Level Sets of Functions and Symmetry Sets of Surface Sections
We discuss the behaviour of vertices and inflexions of one-parameter families of plane curves which include a singular member. These arise a sectons of smooth surfaces by families of planes parallel to the tangent plane at a given point. We cover all the generic cases, namely elliptic, umbilic, hyperbolic, parabolic and cusp of Gauss points. This work is preliminary to an investigation of symmetry sets and medial axes for these families of curves, reported elsewhere.