Geodesic
Design of Infinitesimally and Finitely Flexible Origami Based on Reciprocal Figures
Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 223-234.

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This paper investigates novel computational design method for infinitesimally and finitely foldable rigid origami based on solving a first-order folding mode, which can be represented by a reciprocal figure. We derive these graphical conditions from a matrix representation of rigid origami, and extend the conditions to cases when the surface includes holes. We propose an algorithm to obtain forms that satisfy the conditions and an interactive system to freely design infinitesimally foldable forms. We show design examples of shaky polyhedron and origami, and finitely foldable quadrivalent mesh origami.
Classification : 52C25, 52B10, 52B70, 53A17
Mots-clés : Origami, rigid origami, infinitesimal flexibility, shaky polyhedron, reciprocal figure 
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     author = {T. Tachi },
     title = {Design of {Infinitesimally} and {Finitely} {Flexible} {Origami} {Based} on {Reciprocal} {Figures}},
     journal = {Journal for geometry and graphics},
     pages = {223--234},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JGG_2012_16_2_JGG_2012_16_2_a8/}
}
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T. Tachi . Design of Infinitesimally and Finitely Flexible Origami Based on Reciprocal Figures. Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 223-234. http://geodesic.mathdoc.fr/item/JGG_2012_16_2_JGG_2012_16_2_a8/