Scaling UV map to fit bounds I've been trying to scale the UV map for a 3D arc (i.e. a slice of a hollow sphere) to fit the entire bounds of the UV map.

Unwrapping the mesh results in a circle, which I'm looking to scale up to the bounds of the map as in the following:



I played around with proportional editing - i.e. moved 4 diagonal vertices (top left, top right, etc) to the 4 corners using the sharp falloff, and then moved the 4 edge vertices (top, left, etc) to the 4 edges using the smooth falloff. But the best I could come up with was the following, which results in a really horribly warped map:



If there's a better way to go about doing this (or a better way to use proportional editing correctly), I'd love to hear about it.
Select one side (left/right) from 1 diagonal to the other, only borders, and scale it on X axis to 0 (S, X, 0) then move it away


Continue with other sides (up/down-> Y axis)



Once all four sides scaled and moved away, select the other vertices, scale them down, then select the borders again


scale and move them to fit your UV bounds 


Select everything but the border vertices and from the UV menu, click minimize stretch (or Ctrl+V)

use mouse wheel to blend the effect to your liking, when it's ok, hit enter