Efficient Enumeration of Flat-Foldable Single Vertex Crease Patterns

We investigate enumeration of distinct flat-foldable crease patterns under the following assumptions: positive integer n is given; every pattern is composed of n lines incident to the center of a sheet of paper; every angle between adjacent lines is equal to 2π/n; every line is assigned one of “moun...

Full description

Saved in:
Bibliographic Details
Published inIEICE Transactions on Information and Systems Vol. E102.D; no. 3; pp. 416 - 422
Main Authors OUCHI, Koji, UEHARA, Ryuhei
Format Journal Article
LanguageEnglish
Published Tokyo The Institute of Electronics, Information and Communication Engineers 01.03.2019
Japan Science and Technology Agency
Subjects
Algorithms
computational origami
Enumeration
enumeration algorithm
flat foldability
Kawasaki theorem
Maekawa theorem
Mountains
Theorems
Online AccessGet full text

Cover

More Information
Summary:We investigate enumeration of distinct flat-foldable crease patterns under the following assumptions: positive integer n is given; every pattern is composed of n lines incident to the center of a sheet of paper; every angle between adjacent lines is equal to 2π/n; every line is assigned one of “mountain,” “valley,” and “flat (or consequently unfolded)”; crease patterns are considered to be equivalent if they are equal up to rotation and reflection. In this natural problem, we can use two well-known theorems for flat-foldability: the Kawasaki Theorem and the Maekawa Theorem in computational origami. Unfortunately, however, they are not enough to characterize all flat-foldable crease patterns. Therefore, so far, we have to enumerate and check flat-foldability one by one using computer. In this study, we develop the first algorithm for the above stated problem by combining these results in a nontrivial way and show its analysis of efficiency.
ISSN:0916-8532
1745-1361
DOI:10.1587/transinf.2018FCP0004