The first of the qualitative reasoning systems described above was de Kleer's Newtonian physics problem solver, which operated on the roller coaster example. This example is set in the spatial domain, in that it involves continuous length and height representation of the roller coaster. However, as mentioned, it has only one degree of freedom, because the height component of the motion is dependent on the length component.
This allowed the representation to be simply an ordering of qualitatively different segments of the roller coaster, each with an associated height and slope (the system also required a complete geometric description of the roller coaster, but this information was not used by the qualitative reasoning component). A similar one dimensional system was designed by Forbus, which analysed the one dimensional motion of a block on a spring [For82].
These systems, although operating on problems that involve spatial motion, allow the problem to be abstracted to a degree that it can be easily analysed using techniques for systems without spatial components. Many of the problems that are involved in real world motion analysis are not considered in these systems - the most important of which are the representation of direction of motion, and of relationships between objects.