Topological relations between a directed line and a directed region

Abstract

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.

A topological model of trajectories with road network space

“…Kurata and Egenhofer (2007) then proposed a 9‐intersection model with 26 topological relationships between directed lines and regions. Based on the 9‐intersection model, Shen et al (2020) constructed a topological relationship framework between directed lines and regional elements with positive and negative attributes, and revealed 111 topological relationships. However, these studies did not consider natural language, which is more accessible to allow people to understand how to explain behavioral semantics.…”

“…These trajectory semantic information construction studies did not discuss spatiotemporal topological semantics in detail. However, spatiotemporal topological semantics are critical elements in a semantic trajectory model (Hove & Keller, 2010; Shen et al, 2020; Wu et al, 2019; Xiang et al, 2017), particularly for movements in a limited space, such as driving inside a road network. Spatiotemporal topological semantics are spatiotemporal relations that are invariant under topological transformations (Abraham & Roddick, 1999), such as rotation and scaling.…”

“…All the tables show the differences between the proposed model and the model proposed by Shen et al (2020). Because the topological components of the region elements are composed of the interior, exterior, and boundary, the proposed model is divided into three cases.…”

“…Although there is some research on the spatial relationships between a directed line and basic geographic objects (e.g., line–line relationships; Clementini & Di Felice, 1998; Kurata & Egenhofer, 2006 and line–region relations; Kurata & Egenhofer, 2007; Shen, Huang, & Chen, 2020; Wu & Gong, 2015; Xiang et al, 2017), the spatiotemporal topological semantics of a trajectory have not been systematically studied. This study is motivated by considering this issue.…”

Refinement and Computation Method for Line/Body Topological Relationships

“…Zhou et al proposed the 25I model by decomposing spatial objects into vertex, edge, face, interior, and exterior [26]. Shen et al introduced a topological relationship model that distinguishes between directed lines and directed regions [27] and the 27-intersection model in two-dimensional space [28]. Based on the 9I model, Leng et al proposed the generalized 9-intersection model for regions with multiple holes [29].…”