Stratifications of Generically Illuminated Surfaces with Geometric Features

Abstract

In Chap. 2 we introduced the models for geometric features and the restrictions on the light source. We investigate here the consequences of the light projection being stable for the interaction of the geometric features and the resulting shade/shadow curves. We carry this out by first using the abstract classification of stable germs at geometric feature points, and determining in Sect. 8.1 their distinct geometric realizations to obtain the classification in Theorem 8.7 of the stable projection map germs including visibility for each geometric configuration (FC). Second, we apply this classification in Sect. 8.2 to the light projection maps from geometric feature points to deduce in Theorem 8.8 the classifications of stratifications resulting from the refinement by shade/shadow curves of the stratifications defined by geometric features. We also apply the results to obtain in Theorem 8.9 the classification of stable view projections on geometric features with shade/shadow curves, but without apparent contours (SF).