All shapes in origami

Take a piece of paper, fold it into any flat origami, and make one complete straight cut (i.e., a cut along a line). Now unfold the pieces, and see what you get. Are all shapes possible? Refering back to the original sheet of paper, what patterns of cuts can be achieved by this process?

[...]

The theorem is that every pattern (plane graph) can be made by folding and one complete straight cut. This includes single (possibly nonconvex) polygons, multiple disjoint polygons, nested polygons, adjoining polygons, and even floating line segments and points.