Dan,
What I think I found was that the curve length is not equating to the height of the unfolded surface. For instance, you unfilded your curve length and made it planar, but what nis the length of the new curve created with the through points tools? This is where I was stuck. If you could "clip that original piece" out of the vase from a paper model, that curve length of the edge would be the same laid flat, wouldnt it?

If you refer to the model I posted in this thread:

http://moi3d.com/forum/index.php?webtag=MOI&msg=3042.11

You'll find a surface in there marked as Rhino. This surface is the result of rhino unfolding it. The resultant height of the unfolded surface is different than the curve length extracted. When I created my surface using the original curve length to unfold it, I ended up with an edge curve much longer than the original edge curve, which when trying to bend it back up, doesnt work.

I want to revisit this, as I went through a thread with Michael before regarding unfolding and was given the tools. I just need to figure out how to apply them in a different type model. It involves converting our numbers to Radians for the unfolding. THis number conversion will be critical to the unfolding process. However, My example I did was done with a cone and it may prove beyond me to do with a curved surface like this.

MoI has added expressions for doing the Cone Unfold now which will help with conversion, but we must know the math. View this thread to refer to the expressions using a simple cone for unfolding it quickly using MoI. The million dollar question will be if you can apply it to the Vase!

http://moi3d.com/forum/index.php?webtag=MOI&msg=2558.1