MBR区域方向关系的有效表达。新模型首先将参考目标的MBR区域划分为不同的拓扑区域,提出方向关系拓扑参考定义;基于拓扑参考,分别对不同拓扑区域定义相应的方向关系矩阵;最后,根据参考目标与源目标间的不同拓扑关系,提出不同情况下方向关系分层定性描述策略。实验结果表明,新模型充分反映了拓扑关系对方向关系描述的约束关系,能有效提高方向关系表达的准确性和精确性。     

模糊空间对象拓扑关系的Rough描述

利用Rough Set理论,在四交差模型的基础上,提出适合于描述确定和模糊区域或两个模糊区域目标间拓扑空间关系的扩展模型(4-4ID模型),并且详细讨论模糊对象之间的拓扑关系。     

基于9-Intersection模型的模糊空间对象间的拓扑关系研究

本文将从地理认知的角度上分析并选择一个适合于在GIS中应用9-Intersection模型的模糊空间对象的边界定义,并构建一个能够采用9-Intersection模型精确判断模糊空间对象之间拓扑关系的模糊拓扑空间(CITfts),并进行相应的证明,最后建立简单模糊区域,采用empty/no-empty算子给出模糊空间对象之间的拓扑关系的表达形式。     

引入结点度的线/面拓扑关系细分方法与应用

针对线/面细分拓扑关系研究存在的不足,提出了一种基于结点度的线/面细分拓扑关系描述与计算方法。该方法在定义线/面单元交线并分析其特点的基础上,引入结点度来区分线/面单元交线细分类型。根据单元交线端点在线/面目标组成图形结构中结点度的不同,及线目标在度为3和4的交线端点处是否有相连线段、相连线段位于多边形的边界上、内部或外部4个谓词推导出了21种有意义的线/面交线细分拓扑关系类型。在此基础上分析比较了本文方法与现有方法的异同与优势,举例说明本文方法在复杂线/面细分拓扑关系描述中的应用。最后用Visual C#语言编程实现了该方法,并将其应用到线状道路/面状河流目标间的数据质量检查与修正中,验证可行性。     

基于线段的基本线/线拓扑关系计算

空间拓扑关系是空间数据建模、空间查询、分析、推理、制图综合、数据质量控制、数据更新等的基础。目前空间拓扑关系研究的主要成果仍然集中在拓扑关系的描述方面,在计算方面的阐述都非常薄弱,不足以指导系统开发人员编程实现。本文研究了IR2中两个简单线目标间拓扑关系的计算方法,重点分析了线/线拓扑关系计算的特点,提出了一种基于线段的线/线拓扑关系计算方法,并用VC＋＋采用底层开发模式实现了基本线/线拓扑关系的计算。     

线与面目标间拓扑关系的层次表达方法

拓扑关系已广泛应用于空间查询、相似性分析、制图综合、不一致性探测以及空间推理等实际应用中。本文研究IR2中一条线与一个简单面目标拓扑关系的描述和区分方法,采用的基本策略是分解与组合方法。首先,将线/面拓扑关系分为两类:基本关系和复合关系。其中复合关系描述为若干个基本关系的组合,即基本关系的一个集合。然后,提出了基本拓扑关系分类和区分方法,建立了相应的层次概念邻域图。针对复合拓扑关系,从空间集合的角度提出了具有三个层次的拓扑不变量,分别是(a)集合层次上的分离数和维数,(b)元素层次上的交分量类型和(c)综合层次上的交分量序列。分析发现,在IR2中一条线与一个简单面目标间具有16种潜在的基本关系。其中,它们的13种是描述复合线/面关系的基本构成单元。     

Dealing with spatial relations for spatial objects with randomness in GIS

To design retrieval algorithm of spatial relations for spatial objects with randomness in GIS, this paper builds up the membership functions based on set theory idea, used for determination of topological spatial relations between random objects, such as between point and point, point and line or polygon, which provides theoretical basis for retrieving spatial relations between certain and random objects. Finally, this paper interprets detailed methods and steps of realizing them by means of some simple examples under the GIS's environment.     

DEALING WITH SPATIAL RELATIONS FOR SPATIAL OBJECTS WITH RANDOMNESS IN GIS

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面向带洞面状对象间的拓扑关系描述模型

为研究带洞面状对象间的拓扑关系,提出了一种25IM(25交集模型)。以点集拓扑理论为基础,对带洞面状区域的内部、边界和外部进行定义。分析了9IM(9交集模型)在表达带洞面状对象间拓扑关系方面存在的问题,将带洞面状对象分为内部、外边界、内边界、外边界外部、内边界外部共5部分,提出了一种5×5的矩阵模型,即25IM。基于点集拓扑理论,定义了8条规则来排除不符合逻辑的拓扑关系。基于25IM,对8种基本拓扑关系:相离、相接、重叠、覆盖、包含、相等、被覆盖和被包含,进行细分描述。结果表明,本文提出的25IM能够更为详细地表达带洞面状对象间的拓扑关系。     

