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

折紙計算論に基づく折り可能性の考究と折紙手法発見

Research Project

Project/Area Number 19650001
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field Fundamental theory of informatics
Research InstitutionUniversity of Tsukuba

Principal Investigator

井田 哲雄  University of Tsukuba, 大学院・システム情報工学研究科, 教授 (70100047)

Co-Investigator(Kenkyū-buntansha) MARIN Mircea  筑波大学, 大学院・システム情報工学研究科, 講師 (60396603)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2009: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2008: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords折紙計算論 / 記号計算 / 定理自動証明 / 制約問題 / 計算折紙 / 計算モデル / 計算幾何 / グロブナ基底 / 自動定理証明
Research Abstract

●折紙の理論を構築し,国際雑誌Journal of Symbolic Computationで発表した.この理論では,面の集合と面同士の隣接関係と重なり関係からなる構造により,抽象折紙を定義し,抽象折紙の折り操作を抽象書換え系の書換え操作でモデル化する.さらに,コンピュータの実装に向けて,抽象折紙をラベル付きハイパーグラフで表現し,抽象書換え系をグラフ書き換え系で実現する.さらに,この理論を実装し,本研究の前年度までに構築されているEos(E-Origami System)に組み込んだ.グラフ書き換えのアルゴリズムについても,新たに開発するとともに,アルゴリズムの正当性の基礎になるいくつかの定理を証明した.グラフ書き換えによる折紙の構築過程を可視化することに成功するとともに,折紙をグラフとして見たときの構造の特徴をも明らかにした.
●折紙定理のコンピュータによる自動証明の高速化のために,Eosの定理証明モジュールに様々な方法を組み込んだ.たとえば,証明で用いるグレブナ基底の計算に折紙構築履歴に依存した単項式順序を組み込むこと,折紙幾何に特化した証明ドキュメントの自動生成がある.これらの改良により,折紙定理証明の効率は著しく向上した.たとえば,Morleyの定理の自動証明には当初17時間もかかったが,10分程度で完了するようになった.
●上記EOSシステムのウェブ・インタフェイスの構築研究を継続して行い,ウェブ・インタフェイスの改良をおこなった.
●藤田による折紙の公理をウー・リットの方法で代数的に解釈し直し,折紙の構築の基本操作を与える藤田の公理の代数的な性質を解析した.ウー・リットの手法で用いる特性集合を調べることにより,藤田の公理が記述する幾何の縮退条件を代数的に求めることができた.

Report

(3 results)
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (23 results)

All 2010 2009 2008 2007 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (9 results) Book (1 results) Remarks (2 results)

  • [Journal Article] Origami Fold as Algebraic Graph Rewriting2010

    • Author(s)
      Ida, T, Takahashi, H
    • Journal Title

      Journal of Symbolic Computation 45

      Pages: 393-413

    • NAID

      120007138181

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Origami Fold as Algebraic Graph Rewriting2009

    • Author(s)
      Ida, T, Takahashi, H
    • Journal Title

      Proceedings of the 24th annual ACM, Symposium on Applied Computing(SAC 2009)

      Pages: 1132-1138

    • NAID

      120007138181

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symbolic and Algebraic Methods in Computational Origami2009

    • Author(s)
      Ida, T
    • Journal Title

      Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation

      Pages: 3-4

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Graph Rewriting in Computational Origami2009

    • Author(s)
      Tetsuo Ida
    • Journal Title

      Proceedings of the 10th International Sympo sium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2008), IEEE

      Pages: 20-27

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Origami Fold as Algebraic Graph Rewriting2009

    • Author(s)
      Tetsuo Ida, Hidekazu Takaha shi
    • Journal Title

      Proceedings of the 24th annual ACM, Symposium on Applied Computing (SAC 2009)

      Pages: 1132-1138

    • NAID

      120007138181

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computational Origami Construction as Constraint Solving and Rewriting2008

    • Author(s)
      Tetsuo Ida, Mircea Marin,Hidekazu Takahashi, Fadoua Ghourabi
    • Journal Title

      Electronic Notes in Theoretical Computer Science 216

      Pages: 31-44

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computational Origami Environment on the Web2008

    • Author(s)
      Asem Kasem and Tetsuo Ida
    • Journal Title

      Frontiers of Computer Science in China. 2

      Pages: 39-54

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Modelling Origami for Computational Construction and Beyond2007

    • Author(s)
      Tetsuo Ida, Hidekazu Takahashi, Mircea Marin and Fadoua Ghourabi
    • Journal Title

      International Conference on Computational Science and Its Applications 2007(ICCSA 2007)Lecture Notes in Computer Science, Springer 4706

