In the roller coaster domain, motion of a block over the roller coaster can be described in the same terms as the sliding problem presented in the last chapter. The shape of the roller coaster, including discontinuities, can be represented as an extended polygon boundary. Relative slope of segments of the roller coaster can also be described. State can be represented, as in de Kleer's system, as a combination of qualitative position on a particular segment of the roller coaster, and direction of motion. The only further information required to predict future motion is a representation of the external force acting on the system - gravity. In de Kleer's system, gravity is implicit in the representation, but a reasoning system acting on the PDO/EPB representation could explicitly include gravity as an influence that encourages closer proximity to the ground.
In the bouncing ball domain, it would also be necessary to include an explicit description of gravity - Forbus' representation includes gravity as an implicit direction. The PDO/EPB representation can describe a moving object with real size and shape (whereas the bouncing ball in FROB is just a point mass), and it can describe flying, sliding, and collision, just as Forbus' system does (motions like these are all discussed in the last chapter as ways of avoiding obstacles). The main advantage of this representation over the one used by Forbus is that it can describe change of qualitative state in the position of the ball without dividing space into problem-specific discrete regions. State change could be expressed in terms of changing relative proximity rather than absolute position, and this enables facilities such as describing the relative state of two bouncing balls, rather than just a single ball in a static world.
In the ``mechanism world'', other qualitative analysis systems can describe only the motion of objects which are in contact. The PDO/EPB representation can be used to describe both motion in free space, and motion of objects in contact. The advantages of describing relative position globally are again apparent here, where the state of a mechanism may be a function of many individual parts in relative motion. This representation could therefore provide a basis for more general qualitative analysis of mechanisms, but it would have to be extended to include the influence of moving objects on other objects which they are in contact with. Such an extension could involve a qualitative version of the mechanics of pushing as analysed by Mason [Mas86]. The PDO/EPB representation does not provide the process description of energy transfer which is the central part of most mechanism analysis systems.
The facilities provided by the PDO/EPB representation can be used to carry out the spatial reasoning tasks associated with other qualitative reasoning systems that operate in these various spatial domains. The PDO/EPB methods do not require the use of a numeric preprocessing stage to carry out geometric analysis of possible motion and constraint, and the representation retains much of the spatial content of the scene - the scene geometry is not reduced to a discrete network.