  In this paper we consider planar sections and visual contours of co-dimension
one affine immersions. The main theorem says that the third order Taylor
expansion of the difference between the visual contour and planar section
functions is exactly the cubic form. We also consider parameterizations on two
dimensional affine immersions whose coordinate lines are geodesics, in one
direction, and both planar sections and visual contours in the other direction.
We call such coordinates parallel-meridian. Among other results, we show that
any two dimensional affine sphere that admits parallel-meridian coordinates
with a pole must be a quadric.

Differential Geometry