I've wondered if this would be applicable to data analysis, to automatically generate a 1-d condition based on a hand-drawn 2-d condition. Each fold is equivalent to a piecewise linear transformation, and the cut is equivalent to a 1-d condition.

This would allow for a series of similarly shaped regions to be defined, all with the same transformation, but with different cut heights.

The linked video lecture goes over the problem visually: http://courses.csail.mit.edu/6.849/fall10/lectures/L07.html