• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Towards 3D computational oeigami - theory and software development

Research Project

Project/Area Number 25330007
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Theory of informatics
Research InstitutionUniversity 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(Renkei-kenkyūsha) MINAMIDE Yasuhiko  東京工業大学, 情報理工学院, 教授 (50252531)
Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords計算モデル論 / 計算折紙 / 立体折紙 / 記号計算 / 自動定理証明 / ソフトウェア検証 / 計算幾何 / 折紙幾何定理の自動証明 / Geometric Algebra / 計算理論 / 幾何定理自動証明 / 立体モデル化 / 折紙の理論 / 幾何代数 / 定理証明支援系 / 折紙ソフトウェア / プログラム検証
Outline of Final Research Achievements

We studied 3D origami from a computational point of view. Namely, we modeled the 3D origami folding employing computer algebra systems and proof assistants to construct the theoretical framework for 3D origami technology. At the same time, we have developed software system that supports the development of the research on 3D origami based on E-origami system Eos developed prior to this research project. Specific outcomes are as follows.
(1) We analyzed and implemented knot folding. Knot folding requires the analysis of the overlapping of origami faces from the viewpoint of 3D origami. (2) We found that the geometric algebra is effective for modeling 3D origami. We developed a version of the geometric algebra for 3D origami modeling, and expressed in the geometric algebra the set of fold operations known as Huzita-Justin's set of elementary operations and verified its effectiveness. (3) We proposed an axiomatic system of n-dimensional origami, which generalizes the 2D and 3D origami.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (22 results)

All 2016 2015 2014 2013 Other

All Int'l Joint Research (5 results) Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Acknowledgement Compliant: 5 results,  Peer Reviewed: 4 results,  Open Access: 2 results) Presentation (6 results) (of which Int'l Joint Research: 1 results,  Invited: 3 results) Book (2 results) Remarks (3 results) Funded Workshop (1 results)

  • [Int'l Joint Research] エディンバラ大学(英国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] ティミショアラ西大学(ルーマニア)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] ヨハネスケプラー大学(オーストリア)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] エディンバラ大学(英国)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] ヨハネス ケプラー 大学(オーストリア)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Revisit of "Geometric Exercise in Paper Folding" from a Viewpoint of Computational Origami2016

    • Author(s)
      Tetsuo Ida
    • Journal Title

      Proc. SYNASC 2017

      Volume: - Pages: 23-28

    • DOI

      10.1109/synasc.2016.017

    • Related Report
      2016 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] A New Formalization of Origami in Geometric Algebra2016

    • Author(s)
      Tetsuo Ida, Jacques Fleuriot, Fadoua Ghourabi
    • Journal Title

      Proceedings of ADG 2016: Eleventh International Workshop on Automated Deduction in Geometry, Strasbourg, France, June 27-29, 2016

      Volume: hal-01334334

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Polygonal Knot by Computational Origami2015

    • Author(s)
      Tetsuo Ida and Fadoua Ghourabi
    • Journal Title

      Symmetry: Culture and Science

      Volume: 26 Pages: 171-187

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Interactive Construction and Automated Proof in Eos System with Application to Knot Fold of Regular Polygons2015

    • Author(s)
      Tetsuo Ida and Fadoua Ghourabi and Kazuko Takahashi
    • Journal Title

      Origami6: Proceedings of the Sixth International Meeting on Origami Science, Mathematics, and Education (6OSME). PartI: Mathematics, American Mathematical Society

      Volume: 1 Pages: 55-66

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Formalizing Polygonal Knot Origami2014

    • Author(s)
      Tetsuo Ida and Fadoua Ghourabi and Kazuko Takahashi
    • Journal Title

      Journal of Symbolic Computation

      Volume: 69 Pages: 93-108

    • DOI

      10.1016/j.jsc.2014.09.031

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] Reflection on Geometric Exercises in Origami2016

    • 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
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Verified Construction of Polygonal Knots2015

    • Author(s)
      Tetsuo Ida and Fadoua Ghourabi
    • Organizer
      The 12th International Mathematica Symposium (IMS 2015)
    • Place of Presentation
      Prague, Czech
    • Year and Date
      2015-01-12 – 2015-01-14
    • Related Report
      2014 Research-status Report
  • [Presentation] Huzita's basic origami fold in geometric algebra2014

    • Author(s)
      Tetsuo Ida
    • Organizer
      The 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2014)
    • Place of Presentation
      Timisoara, Rumania
    • Year and Date
      2014-09-22 – 2014-09-25
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Automated Construction and Proving of Knot Fold by Eos System2014

    • Author(s)
      Fadoua Ghourabi and Tetsuo Ida and Kazuko~Takahashi
    • Organizer
      The 6th International Conference on Origami in Science, Mathematics and Education and Folding Convention (6OSME)
    • Place of Presentation
      東京大学、東京
    • Year and Date
      2014-08-10 – 2014-08-13
    • Related Report
      2014 Research-status Report
  • [Presentation] Knot Fold of Regular Polygons: Computer-Assisted Construction and Verification2013

    • Author(s)
      Tetsuo Ida, Fadoua Ghourabi, and Kazuko Takahashi
    • Organizer
      15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2013)
    • Place of Presentation
      West University of Timisoara, Timisoara, Rumania
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Logical and Algebraic Views of a Knot Fold of a Regular Heptagon2013

    • Author(s)
      Fadoua Ghourabi, Tetsuo Ida and Kazuko Takahashi
    • Organizer
      Fifth International Symposium on Symbolic Computation in Software Science (SCSS 2013)
    • Place of Presentation
      Research Institute for Symbolic Computation. Hagenberg, Austria
    • Related Report
      2013 Research-status Report
  • [Book] Post-Proceedings of 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, {SYNASC} 2016, Timisoara, Romania, September2016

    • 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
    • Related Report
      2016 Annual Research Report
  • [Book] Automated Deduction in Geometry, 9th International Workshop, ADG 2012, Edinburgh, UK, September 17-19, 2012. Revised Selected Papers, Series: Lecture Notes in Computer Science, Vol. 7993 Subseries: Lecture Notes in Artificial Intelligence2013

    • Author(s)
      Tetsuo Ida and Jacques Fleuriot (Eds.)
    • Total Pages
      199
    • Publisher
      Springer Verlag
    • Related Report
      2013 Research-status Report
  • [Remarks] Eos Project

    • Related Report
      2016 Annual Research Report
  • [Remarks] EOS Project

    • Related Report
      2014 Research-status Report
  • [Remarks] Eos Project

    • Related Report
      2013 Research-status Report
  • [Funded Workshop] The 7th International Symposium on Symbolic Computation in Software Science2016

    • Place of Presentation
      お茶の水女子大学,東京
    • Year and Date
      2016-03-28
    • Related Report
      2015 Research-status Report

URL: 

Published: 2014-07-25   Modified: 2022-02-16  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi