Development of methods for computational origami based on geometric algebra

• Project/Area Number: 16K00008
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: University of Tsukuba
• Principal Investigator: IDA Tetsuo 筑波大学, システム情報系(名誉教授), 名誉教授 (70100047)
• Co-Investigator(Kenkyū-buntansha): Ghourabi Fadoua お茶の水女子大学, 理学部, 学部教育研究協力員 (30709324)
• Project Period (FY): 2016-04-01 – 2023-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 記号計算 / Geometric Algebra / 折紙計算論 / 折紙プログラミング / 計算折紙システム / 自動定理証明 / 計算幾何学 / 計算折紙 / geometric algebra / 折紙幾何学 / 計算折紙の理論とソフトウェアシステム / 記号代数計算 / 書き換えシステム / 幾何代数 / 折紙定理証明 / 立体折紙 / 折紙の形式化 / 折紙 / 幾何定理証明 / 記号代数 / 計算理論 / 計算幾何 / 幾何定理自動証明 / 立体モデル化

Outline of Final Research Achievements

In this research, we aimed to abstract traditional origami and extend it to three and more dimensions. In particular, we focused on a computer implementation of geometric algebra, allowing it to be used as part of an algebraic model of our computational origami system Eos. We also presented the idea of cutting and gluing the edges of the folding faces. We showed that traditional folding could be realized by combining it with the Huzita-Justin folding method.
We received the Wolfram Innovator Award 2022 and are leading the research and development of symbolic computation systems for computational origami.

Academic Significance and Societal Importance of the Research Achievements

折紙は我が国で独自に発展した工芸であるとともに、幾何学における幾何オブジェクトの構成の基本手順を与える重要な学問である。折紙の手法を深く研究することにより、複雑な物体を構築する上での工学的な手法の開発に導くことができる。これを可能にするには、折紙の数学的なモデル化が不可欠である。本研究では、我々がすでに開発してきた、折紙の代数モデルをgeometric algebra (幾何代数)で拡張し、実用につながる強力な折紙手法の提示ができた。

Research Products

• [Int'l Joint Research] University of Waterloo(Canada)
• [Int'l Joint Research] ウオータルー大学(カナダ)
• [Int'l Joint Research] ウィーン工科大学(オーストリア)
• [Int'l Joint Research] ヨハネスケプラー大学(オーストリア)
• [Journal Article] A New Modeling of Classical Folds in Computational Origami (2021)
  • Author(s): Tetsuo Ida and Hidekazu Takahashi
  • Journal Title: EPTCS Volume: 352 Pages: 41-53
  • DOI: 10.4204/eptcs.352.5
  • Peer Reviewed / Open Access
• [Journal Article] Foreword, Formalization of geometry, automated and interactive geometric reasoning (2019)
  • Author(s): Pascal Schreck, Tetsuo Ida and Laura Kovacs
  • Journal Title: Annals of Mathematics nd Artificial Intelligence Volume: 85 Issue: 2-4 Pages: 71-72
  • DOI: 10.1007/s10472-019-9617-2
  • Int'l Joint Research
• [Journal Article] Models of computation for origami (2018)
  • Author(s): Tetsuo Ida
  • Journal Title: SYNASC 2017, post-proceedings Volume: 印刷中
• [Journal Article] Toward non-flat geometrical origami folds with Eos system (2018)
  • Author(s): Fadoua Ghourabi
  • Journal Title: SYNASC 2017, post-proceedings Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Origami folds in higher-dimension (2017)
  • Author(s): Tetsuo Ida、Stephen Watt
  • Journal Title: EPiC Series in Computing Volume: 45 Pages: 83-95
  • DOI: 10.29007/n76q
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Revisit of "Geometric Exercise in Paper Folding" from a Viewpoint of Computational Origami (2016)
  • Author(s): Tetsuo Ida
  • Journal Title: Proc. SYNASC 2017 Volume: - Pages: 23-28
  • DOI: 10.1109/synasc.2016.017
  • Acknowledgement Compliant
• [Journal Article] A New Formalization of Origami in Geometric Algebra (2016)
  • Author(s): Tetsuo Ida, Jacques Fleuriot, Fadoua Ghourabi
  • Journal Title: Proceedings of ADG 2016: Eleventh International Workshop on Automated Deduction in Geometry Volume: hal-01334334
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] Virtual Origami (2022)
  • Author(s): Tetsuo Ida
  • Organizer: Wolfram Technology Conference
  • Int'l Joint Research / Invited
• [Presentation] Computation models in e-origami system Eos (2021)
  • Author(s): Tetsuo Ida
  • Organizer: SYNASC 2021
  • Int'l Joint Research / Invited
• [Presentation] Reflection on Geometric Exercises in Origami (2016)
  • Author(s): Tetsuo Ida
  • Organizer: The 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2016)
  • Place of Presentation: Timisoara, Rumania
  • Year and Date: 2016-09-24
  • Int'l Joint Research / Invited
• [Book] An Introduction to Computational Origami (2020)
  • Author(s): Tetsuo Ida
  • Total Pages: 217
  • Publisher: Springer
  • ISBN: 9783319591889
• [Book] Post-Proceedings of 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, {SYNASC} 2016, Timisoara, Romania, September 24-27, 2016 (2016)
  • Author(s): James H. Davenport, Viorel Negru, Tetsuo Ida,Tudor Jebelean, Dana Petcu,Stephen M. Watt,Daniela Zaharie
  • Total Pages: 476
  • Publisher: {IEEE} Computer Society
• [Remarks] 2022 Wolfram Innovator賞 受賞者
  • URL: https://blog.wolfram.com/2022/10/19/announcing-the-2022-wolfram-innovator-award-winners/
• [Remarks] Eos Project
  • URL: https://www.i-eos.org
• [Remarks] Eos Project
• [Remarks] Eos Project
• [Remarks] Eos-project
• [Remarks] Eos Project
  • URL: http://www.i-eos.org
• [Funded Workshop] SCSS 2017 (Symbolic Computation and Software Science 2017) (2017)
• [Funded Workshop] First International Workshop on Computational Origami and Applicationss (2016)
  • Place of Presentation: Vienna, Austria