Below is an image of the surfaces to be cut. These were modeled in Rhino. Each of these will be cut with a wire that's stretched between two sides of a rigid frame. Thus the wire stays in a straight line. This means that each shape needs to be a ruled surface. However, as you can see, one can achieve quite a bit of curvature using only a straight line.
Here's the file loaded into Mastercam. Mastercam and Robotmaster software are used to set up and preview the cuts. All that's necessary to cut are two curves, each with the same number of segments.
Here's the robot in the Taubman College of Architecture Fab Lab. The foam block is clamped in place and ready to go.
These are the pieces which were cut from the top of the block.
The curves used to cut them are shown below:
In this image, the middle pieces were cut using very simple geometry:
Two lines at 45 degrees, out phase, are all that was required:
This next piece was cut using two pairs of parabolas.
Here are all the blocks lined up.