Seems like all the algorithms in this lecture were approximating ones, not interpolating? Would love if someone could confirm. What are some interpolation algorithms? When might one use one or the other?
I think all the ones covered in this lecture have been approximating, seems like an approximating subdivision algorithm is allowed to move around the original vertices, while an interpolating one will not. Using an approximating algorithm usually ends up with a smoother surface, but an interpolating one gives more control over the outcome.
From this slide, you can intuitively see why every vertex (after splitting) needs a new coordinate. The large upside down triangle in the first picture can be seen in the second picture, but slightly distorted.
Interesting to not that splitting the triangles into 4 can be done with just the half-edge datastructure. The way it looks more more 3d and textured as you split more is facinating. But you can tell that it loses it's shape. I wonder what the inner edges would have to look at for it to keep more of it's outer appearance. How do people determine what the inner edges should look like to get the shape you want after splitting actually?