sin(1/x), discussed before in class, is not a manifold.
How do we define the center of a shape?
Is there some broad use case for using non-manifold shapes in computer graphics (beyond drawing non-manifold objects directly)? Specifically, is there some object/class of objects in the real world that is best represented by non-manifold geometry?
Can every non-manifold shape be represented by multiple manifold shapes?
How does one in the general check if something is a manifold in a more precise way? In the lecture it was mentioned that a formal definition of manifold is not super relevant in computer graphics, but I am wondering if given some explicit representation of a structure, if there is some sort of straightforward algorithm that could work with some level of accuracy.
What about the edges at the top and bottom? I can see how we can parameterize it in one dimension (just around the edge) but how does the second dimension work? Can we go over the edge and end up on the inside of the surface?
So this check also means that every point on the polygon must satisfy the condition for it to be considered manifold?
EVen though there is no 2D grid at the center, is there not a way to approximate this using limits or some other method?
Can we also think about manifolds in terms of if we can unwrap the shape and lay it flat as a piece of paper?
Can we have a formal definition of manifolds, instead of the attribute?