  Classes of an equivalence relation on a module V over a supertropical
semiring, called rays, carry the underlaying structure of "supertropical
trigonometry" and thereby a version of convex geometry which is compatible with
quasilinearity. In this theory the traditional Cauchy-Schwarz inequality is
replaced by the CS-ratio which gives rise to special characteristic functions,
called CS-functions. These functions partite the ray space Ray(V) into convex
sets and establish a main tool for analyzing varieties of quasilinear stars in
Ray(V). They provide stratifications of Ray(V) and therefore a finer convex
analysis that helps for a better geometric understanding.
