Research On The Uniform Expressions Of Models Of Internal And External Direction Relations In Minimum Bounding Rectangle

Spatial reasoning is to model, represent and analy spatial objects. This process requires acombination of space knowledge and artificial intelligence technology. At present, the maincontents of spatial reasoning roughly divided into the following aspects: the expression ofdirectional relations, modeling and reasoning, and so on. Directional relation as an importantresearch of qualitative spatial reasoning, has been the focus and difficulty of the study ofspatial reasoning and also has made important theoretical and application of the results. Theresearch of directional relation model has gradually become a hot field of spatial reasoning inrecent years.In order to solve the directional relations models can not describe direction informationinside the Minimum Bounding Rectangle (MBR) of a reference region, interior directionalrelations models emerged. Currently, the separate research of the directional relations insideand outside the MBR (Minimum Bounding Rectangle) has made more results.But theresearch of unified model which can accurately describe directional relations inside andoutside the MBR is relatively small.So far, these classic models contain projection-based model and the cone-based model. Theprojection-based model partitions the space by using lines parallel to the axes, whereas thecone-based model partitions the space by using lines with an origin angle. Both of thesemodels can express the directional relations between objects. So Skiadopoulos combined theadvantages of both models, and proposed the CDR family of directional relation models.CDR models introduced the concept of perspective that is close to the human perception ofdirection. In addition, the expression of directional relations is relatively simple. Finally, foreach particular application, by choosing a suitable characteristic angle, we can find anappropriate model in the CDR family. However, this family of models can not describedirection information inside the Minimum Bounding Rectangle (MBR) of a reference region.Based on CDR family of directional relations models, we further partition the MBR of thereference object. Then the plane is divided into9tiles. Finally, the extended CDR models areproposed, namely ICDR family of directional relations models. We formally define thedirectional relations that can be expressed in each model of the family. In addition, we introduce two computing algorithms respectively in qualitative and quantitative aspect. Wedesign and complete these computing algorithms.The concrete work is as follows:1. Summarize the research background and present situation, purpose and meaning of thispaper. We analyze the important and difficult parts in directional relation.2. Uniform expressions of ICDR models of internal and external direction relations inminimum bounding rectangle.Based on CDR family of directional relations models, we further partition the MBR ofthe reference object with the MNR. Finally, the extended CDR models are proposed,namely ICDR family of directional relations models. We formally define thedirectional relations that can be expressed in each model of the family. Furthermorethis paper introduces cross direction-relation matrix whose elements are encoded bybinary codes to represent the directional relations. Then, we propose the deep crossdirection-relation matrix.3. The reasoning of CDR models and ICDR modelsStudy on the reasoning of CDR models and ICDR models. We carry out the researchon these reasoning algorithms of the family of CDR models and the family of ICDRmodels respectively in qualitative and quantitative aspect.4. Design and implement a demonstration systemWe design and complete these reasoning algorithms CDR_φ_compute,CDR_φ%_compute, the ICDR_φ_compute and the ICDR_φ%_compute.