Singularities in drawings of singular surfaces

Tom 82 / 2008

Alain Joets Banach Center Publications 82 (2008), 143-156 MSC: Primary 57R45; Secondary 57R42. DOI: 10.4064/bc82-0-10


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.


  • Alain JoetsLaboratoire de Physique des Solides
    bât. 510
    Université de Paris-Sud
    CNRS, UMR 8502
    F-91405 Orsay Cedex, France

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