# Introduction to Computational Origami

## The World of New Computational Geometry

• Ryuhei Uehara
Book

1. Front Matter
Pages i-xviii
2. ### Introduction to Unfolding

1. Front Matter
Pages 1-1
2. Ryuhei Uehara
Pages 3-7
3. Ryuhei Uehara
Pages 9-22
3. ### Common Nets

1. Front Matter
Pages 23-23
2. Ryuhei Uehara
Pages 25-58
3. Ryuhei Uehara
Pages 59-76
4. ### Algorithm and Complexity of Folding

1. Front Matter
Pages 77-79
2. Ryuhei Uehara
Pages 81-93
3. Ryuhei Uehara
Pages 95-120
5. ### Advanced Problems

1. Front Matter
Pages 121-122
2. Ryuhei Uehara
Pages 123-142
3. Ryuhei Uehara
Pages 143-153
4. Ryuhei Uehara
Pages 155-180
5. Ryuhei Uehara
Pages 181-195
6. Ryuhei Uehara
Pages 197-207
7. Ryuhei Uehara
Pages 209-217
6. Back Matter
Pages 219-220

### Introduction

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.

### Keywords

Computational Origami Computational Geometry Algorithms Origami Geometry Folding Unfolding

#### Authors and affiliations

1. 1.JAISTIshikawaJapan

### Bibliographic information

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