Paper by Erik D. Demaine

Reference:

Zachary Abel, Jason Cantarella, Erik D. Demaine, David Eppstein, Thomas C. Hull, Jason S. Ku, Robert J. Lang, and Tomohiro Tachi, “Rigid Origami Vertices: Conditions and Forcing Sets”, Journal of Computational Geometry, volume 7, number 1, 2016, pages 171–184.

Abstract:

We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as in the unassigned case. We also illustrate the utility of this result by applying it to the new concept of minimal forcing sets for rigid origami models, which are the smallest collection of creases that, when folded, will force all the other creases to fold in a prescribed way.

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