Classifications of Stable Multilocal Configurations and Their Generic Transitions

Abstract

In the preceding chapters we used the results developed in Part II to determine the generic transitions for the local cases. We complete the analysis by treating the remaining cases which involve multilocal classifications. These are of two types. The first arises from the light projection when a distant cast shadow curve intersects a geometric feature. The case where a cast shadow of types smooth curve, C ¹-parabola, or V -point occurs on a smooth sheet have already been treated. The second case involves one surface locally occluding part(s) of one or more other surfaces. This corresponds to the case of multigerms for the view projection. In this chapter we classify both the stable multilocal cases yielding the resulting stratifications for cast-shadows and geometric features which were listed in Corollary 8.10 of Chap. 8, and the stable multilocal views which involve occlusions and their generic transitions.