This is joint work with James Damon (UNC Chapel Hill) and Gareth Haslinger (Liverpool).
We consider the mutual interactions of apparent contours, marking curves, shade and cast shadow boundaries, on surfaces which are smooth or piecewise smooth, such as valley/ridge creases and corners of various types. We consider only stable illumination but allow up to codimension 2 in the viewing.
The most complete results are codimension 1, which amounts to a `flypast' of a surface. We use the methods of singularity theory to derive rigorously the abstract classification of view projections and then apply geometrical arguments to realise the various possibilities or, in many cases, to prove that realisation is not possible. Our work corrects several errors in earlier attempts to do this classification, which depended on applying theorems of singularity theory to situations where they are not valid, leading to incorrect results.