Minimize stretch tool gives inconsistant results

Question

After straightening out UV islands, I often find that there is a lot of "Noise" in the positions of the vertices in my UV map. This results in small distortions when applying a texture to the mesh. Sometimes the "Minimize stretch" tool in the UV editor will fix this, but most of the time I just get a result like this:[![enter image description here][1]][1]

This issue is also very inconsistent. Just small changes to the geometry will drastically effect whether or not this happens. In fact, it was hard to get a screenshot of it, since adding a few sharpening loops to my mesh fixed the issue for most of the UV islands.

EDIT:

here is a file demonstrating the issue.

[1]: https://i.stack.imgur.com/tJ3PV.png

Answer 1

The fix for the issues caused by minimize stretch operation is to mirror your UV map for the affected islands-- ie, scale each UV map by -1 in the X axis. (Or the Y axis. It doesn't matter which.)

If we take a look at the mesh and the UV map that you've provided, we can see that there's a difference in coordinate handedness between the world position of the verts and the UV position of the verts (for the bad islands): moving up the strand moves it in the +V, but moving right along a ring in a strand (looking down from the normal, with the "top" being the +V side of the strand) moves it in -U.

I don't know exactly how Blender calculates stretch in order to minimize it, but it's very easy to imagine it getting confused by this difference in coordinate handedness. We can see that when we mirror the bad UVs, we get appropriate operation from minimize stretch: