I hope this explains it clearly. I don't know how useful it would be on Curvature but I'd find it very useful on Straighten (both example GIFs are Straighten). Unconstrained Straighten creates the shortest path between the two end vertices. Constraints - Edge - Straighten would constrain it to the surface's edges. In the…
Yep tried it this morning on a real world example and it worked as expected (in that it didn't work). Sorry about that, it would be brilliant to have what you're describing.
Unfortunately, it doesn't work as hoped. The action also pushes the vertices in the other axis which changes the geometry too much in the cases I've tried it with. The reason it's worked cleanly in your example with the sphere is because you used Set Flow, which perfectly corrected the geometry of the sphere (you could…
In your examples what you want can be achieved by just using the make planar buttons under edit geometry...as long as its on that plane of course. Loop select, convert to verts, deselect the end verts, make planar, vertex snap back to the end verts.