Qualitative reasoning about physical processes is based on the notion of "quantity space" [Forbus, 1984a, 1984b]. The question is how to construct a quantity space for a particular physical process. One line of research is to establish a set of so called "landmark points" by selecting some values of the continuous physical parameters characterizing the physical process under consideration [Kuipers, 1985a, 1985b]. The landmark points are to delimit operating regions of qualitative processes. In most practical situations it is impossible to find a finite set of such points. This is because the operating regions of physical processes are delimited not by some specific values of physical parameters but by some hypersurfaces in the cross-product of the parameters, they are called here "critical hypersurfaces". The paper presents a relatively complete methodology for establishing critical hypersurfaces.