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3D Origami Design based on Tucking Molecule

This paper presents a new approach for folding a piece of paper into an arbitrary three-dimensional polyhedral surface based on ”tucking molecules.” The approach is to align the polygons of the three-dimensional surface onto a convex region of a plane and fill the blank area between the polygons with ”tucking molecules.” Tucking molecules are aligned between segments and vertices of the polygons, and ”paste” them together by being folded flat. We propose a novel method for generating crease pattern for tucking molecules. Necessary and sufficient conditions to enable construction of the required surface are also shown. Additionally we show that the necessary conditions can be represented in inequality conditions by using the ”tuck proxies.”