I have a torus that I want to project the earth onto, but the current shape of the UV can't be simply scaled into a square. Is it possible to deform this into a perfect grid-like square (I'm not worried about preserving area).

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2https://blender.stackexchange.com/questions/78358/how-to-straighten-curved-uvs-into-straight-belt/78362#78362 This should help you. Don't forget to mark seam. – cgslav May 17 '17 at 16:29
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Related: https://blender.stackexchange.com/questions/65565/straighten-the-series-of-vertices-in-uv-editor – Paul Gonet May 17 '17 at 18:29