Efficient Algorithm for Box Folding

  • Koichi Mizunashi
  • Takashi Horiyama
  • Ryuhei UeharaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11355)


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.


Computational Origami Computational geometry Box folding 



A part of this research is supported by JSPS KAKENHI Grant Number JP17H06287 and 18H04091.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Koichi Mizunashi
    • 1
  • Takashi Horiyama
    • 1
  • Ryuhei Uehara
    • 2
    Email author
  1. 1.Graduate School of Science and EngineeringSaitama UniversitySakuraJapan
  2. 2.School of Information ScienceJapan Advanced Institute of Science and Technology (JAIST)NomiJapan

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