When cutting potatoes into chunks, for something like a stew, I often find myself thinking about this problem, and how I would write a program for a robot to do it.
They are fairly well approximated as ellipsoids of different sizes. Typically, I want pieces around half the volume of the smallest potatoes, but with the range of sizes, this means cutting the larger ones into at least 5 pieces.
While it would be simple to make parallel slices giving equal volume, these would have very different shape to the halved smalls. Some can be quartered to give nice chunks, others into thirds with 2 perpendicular cuts...
