ABSTRACT
In the last chapter we proposed representing surfaces in terms of geometric descriptors such as parabolic curves and ridges (see the ROADMAP at the end of
Chapter 6). When we deform a surface these descriptors may change qualitatively. For example, a hyperbolic patch might acquire an elliptic 'island' so that a parabolic curve appears from nowhere. Thus transitions may occur in which, for example, one of the curvatures passes through zero and changes sign. In mathematical shorthand, these transitions occur when one or more of the inequalities in the ROADMAP become equalities.
