A Coordinate-Based Quantitative Directional Relations Model

Directional relations have been gain more attention in spatial analysis and reasoning. The conventional quantitative directional relations models are mostly based on the measure of angle. But angle-based model can not distinguish the case of the difference of the directional relations between different points in the same ray. In order to resolve this problem, we propose a new concept of directional coordinate and a new quantitative representation model based on it. The basic directional coordinate is defined between two points. Then the basic directional coordinates are combined to represent the directional relations between various kinds of objects. Our analysis of the directional reasoning performance using directional coordinate show that it can differentiate the directional relations between the different objects in the same ray and increases the reasoning efficiency in some cases. Both theoretical and numerical analysis proved the model is more sensitive to the factors including location, distance, size and shape.