Efficient Algorithm for Box Folding
For a given polygon P and a polyhedron Q, the folding problem asks if Q can be obtained from P by folding it. This simple problem is quite complicated, and there is no known efficient algorithm that solves this problem in general. In this paper, we focus on the case that Q is a box, and the size of Q is not given. That is, input of the box folding problem is a polygon P, and it asks if P can fold to boxes of certain sizes. We note that there exist an infinite number of polygons P that can fold into three boxes of different sizes. In this paper, we give a pseudo polynomial time algorithm that computes all possible ways of folding of P to boxes.
KeywordsComputational Origami Computational geometry Box folding
A part of this research is supported by JSPS KAKENHI Grant Number JP17H06287 and 18H04091.
- 1.Abel, Z.R., Demaine, E.D., Demaine, M.L., Ito, H., Snoeyink, J., Uehara, R.: Bumpy Pyramid Folding. Computational Geometry: Theory and Applications (2018, accepted). https://doi.org/10.1016/j.comgeo.2018.06.007
- 2.Akiyama, J.: Tile-Makers and Semi-Tile-Makers. The Mathematical Association of Amerika, Monthly 114, pp. 602–609, August–September 2007Google Scholar
- 5.Buchin, K., et al.: On rolling cube puzzles. In: 19th Canadian Conference on Computational Geometry (CCCG 2007), pp. 141–144 (2007)Google Scholar
- 7.Dürer, A.: Underweysung der messung, mit den zirckel un richtscheyt, in Linien ebnen unnd gantzen corporen (1525)Google Scholar
- 8.Horiyama, T., Mizunashi, K.: Folding orthogonal polygons into rectangular boxes. In: Proceedings of the 19th Japan-Korea Joint Workshop on Algorithms and Computation (WAAC 2016) (2016)Google Scholar
- 10.Mitani, J., Uehara, R.: Polygons folding to plural incongruent orthogonal boxes. In: Canadian Conference on Computational Geometry (CCCG 2008), pp. 39–42 (2008)Google Scholar