When drawing regular surfaces, one creates a concrete and visual example of a projection between two spaces of dimension 2. The singularities of the projection define the apparent contour of the surface. As a result there are two types of generic singularities: fold and cusp (Whitney singularities). The case of singular surfaces is much more complex. A priori, it is expected that new singularities may appear, resulting from the "interaction" between the singularities of the surface and the singularities of the projection. The problem has already been solved for the projection of a surface with a boundary. We consider here additional examples: the drawing of caustics and the drawing of the eversion of a sphere.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-10,
author = {Alain Joets},
title = {Singularities in drawings of singular surfaces},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {143-156},
zbl = {1149.57042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-10}
}
Alain Joets. Singularities in drawings of singular surfaces. Banach Center Publications, Tome 83 (2008) pp. 143-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-10/