IS "bad" geometry completely unusable, or does it ever become useful to have this capability to represent "bad" geometry?
The previous slide mentions that halfedge connectivity is always manifold, but the examples in this slides seem to suggest that halfedge can also be used to encode "bad" shapes that are not manifold. Can we just encode any non-manifold shape using halfedge by manipulating vertex positions?
What makes a geometry good or bad? Is there some characteristic of bad geometries that we can check for in a manifold to avoid?
How do we enforce good geometry then?
Is there a way to check for bad geometries or work around them?
I assume that the "same connectivity, random vertex positions" figure is representative of bad geometry, but what would be the biggest problem if it was used to 'shortcut' a more complex shape? i.e. the actual shape is the same, but there are vertices at every intersection of the connection with a face and the connectivities are otherwise broken up appropriately instead of going through the solid parts - would that cause problems with rendering or something similar?
How do we test for geometry being "bad"?
Does that mean that the two conditions above (for polygons) don't correspond exactly to the mathematical definition of a manifold (something something locally homeomorphic to R^n...)? Is "manifold connectivity" weaker than actually being manifold?
If a polygon has edges on every faces intersections, is the polygon good?
How do we ensure that the geometry is good then, is there some way to check for this in code or is it just something we can see with our eye?
Are the cases where using manifold mesh gives good geometry but bad connectivity?
Is bad geometry just tested visually?
How can I check it is good? By eyes? The users may do wrong things.
What is "good" geometry? If the connectivity is fine and the user is the one manipulating the geometry through editing subdivisions, then does it matter?
How often do we end up having to worry about this bad geometry if we mainly rely on non-intersecting triangle meshes? Do we enforce some strict constraint on the turning angles at each edge or the angles within the triangles?
What's the consequences of bad geometry?
Is there any methods to improve the bad geometry?