Spatial Representation and Reasoning Using the N-Dimensional Projective Approach

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In this paper, we introduce a novel pictorial approach for solving problems in n-dimensional Euclidean spaces called the n-dimensional projective approach. The projective approach is based on a hierarchical and modular architecture, where its ground module is rooted on geometrical concepts. The result is an effective and consistent spatial approach able to solve problems in ndimensional spaces with a quadratic computational cost in order to the number of domain entities and a linear cost in order to the space dimensionality. The projective approach has been used in simulation of physical real-world problems, where physical properties of entities exercise influence on results.