Origami tesselations: folding algorithms from local to global

Abstract

Rigid Origami folding surfaces have very interesting qualities for Architecture and Engi-neering for their geometric, structural and elastic qualities. The ability to turn a flat element, isotropic, without any structural capacity, into a self-supporting element through folds in the material opens the door to a multitude of uses. Besides that the intrinsic geometry of the crease pattern may allow the surface to assume doubly curved forms while the flat element, before the folding, could never do it without the deformation of the material. (Schenk, 2011) (Demaine, 2011). The main objective of this PhD research is to reach a workflow from the definition of the geometry of the flat foldable surfaces to their implementation on a construction site. This paper will address mainly the steps taken to the parameterization of the Rigid Origami ge-ometries. We intend to establish a method to simulate the folding of regular crease pat-terns (tessellations) by understanding the geometric operations on the smallest set of faces (local) that can be reproduced to simulate the whole group (global).