Why is orientability important in graphics? Conceptually, shouldn't a non-orientable surface like a Mobius strip be able to be rendered in a similar way to an orientable surface?

Here's what I added to my notes for this slide:

Triangle Orientation: “front” = “outside”, “back” = “inside”, orientation is based on the order in which the vertices are listed: the front is the side from which the triangle’s three vertices are arranged in counterclockwise order.

Consistent Orientation: All triangles must agree on which side is the front, this is true only if two shared vertices appear in opposite orders in the two triangles’ vertex lists.

I took some definitions from the book

Relating to the earlier part of the class, where we had to deal with the orientation of triangles when rasterizing, I am curious as to why we cannot just flip the vectors to make triangle and more importantly the surface as a whole have all one consistent orientation.

Is there some clever datastructure format in which the triangles which contain a vertex are easily retrievable? This seems potentially helpful for the validation of the manifold property and orientation.

Edit: Nvm this is resolved shortly after in the lecture