Projections of Piecewise-smooth Surfaces

In this paper we consider singularities of orthogonal projections of piecewisesmooth surfaces on planes. For a generic smooth surface, the apparent contour (outline, profile) of the surface associated with a projection onto a plane is the set of critical values of the projection. The singularities of apparent contours of smooth surfaces have been studied by several authors [1, 3, 8, 9, 10, 11, 12]. J. W. Bruce and P. J. Giblin investigated in [4] the singularities of projections of generic surfaces with boundary. A surface with boundary in IR is an embedding of the half-plane {(x,y):y^ 0}, and an orthogonal projection of the surface is represented by a germ of a map from the plane to the plane in a neighbourhood of the jc-axis. A classification of map-germs R,0 -> U,0, up to smooth changes of coordinates in the source which preserve the x-axis and any smooth changes of coordinates in the target, is given in [4].