The first thing that came to my mind when I saw that you can upload an equation on this site is, 'I wonder what the equation is for a duck?'
You may also want to consider trying to arrange the cut-outs so that the flat edge aligns with the flat edge of the page. Might result in less cutting for the user.
I think I'll try to create an actual set-design using the generator/plotter.
Thanks for sharing this!