Spatial Reasoning Using the Quad Tesseral Representation

A review of the application of the quad tesseral representation tosupport spatial reasoning is presented. The principal feature of therepresentation is that it linearises multi-dimensional space, while stillproviding for the description of individual objects within that space andthe relationships that may exist between those objects (in any directionand through any number of dimensions). In addition the representation issupported by an arithmetic which allows the manipulation (translation etc.)of spatial objects. Consequently, when incorporated into a spatialreasoning system, all necessary processing can be implemented as if in onlyone dimension. This offers two significant advantages over moreconventional multi-directional approaches to spatial reasoning. Firstly,many of the concerns associated with the exponential increase in the numberor relations that need to be considered (as the number of dimensions underconsideration increases) are no longer relevant. Secondly, the computationalcost of manipulating and comparing spatial objects remains static at itsone dimensional level, regardless of the number of dimensions underconsideration.