共查询到18条相似文献，搜索用时 109 毫秒
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目前研究已提出了多种带洞面域拓扑关系的描述模型,建立不同模型之间的联系可发挥这些模型在拓扑关系推导和分析中的优势。本文对比分析了基于点集拓扑和对象分解两种方法的6种拓扑关系描述模型,通过定义两个25交关系矩阵操作算子,建立整体面域与分解区域间的拓扑关系计算方法,实现了拓扑关系描述模型之间的转换。理论证明,表明关系矩阵表和扩展9交集模型,以及4元组模型与25交模型在表达拓扑关系的能力方面是一致的且可以相互转换,关系矩阵表可转换为25交模型和9交模型。实例分析说明本文方法可以利用25交模型的“桥梁”作用实现多种模型之间的转换,描述具有特定结构带洞面域间的拓扑关系。 相似文献
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三维体目标间拓扑关系与方向关系的混合推理 总被引：1，自引：1，他引：0
重点研究了三维空间中拓扑关系和方向关系间的混合空间关系推理。用Allen区间关系对描述基于投影的空间划分方法得到的方向区域和用九交矩阵描述的拓扑关系,用定义法研究混合空间关系推理,推理结果用组合推理表表示。 相似文献
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面向带洞面状对象间的拓扑关系描述模型 总被引：1，自引：1，他引：0
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。 相似文献
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球面四元三角网的基本拓扑关系描述和计算 总被引：6，自引：1，他引：5
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。 相似文献
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基于区间Ⅱ-型模糊区域模型,讨论了区间Ⅱ-型模糊区域的结构,通过对传统的n-交模型进行扩展,提出了区间Ⅱ-型模糊区域拓扑关系的n-交矩阵和各原子的计算方法,并提出了拓扑关系的形式化分析方法。通过计算区间Ⅱ-型模糊拓扑关系矩阵与8种基本拓扑关系矩阵的相似度并排序,确定其首要拓扑关系,结合拓扑关系距离确定其可能存在的次要拓扑关系。 相似文献
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利用OracleSpatial提供的简单的空间关系查询操作算子,对九交模型所描述的任意两个2维空间不自相交的线目标与面目标（不合空洞）的拓扑关系判断设计了算法,最终进行了试验验证,实现了线目标与面目标间的19种空间拓扑关系的判断。 相似文献
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Qualitative locations describe spatial objects by relating the spatial objects to a frame of reference (e.g. a regional partition in this study) with qualitative relations. Existing models only formalize spatial objects, frames of reference, and their relations at one scale, thus limiting their applicability in representing location changes of spatial objects across scales. A topology‐based, multi‐scale qualitative location model is proposed to represent the associations of multiple representations of the same objects with respect to the frames of reference at different levels. Multi‐scale regional partitions are first presented to be the frames of reference at multiple levels of scale. Multi‐scale locations are then formalized to relate multiple representations of the same objects to the multiple frames of reference by topological relations. Since spatial objects, frames of reference, and topological relations in qualitative locations are scale dependent, scale transformation approaches are presented to derive possible coarse locations from detailed locations by incorporating polygon merging, polygon‐to‐line and polygon‐to‐point operators. 相似文献
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Kimfung Liu Wenzhong Shi 《International Journal of Applied Earth Observation and Geoinformation》2009
This paper presents a study on the modeling of fuzzy topological relations between uncertain objects in Geographic Information Systems (GIS). Based on the recently developed concept of computational fuzzy topological space, topological relations between simple fuzzy spatial objects are modeled. The fuzzy spatial objects here cover simple fuzzy region, simple fuzzy line segment and fuzzy point. To compute the topological relations between the simple spatial objects, intersection concepts and integration methods are applied and a computational 9-intersection model are proposed and developed. There are different types of intersection, and we have proposed different integration methods for computation in different cases. For example, surface integration method is applied to the case of the fuzzy region-to-fuzzy region relation, while the line integration method is used in the case of fuzzy line segment-to-fuzzy line segment relation. Moreover, this study has discovered that there are (a) sixteen topological relations between simple fuzzy region to line segment; (b) forty-six topological relations between simple fuzzy line segments; (c) three topological relations between simple fuzzy region to fuzzy point; and (d) three topological relations between simple fuzzy line segment to fuzzy point. 相似文献
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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. 相似文献
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Zhaoyuan Yu Wen Luo Linwang Yuan Yong Hu A‐xing Zhu Guonian Lü 《Transactions in GIS》2016,20(2):259-279
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. 相似文献
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Consistency among parts and aggregates: A computational model 总被引：2，自引：0，他引：2
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. 相似文献
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Eliseo Clementini Brahim Lejdel Sabrina Mazzagufo Robert Laurini 《Transactions in GIS》2021,25(1):491-515
In GIS, spatial analysis is based on the use of spatial operations such as testing the spatial relations between features. Often, such tests are invalidated by errors in datasets. It is a very common experience that two bordering regions which should obey the topological relation “meet” fall instead in the “overlap” category. The situation is exacerbated when applying topological operators to regions that come from different datasets, where resolution and error sources are different. Despite the problem being quite common, up to now no standard approach has been defined to deal with spatial relations affected by errors of various origins. Referring to topological relations, we define a model to extend the eight Egenhofer relations between two simple regions: we call them homological relations (H‐relations). We discuss how exact topological relations can be extracted from observed relations and discuss the case of irregular tessellations, where errors have the most impact on vector data. In the proposed case study within the domain of geographic crowdsourced data, we propose algorithms for identifying homological regions and obtaining a corrected tessellation. This methodology can be considered as a step for quality control and the certification of irregular tessellations. 相似文献
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ABSTRACTThere is growing interest in globally modelling the entire planet. Although topological relations between spherical simple regions and topological relations between regions with holes in the plane have been investigated, few studies have focused on the topological relations between spherical spatial regions with holes. The 16-intersection model (16IM) is proposed to describe the topological relations between spatial regions with holes. A total of 25 negative conditions are proposed to eliminate the impossible topological relations between spherical spatial regions with holes. The results show that (1) 3 disjoint relations, 3 meet relations, 66 overlap relations, 7 cover relations, 3 contain relations, 1 equal relation, 7 coveredBy relations, 3 inside relations, 1 attach relation, 52 entwined relations, and 28 embrace relations can be distinguished by the 16IM and that (2) the formalisms of attach, entwined, and embrace relations between the spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on the simplified 16IM are different, whereas the formalisms of other types of relations between spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on a simplified 16IM are the same. 相似文献
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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。 相似文献