Compute mesh of the projection of a 3D surface triangulation

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? • I guess you could try to compute the convex hull of the projected point set and mesh it, but you'd still have to figure out how to deal with multiply-connected surfaces like the torus in your example. Mar 25 '18 at 22:30
• I think that you can take your projected mesh and then some cleanup. Using, for example, MeshLab: meshlab.net Mar 25 '18 at 23:46