Improving 9-intersection model by replacing the complement with voronoi region

1 Overview of the original 9-inter-section modelThe spatial re1ations betWeen spatial entities areknown as important as the entities themselves. It istherefore very essential to know what poSSibIe spa-tial relationships are and how they can be deter-mined. The 9-intersection model is the most POpu-lar mathematical framework fOr formalizing spatialrelations and have been widely used in spatial querylanguages(EngenhOfer, l991; Clementinietal., l994;Mark et al., l995). Using this medel the t…     

复杂面实体拓扑关系的精细化模型

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。     

球面四元三角网的基本拓扑关系描述和计算

球面四元三角网具有多分辨率和层次组织的特性,已成为目前研究球面问题的有效方法之一。本文在此基础上,利用引入集合多算子和对称差的欧拉数,给出描述和计算球面栅格拓扑关系的四元组模型。该模型利用两空间目标间的交(∩)、差(\)、被差(/)和对称差(Δ)的内容是否为空来初步区分相离/相接、交叉、相等、包含/覆盖、被包含/被覆盖这五对拓扑关系。然后通过引入对称差的欧拉数来进一步区分传统模型难以区分的相离/相接、包含/覆盖和被包含/被覆盖这三对拓扑关系。     

Consistency among parts and aggregates: A computational model

Heterogeneous geographic databases contain multiple views of the same geographic objects at different levels of spatial resolution. When users perceive geographic objects as one spatial unit, although they are physically separated into multiple parts, appropriate methods are needed to assess the consistency among the aggregate and the parts. The critical aspect is that the overall spatial relationships with respect to other geographic objects must be preserved throughout the aggregation process. We developed a systematic model for the constraints that must hold with respect to other spatial objects when two parts of an object are aggregated. We found three sets of configurations that require increasingly more information in order to make a precise statement about their consistency: (1) configurations that are satisfied by the topological relations between the two parts and the object of interest; (2) configurations that need further information about the topological relation between the object of concern and the connector in order to be resolved unambiguously; and (3) configurations that require additional information about the topological relation between the aggregate's boundary and the boundary or interior of the object of interest to be uniquely described. The formalism extends immediately to relations between two regions with disconnected parts as well as to relations between a region and an arbitrary number of separations.     

复合面状对象拓扑关系的表达模型

为表达复合面状对象间的细节拓扑关系,对经典9-交集模型进行了改进,给出两种基于分解思想的9-交集模型,其中分解成简单区域的9-交集模型方法相对简单,但表现形式繁琐;分解成点集的9-交集模型的表现形式符合经典9-交集模型,但计算较为复杂。通过示例比较了两种扩展9-交集模型及经典9-交集模型的表达能力。结果表明,两种扩展交集模型均能准确地表达出复合面状对象各子部分之间的拓扑关系的细节,扩充了9-交集模型的表达能力。     

Geometric Algebra Model for Geometry‐oriented Topological Relation Computation

Classical topological relation expressions and computations are primarily based on abstract algebra. In this article, the representation and computation of geometry‐oriented topological relations (GOTR) are developed. GOTR is the integration of geometry and topology. The geometries are represented by blades, which contain both algebraic expressions and construction structures of the geometries in the conformal geometric algebra space. With the meet, inner, and outer products, two topology operators, the MeetOp and BoundOp operators, are developed to reveal the disjoint/intersection and inside/on‐surface/outside relations, respectively. A theoretical framework is then formulated to compute the topological relations between any pair of elementary geometries using the two operators. A multidimensional, unified and geometry‐oriented algorithm is developed to compute topological relations between geometries. With this framework, the internal results of the topological relations computation are geometries. The topological relations can be illustrated with clear geometric meanings; at the same time, it can also be modified and updated parametrically. Case studies evaluating the topological relations between 3D objects are performed. The result suggests that our model can express and compute the topological relations between objects in a symbolic and geometry‐oriented way. The method can also support topological relation series computation between objects with location or shape changes.     

GIS线目标间拓扑关系描述的层次方法

拓扑关系是一种相对较弱的空间目标位置约束,已广泛应用于空间查询、分析和推理等实际应用中。本文主要研究IR2中两个线目标间拓扑关系的描述和区分方法,采用的基本思路是将两个线目标间的关系描述为若干个基本关系的组合。在拓扑关系描述和区分时,提出了具有不同分类能力的拓扑不变量,分别是：维数、分离数、交分量类型和交分量全序,并依次建立了相应的分类方法。分析发现,在IR2中的两个线目标间具有17种潜在的基本关系。其中的11种是描述复合线/线关系的基本构成单元。