My initial approach to qualitatively representing objects and their interactions and relationships was to adapt and extend commonly used solid modelling techniques, so that they could be implemented using qualitative methods, while meeting some of the requirements discussed in the previous section. Using solid modelling techniques resulted in two different approaches to the problems involved: one developed from boundary representation methods, and the other from constructive solid geometry methods. Although my initial investigations recognised that any development aimed at robotics should take a three dimensional approach, both of the modelling methods involved sufficiently complex problems in two dimensions that my implementation was restricted to that case, and I made no attempt at implementing a three dimensional representation.
Following relatively independent paths in developing these two representations has resulted in interesting differences between the two. Both two dimensional methods will therefore be described in detail below, although more space is devoted to the one that I conclude is superior. As an introduction to the two dimensional shape representations, this section describes the way that they were derived from three dimensional representations.