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

Consistency checking, as a key and challenging problem in the research of three-dimensional spatial direction relation reasoning, has attracted increasing attention and exploration from researchers. It is widely used in 3D spatial configuration and anomaly detection in urban planning. To enrich and enhance the ability of the existing models for reasoning and predicting with 3D cardinal direction relations, the spatial projection method for each axis based on the 3D cardinal direction relation model (3DR27) is proposed.This paper divides the consistency checking of spatial direction relation networks into two processes. Firstly, the projection method is employed to determine whether a network with three-dimensional cardinal directional relations is a convex relation network. Then, using the interval algebra good calculation properties and establishing the mapping between 3D rectangular cardinal direction and 3-block algebra, based on a consistency checking algorithm is proposed to determine whether one or more than one solution can be found to satisfy the network constraints. Theoretical analysis and experimental results demonstrate that the algorithm is correct and complete. The method effectively improves the intelligent analysis and processing ability of complex 3D spatial direction relations.