It's best to use curve-to-curve flow to make sure you get an accurate result. Surface-to-surface flow works inside the UV parameter space of the surface, if the surface has things like some control points spaced out larger than others it will influence the result. But curve to curve flow works by distance traveled along the curve and not parameterization.
So for your case here I used Ctrl+drag to drag off a copy of one edge, then squeezed it in the Top view using "flat" snap ( http://moi3d.com/forum/index.php?webtag=MOI&msg=3378.4) to make a planar silhouette of the surface:
Then draw in a line like this:
Now select the surface, and run Transform > Deform > Flow. At the first prompt that says "Select base curve or surface", click the surface silhouette. Click on it somewhere near the bottom.
Then on the next prompt that says "Select target curve near matching end", click the line somwhere nearby the end where it touches the surface silhouette. That should generate a flattened surface:
But you would need to use Rhino's UnrollSrf command for other cases, this way will only work for something like this that has all ruling lines in a single common direction.
- Michael
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