In this slide, the manifold polygons could just be drawn in 2D, but the non manifold polygons were drawn in 3D. Is this generally the case? If we were to draw the surface connectivity in 2D and notice bad behavior like edges crossing, is that generally a sign of a non-manifold polygon?
Do the manifolds have to be able to be represented in 2D?
I do not understand why the last shape is not manifold, but the first one is manifold. For the first shape, the left most edge is only contained by one polygon instead of two right? For the last one, I think I simply do not understand how you define a "fan".