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Introduction to Computational Origami

The World of New Computational Geometry

  • Book
  • © 2020

Overview

Authors:
  1. Ryuhei Uehara

    1. JAIST, Ishikawa, Japan

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  • Introduces basic theorems and the latest research results

  • Focuses on origami from the point of view of computer science

  • Contains many unsolved problems, exercises, and answers to the exercises

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction to Unfolding

    1. Front Matter

      Pages 1-1
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    2. Unfolding

      • Ryuhei Uehara
      Pages 3-7

    3. Basic Knowledge of Unfolding

      • Ryuhei Uehara
      Pages 9-22

  3. Common Nets

    1. Front Matter

      Pages 23-23
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    2. Common Nets of Boxes

      • Ryuhei Uehara
      Pages 25-58

    3. Common Nets of (Regular) Polyhedra

      • Ryuhei Uehara
      Pages 59-76

  4. Algorithm and Complexity of Folding

    1. Front Matter

      Pages 77-79
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    2. One-Dimensional Origami Model and Stamp Folding

      • Ryuhei Uehara
      Pages 81-93

    3. Computational Complexity of Stamp Folding

      • Ryuhei Uehara
      Pages 95-120

  5. Advanced Problems

    1. Front Matter

      Pages 121-122
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    2. Bumpy Pyramids Folded from Petal Polygons

      • Ryuhei Uehara
      Pages 123-142

    3. Zipper-Unfolding

      • Ryuhei Uehara
      Pages 143-153

    4. Rep-Cube

      • Ryuhei Uehara
      Pages 155-180

    5. Common Nets of a Regular Tetrahedron and Johnson-Zalgaller Solids

      • Ryuhei Uehara
      Pages 181-195

    6. Undecidability of Folding

      • Ryuhei Uehara
      Pages 197-207

    7. Answers to Exercises

      • Ryuhei Uehara
      Pages 209-217

  6. Back Matter

    Pages 219-220
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Keywords

About this book

This book focuses on origami from the point of view of computer science. Ranging from basic theorems to the latest research results, the book introduces the considerably new and fertile research field of computational origami as computer science.

 Part I introduces basic knowledge of the geometry of development, also called a net, of a solid. Part II further details the topic of nets. In the science of nets, there are numerous unresolved issues, and mathematical characterization and the development of efficient algorithms by computer are closely connected with each other. Part III discusses folding models and their computational complexity. When a folding model is fixed, to find efficient ways of folding is to propose efficient algorithms. If this is difficult, it is intractable in terms of computational complexity. This is, precisely, an area for computer science research. Part IV presents some of the latest research topics as advanced problems. Commentaries on all exercises included in the last chapter. 

The contents are organized in a self-contained way, and no previous knowledge is required. This book is suitable for undergraduate, graduate, and even high school students, as well as researchers and engineers interested in origami.

Authors and Affiliations

  • JAIST, Ishikawa, Japan

    Ryuhei Uehara

About the author

Ryuhei Uehara is a professor in the School of Information Science at the Japan Advanced Institute of Science and Technology. After working as a researcher at Canon Inc., he joined Tokyo Woman's Christian University as an assistant professor. He was later a lecturer and associate professor at Komazawa University. He was a visiting scholar at the University of Waterloo (Canada), the Massachusetts Institute of Technology (USA), Simon Fraser University (Canada), Université libre de Bruxelles (Belgium), ETH  Zürich (Switzerland), and Universitat Politècnica de Catalunya (Spain).  His research interests include computational complexity, algorithms and data structures, and graph algorithms. He is especially engrossed in computational origami, games, and puzzles from the point of view of theoretical computer science. He is one of two translators of the New Martin Gardner Mathematical Library into Japanese.

Bibliographic Information

  • Book Title: Introduction to Computational Origami

  • Book Subtitle: The World of New Computational Geometry

  • Authors: Ryuhei Uehara

  • DOI: https://doi.org/10.1007/978-981-15-4470-5

  • Publisher: Springer Singapore

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer Nature Singapore Pte Ltd. 2020

  • Hardcover ISBN: 978-981-15-4469-9Published: 30 June 2020

  • Softcover ISBN: 978-981-15-4472-9Published: 30 June 2021

  • eBook ISBN: 978-981-15-4470-5Published: 29 June 2020

  • Edition Number: 1

  • Number of Pages: XVIII, 220

  • Number of Illustrations: 107 b/w illustrations, 25 illustrations in colour

  • Topics: Algorithm Analysis and Problem Complexity, Geometry, Mathematical and Computational Engineering

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