document: Based on the description model of object-orientation-based direction relation in two-dimensional space, the description mode of object-orientation-based direction relation in three-dimensional space is proposed. The basic idea is that the actual direction region is modeled as an open shape. The computation related to the world boundary of spatial direction region is eliminated, and the processing of the direction predicates is converted into the processing of topological operations between open shapes and closed geometry objects. The algorithms of topological operations between open shapes and closed geometry objects are presented and the theoretical proof for the correctness and completeness of the algorithms is performed.
doc_bio_tags: O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O B I O B O O O B I O O B I O O O O B I I I I O O O O B I I I O B I O O B I O B O O O O B I O O B I O O O O O O O O O O O O O B O O
extractive_keyphrases: algorithms computation description mode description model direction region geometry objects open shape open shapes processing of the direction predicates processing of topological operations world boundary
abstractive_keyphrases: algorithms of topological operations description mode of object-orientation-based direction relation in three-dimensional space is proposed object-orientation-based direction relation spatial direction region theoretical proof for the correctness and completeness of the algorithms two-dimensional space