Given a triangulated surface in $\Bbb{R}^3$ we can simply project it on a plane. This will result in a family of triangles which do not form a mesh of the projection for the following reasons:
- each point of the projection is covered by at least two triangles (see the picture).
- the orientation of the triangles is not right
- things may get more complicated for more complex surfaces
Even if the projection is not a mesh, every point of the projected surface is inside one of the triangles, so this could give a good idea of the projection.
Is there a way to extract/construct a mesh of the projection, starting from the projection of the surface?