algorithmic modeling for Rhino
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The top surface (the planar one) is actually a trimmed surface such that the bounding box of the curve is found and then the surface gets trimmed to fit the closed curve.
The 4 point surface has its UV domain based on the 4 points so it divides perfectly.
you could explode the curve and make an "edge surface" but that seems like a silly workaround
the way you can verify the trimming is to plug the surface directly into a panel and see if it says "trimmed" or "untrimmed" surface
if it is "trimmed" then the UV coordinates are simply falling off the surface.
good luck
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