Is a Mobius strip a manifold? It’s possible to draw a 2D grid anywhere along its surface, but not along the side edge and it’s also not possible to define a normal vector
Can we approximate nonmanifold geometry with manifold geometry? After all, the two nonmanifold structures on this slide can be split into manifolds.
Are manifold geometry closed by definition? Then no matter what we do we can't transform approximate an open geometry to a manifold geometry?
Why is the top right geometry non-manifold? I feel like we could zoom in on the joint and get a 2D coordinate grid. We can define the coordinate plane over a regular plane and then just bend it into this shape. If it is non-manifold, is a tetrahedron non-manifold as well because zooming in on one point yields the same tetrahedron shape and doesn't reduce to 2D?
If we give the surface some "thickness" instead of just being a flat plane, can we turn every nonmanifold shape into a manifold one? For example, we could think of any face as two faces that are stacked on top of each other (being very informal about the connectivity).
A double cone is not manifold, but is a cone manifold? If you zoom in enough on the point, you can never get a 2d grid.
How do people handle meshes that are not manifold?
Can we segment the non-manifolds to be a set of manifolds?
How to tell the difference between curve and manifold?
Is a plane manifold? On the top right, if I’m understanding correctly, the shape is not manifold because it folds in on itself. If it didn’t have that intersection, would it be manifold?
What makes a cube a manifold? It seems like both cubes and the weird shape on the top right have sharp edges, but one is ok while the other is not.