ABSTRACT
The mathematics of 3D vector spaces is described well in any basic course on computer graphics and rendering. The plate model of origami is very well suited to modeling a folded form when the crease pattern is known, so that the edge lengths and facet corner angles can be regarded as fixed and the only variables needed are the fold angles. One of the strengths of the truss model is that it naturally allows inclusion of stress/strain within the model by constructing the model as a constrained optimization. Both plate model and truss model descriptions can be used to construct realizable folded forms from a specified crease pattern. The crease assignments in the crease pattern are, of course, determined by the signs of the fold angles around each vertex in the folded form. Isometry captures the requirement that geodesic distance measured on the crease pattern and the folded form have the same length.
