
Given a curve C1, a point O, and a line l, then the hyperbolism of C1 is the curve C2 formed by the points P as follows:
Look at the witch of Agnesi to illustrate the construction: We can normalize the hyperbolism
to a curve C1 with respect to a point O and a line x = 1. The
inverse of the hyperbolism is the antihyperbolism:
when C2 is the hyperbolism of C1, then C1 is the antihyperbolism of C2.
