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Unproject 3D shape so you can print it n paper and cut it out with scissors

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Imagine this i would like to somehow project the top curvy surface onto a 2D plane (lets assume its a 0,1,0 surf (a piece of paper) so i could print it on the printer and cut the shape off and bend it to original curve.

Simple projection of all verts wont work cause it wont preserve original size 


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