The Reasoning Of Ternary Projective Relationship Based On The Sphere

Spatial reasoning is an emerging integrated science acrossing computers. geographic information, cognition, mathematics and so on. is an important sub-field of artificial intelligence, and is one of the important theoretical foundations of geographic information systems. computer vision, database query systems. natural language understanding areas.Since most practical applications involves multiple space, and sometimes need to deal directly with spherical information, such as the weather analysis of global warming and studies of the global spread, and to meet the need of considering that the spatial information of topological. orientation, size and distance on the sphere. Clementini et al defined a projective relation that can describe the topological relations, direction relations and the information of size and shape of spatial objects, and put the relation to the sphere. However. they gave only in the form of spherical projective relational model and did not give the reasoning algorithm.This paper studies and discusses the model for spherical projection relation. Based on the analysis of the unique properties of spherical surface, of the reasoning method of the planar projection relation. and of the comparison of the similarities and differences between the spherical model and the planar model, gives a reasoning method of spherical model, then completes the spherical projective relational model.In this paper do some specific work and research results are as follows:(1) Describes the historical background, purpose and meaning of this article, generalizes the latest results of the projective relations and spherical spatial relationships projection, and analyzes the current situation.(2) Introduces the theoretical background related to this article in detail.Describes the unique spherical properties as opposed to planar properties. the representation and reasoning methods of the plane projective relational model. and the representation of the spherical projective relational model.(3) Gives the reasoning method of spherical projection relational model respectively from the respects of the spherical point and spherical region.Based of analyzing the cause of being unable to use the planar method to spherical projective relation, gives the spherical reasoning method. The method contains two operations that is permutation operation and composition operation.For the spherical point. designs algorithms to achieve the permutation operation and composition operation of the projective relation. As the result of the permutation operation, it can be calculated that the permutation relation of any point, then permutation table can be gotten:As the result of the composition operation, it can be calculated that the composition relation among any points, then composition table that contains 8*8 terms can be gotten.For the spherical region. designs algorithms to achieve the permutation and composition operation of the projective relation. As the result of the permutation operation, the permutation relation of any regions can be calculated, and then permutation table can be gotten containing 11 single-tile relations and 30 multi-tile relations. As the result of the composition operation, the composition relation among any regions can be calculated consisting of the composition between the single-tile and the single-tile projective relations and the composition between the single-tile and multi-tile projective relations. Finally, maps the spherical projective relations for regions to spherical directional relations. then using the permutation table and composition table of the spherical projective relations for regions. realizes the judgment and reason of the direction relations among spherical objects.(4) Designs and implements the of the demonstration system of the reasoning of ternary projective relationship based on the sphere. It shows the function of system, the process of manipulation and the demo results in the form of interface drawing.On the basis of the spherical projective relational model. this paper gives the reasoning method of it. On the respect of the theory, this work improved the spherical projective relational model established by Clementini and provided a relatively new research aspect for the representation and reason of directional relation. On the respect of the practical application, this work can be used in the spatial inquiry database, aircraft navigation geographical information systems that related to analysis and process the information in the spherical field and so on.