      Pages: 653-665

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computational Origami Construction as Constraint Solving and Rewriting2007

    • Author(s)
      Tetsuo Ida, Mircea Marin, Hidekazu Takahashi and Fadoua Ghourabi
    • Journal Title

      Proceedings of the 16th International Workshop on Functional and(Constraint)Logic Programming(WELP 2007)

      Pages: 139-152

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Modeling Origami and Beyond2007

    • Author(s)
      Tetsuo Ida
    • Journal Title

      Proceedings of SYNASC 2007, 9th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE Computer Society

      Pages: 13-13

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A System of Web Services for Symbolic Computation2007

    • Author(s)
      Monem Naifer, Asem Kasem and Tetsuo Ida
    • Journal Title

      Proceedings of the 5th Asian Workshop on Foundations of Software, Beihang University

      Pages: 145-152

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Symbolic and Algebraic Methods in Computational Origami2009

    • Author(s)
      Ida, T
    • Organizer
      ISSAC2009
    • Place of Presentation
      KIAS(Korea Institute for Advanced Study)韓国
    • Year and Date
      2009-07-30
    • Related Report
      2009 Annual Research Report
  • [Presentation] Experiences with Web Environment Origamium2008

    • Author(s)
      Asem Kasem, Tetsuo Ida
    • Organizer
      日本ソフトウェア科学会第25回大会
    • Place of Presentation
      筑波大学(東京キャンパス)
    • Year and Date
      2008-09-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] グラフ書換による計算折り紙のモデル化と実現2008

    • Author(s)
      高橋英和、井田哲雄
    • Organizer
      日本ソフトウェア科学会第25回大会
    • Place of Presentation
      筑波大学(東京キャンパス)
    • Year and Date
      2008-09-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Computational Origami of Angle Quintisection2008

    • Author(s)
      Fadoua Ghourabi, Tetsuo Ida . Hidekazu Takahashi
    • Organizer
      日本ソフトウェア科学会第25回大会
    • Place of Presentation
      筑波大学(東京キャンパス)
    • Year and Date
      2008-09-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Graph Rewriting in Computational Origami2008

    • Author(s)
      Tetsuo Ida, Hidekazu Takahashi
    • Organizer
      Austrian-Japanese Workshop on Symbolic Computation in Software Science (SCSS 2008)
    • Place of Presentation
      RISC, Hagenberg, Austria
    • Year and Date
      2008-07-13
    • Related Report
      2008 Annual Research Report
  • [Presentation] Computational Origami of Angle Quintisection2008

    • Author(s)
      Fadoua Ghourabi, Tetsuo Ida, Hidekazu Takahashi
    • Organizer
      Austrian-Janese Workshop on Symbolic Computation in Software Science (SCSS 2008).
    • Place of Presentation
      RISC, Hagenberg, Austria
    • Year and Date
      2008-07-13
    • Related Report
      2008 Annual Research Report
  • [Presentation] Experiences with Web Environment Origamium: Examples and Applications2008

    • Author(s)
      Asem Kasem, Tetsuo Ida
    • Organizer
      Austrian-Japanese Workshop on Symbolic Computation in Software Science (SCSS 2008).
    • Place of Presentation
      RISC, Hagenberg, Austria
    • Year and Date
      2008-07-13
    • Related Report
      2008 Annual Research Report
  • [Presentation] webOrigami2: A System for Origami Construction and Proving Using Web 2.0 Technologies2007

    • Author(s)
      Asem Kasem, Hidekazu Takahashi, Mircea Marin and Tetsuo Ida
    • Organizer
      日本ソフトウェア科学会第24回大会
    • Place of Presentation
      奈良先端科学技術大学院大学
    • Year and Date
      2007-09-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] Analysis of Layers of Faces in Computational Origami Modeling2007

    • Author(s)
      Fadoua Ghourabi, Hidekazu. Takahashi, Tetsuo Ida
    • Organizer
      日本ソフトウェア科学会第24回大会
    • Place of Presentation
      奈良先端科学技術大学院大学
    • Year and Date
      2007-09-14
    • Related Report
      2007 Annual Research Report
  • [Book] WEBEOS:A System for Origami Construction and Proving on the Web2008

    • Author(s)
      Tetsuo Ida and Asem Kasem
    • Total Pages
      5
    • Publisher
      The INTERNATIONAL INSTITUTE for ADVANCED STUDIES in SYSTEMS RESEARCH and CYBERNETICS, Tecumseh, Canada
    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www2.score.cs.tsukuba.ac.jp/projects/origami

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www2.score.cs.tsukuba.ac.jp/bibliography_view

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi