SPATIAL REASONING USING THE QUAD TESSERAL REPRESENTATION

A review of the application of the quad tesseral representation to sup port spatial reasoning is presented. The principal feature of the repr esentation is that it linearises multidimensional space, while still p roviding for the description of individual objects within that space a nd the relationships that may exist between those objects (in any dire ction and through any number of dimensions). In addition the represent ation is supported by an arithmetic which allows the manipulation (tra nslation etc.) of spatial objects. Consequently, when incorporated int o a spatial reasoning system, all necessary processing can be implemen ted as if in only one dimension. This offers two significant advantage s over more conventional multi-directional approaches to spatial reaso ning. Firstly, many of the concerns associated with the exponential in crease in the number or relations that need to be considered (as the n umber of dimensions under consideration increases) are no longer relev ant. Secondly, the computational cost of manipulating and comparing sp atial objects remains static at its one dimensional level, regardless of the number of dimensions under consideration.