WALCOM 2019: WALCOM: Algorithms and Computation pp 277-288

# Efficient Algorithm for Box Folding

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

## Abstract

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.

## Keywords

Computational Origami Computational geometry Box folding

## Notes

### Acknowledgements

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

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© 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