Reasoning about the Inverse of Cardinal Direction Relation

Reasoning with the Inverse of 3D Cardinal Direction Relations Based on Direction Matrices

“…In addition, most of the current studies mainly focus on this problem in 2D space for computing the inverse of cardinal direction relations [34][35][36][37], and the research on reasoning with direction relations in 3D space is lagging behind. Wang et al [38] studied the inverse operation of basic rectangle cardinal direction relations defined by 3DR27 model by means of 3D algebra theory. By using the equivalent correlations between 3D algebra and 3D rectangle cardinal direction relations, the inverse of 3D rectangle cardinal direction relations is transformed into the inverse operation on the equivalent 3D algebra relations.…”

“…By using the equivalent correlations between 3D algebra and 3D rectangle cardinal direction relations, the inverse of 3D rectangle cardinal direction relations is transformed into the inverse operation on the equivalent 3D algebra relations. On this basis, Wang et al [39] studied the correlation between 3D rectangular cardinal direction and 3D block algebra relations, and then proposed an algorithm for computing the inverse of the 3D rectangular cardinal direction relations. What is more, we introduce the theory of block algebra into the research area of reasoning with the inverse of the 3D cardinal direction relations.…”

“…Direction relation is an important part of spatial relations, which reflects the order relations between spatial objects, such as front side, back side, left side, right side, etc. It is widely used in many fields such as Spatial Intelligent Analysis and Processing, Urban Pipeline Network, Robot Navigation, Disaster Prevention and Mitigation, etc [1,2].And it is increasingly becoming a hot and difficult problem in the fields of Data Modeling, Cartographic Synthesis, Multimedia Design, Image Retrieval, etc [3]. The expression and reasoning with direction relation is a foundmental problem in the research field of spatial direction relations [4], which is important in Spatial Retrieval [5,6], Spatial Localization [7,8], Quality Inspection [9,10] and Spatial Storage [11] in the field of spatial database.…”

Block Algebra-Based Consistency Checking With Cardinal Direction Relations in 3D Space

“…As the premise of spatial cognition and reasoning, spatial direction relation describes the order relation between spatial objects, which is widely used in the field of spatial analysis and processing [1], spatial-temporal database [2], [3], [4], computer graphics [5], [6], [7] and natural language processing [8], [9], [10]. With the application of spatial direction relation, we are not satisfied with the simple description and storage of spatial direction relation, and it also requires that the spatial database system has the ability to intelligent prediction, analysis, and qualitative reasoning with directions [11], [12], [13].…”