Efficient Origami Construction of Orthogonal Terrains using Cross Section Evolution

We introduce a new method of origami construction, using cross section diagrams. Instead of beginning our construction from a 2-dimensional sheet of paper, we consider a 1-dimensional cross section moving forwards in time. We obtain conditions for the validity of a particular cross section evolution sequence, and prove that the resulting folded state is isometric to a flat sheet of paper. Subsequently, we use this machinery to design an efficient construction of orthogonal terrains, with arbitrary rational extrusion heights.