Abstract
We give an efficient algorithmic characterization of simple polygons whose edges can be aligned onto a common line, with nothing else on that line, by a sequence of all-layers simple folds. In particular, such alignments enable the cutting out of the polygon and its complement with one complete straight cut. We also show that these makeable polygons include all convex polygons possessing a line of symmetry.
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References
Arkin, E.M., Bender, M.A., Demaine, E.D., Demaine, M.L., Mitchell, J.S.B., Sethia, S., Skiena, S.S.: When can you fold a map? Computational Geometry: Theory and Applications 29(1), 23–46 (2004)
Bern, M., Demaine, E., Eppstein, D., Hayes, B.: A disk-packing algorithm for an origami magic trick. In: Origami3: Proceedings of the 3rd International Meeting of Origami Science, Math, and Education, Monterey, California, pp. 17–28 (March 2001); Improvement of version appearing in Proceedings of the International Conference on Fun with Algorithms, Isola d’Elba, Italy, pp. 32–42 (June 1998)
Demaine, E.D., Demaine, M.L., Lubiw, A.: Folding and Cutting Paper. In: Akiyama, J., Kano, M., Urabe, M. (eds.) JCDCG 1998. LNCS, vol. 1763, pp. 104–118. Springer, Heidelberg (2000)
Demaine, E.D., Demaine, M.L., Mitchell, J.S.B.: Folding flat silhouettes and wrapping polyhedral packages: New results in computational origami. Computational Geometry: Theory and Applications 16(1), 3–21 (2000)
Demaine, E.D., Devadoss, S.L., Mitchell, J.S.B., O’Rourke, J.: Continuous foldability of polygonal paper. In: Proceedings of the 16th Canadian Conference on Computational Geometry, Montréal, Canada, pp. 64–67 (August 2004)
Demaine, E.D., O’Rourke, J.: Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press (July 2007)
Melkman, A.A.: On-line construction of the convex hull of a simple polyline. Information Processing Letters 25(1), 11–12 (1987)
Wolter, J.D., Woo, T.C., Volz, R.A.: Optimal algorithms for symmetry detection in two and three dimensions. The Visual Computer 1(1), 37–48 (1985)
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Demaine, E.D. et al. (2011). Making Polygons by Simple Folds and One Straight Cut. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds) Computational Geometry, Graphs and Applications. CGGA 2010. Lecture Notes in Computer Science, vol 7033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24983-9_4
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DOI: https://doi.org/10.1007/978-3-642-24983-9_4
Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-642-24983-9
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