Lol I just had an idea.
https://imgur.com/a/bA78e
If you have a texture mask in form of a pie slice you can have a circular texture that is masked by that slice.
Now all you need to do is to scale the texture from 0 to 1 and it will fill the slice from inside out.
You could even overlay it and make it look like a ring.
You would need one slice texture per mask. The mask texture itself can be rotated but the width is fixed. If you need different slice sizes I would generate different mask textures. One for each size.