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

副作用の生じない幾何摂動法の開発

Research Project

Project/Area Number 19650003
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field Software
Research InstitutionMeiji University (2009)
The University of Tokyo (2007-2008)

Principal Investigator

杉原 厚吉  Meiji University, 研究・知財戦略機構, 教授 (40144117)

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: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2008: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
Keywords数理工学 / アルゴリズム / 幾何学 / 記号摂動 / ラゲールドロネーメッシュ / 配線レイアウトチェック / 超摂動 / 副作用 / 幾何的退化 / 摂動 / 線分交差検出 / 超大規模集積回路 / 配線設計 / 異常交差 / 3次元ドロネー図 / メッシュ生成 / 体積0四面体 / ボロノイ図
Research Abstract

本研究の目的は,幾何的退化を解消する従来の記号摂動法が望ましくない副作用をもたらすことを反省し,除きたい退化だけを選択的に解消できる新しい摂動法を開発することである.初年度は,3次元ドロネーメッシュ生成問題を取り上げ,従来の摂動では体積0の四面体が生じるという副作用の防止法を開発した.2年度目は,線分交差判定問題における記号摂動の副作用防止方法を開発し,超大規模集積回路の配線チェックを,例外処理なしで実行できる方法を構築した.最終年度の本年度は,これまでの成果に基づいて,副作用を避けることのできる選択的例外解消法の一般論を追求した.その基本アイデアは,入力データに摂動を加えるという従来の方法をやめて,問題自身に摂動を加えるという発想の転換である.実際に,ドロネーメッシュで体積0の四面体を避けるためには,問題自身をラゲールドロネーメッシュ問題へ置き換え,配線の交差チェックでは,線分をひし形図形に置き換え,いずれの場合も問題自身を変更した.この発想の転換は,データに摂動を加える従来法に対して,「超摂動」とよぶことができる.この新しい考え方を適用することによって,多面体の集合演算における縮退頂点の位相的整合性の確保,コンピュータグラフィックスにおける立体表面模様のすき間解消などの手法を開発できた.これらの研究を通して,「例外は記号摂動によって解消できるからアルゴリズムの設計においては例外は考えなくてもよい」という記述の欺瞞性を告発することもできた.

Report

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

    (29 results)

All 2010 2009 2008 2007

All Journal Article (13 results) (of which Peer Reviewed: 11 results) Presentation (10 results) Book (5 results) Patent(Industrial Property Rights) (1 results) (of which Overseas: 1 results)

  • [Journal Article] How to cope with undesired side effects of symbolic perturbation2010

    • Author(s)
      Shuhei Takahashi, Kokichi Sugihara
    • Journal Title

      26th European Workshop on Computational. Geometry

      Pages: 261-264

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computer-aided generation of Escher-like Sky and Watter tiling patterns2009

    • Author(s)
      Kokichi Sugihara
    • Journal Title

      Journal of Mathematics and the Arts 3(4)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Boat-sail Voronoi diagram and its applications2009

    • Author(s)
      T.Nishida, K.Sugihara
    • Journal Title

      International Journal of Computational Geometry and Applications 19

      Pages: 425-440

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maximum eigenvalue problem for Escherization2009

    • Author(s)
      H.Koizumi, K.Sugihra
    • Journal Title

      Abstracts on the 7th Japan Conference on Computational Geometry and Graphs

      Pages: 53-54

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computer-aided design of pop-up books with two-dimensional V-hold structures2009

    • Author(s)
      T.Hara, K.Sugihara
    • Journal Title

      Abstracts on the 7th Japan Conference on Computational Geometry and Graphs

      Pages: 109-110

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Unsolved problems in robustness of geometric algorithms2009

    • Author(s)
      Kokichi Sugihara
    • Journal Title

      Computational Geometry and Discrete Mathematics, RIMS Kokyuroku 1641

      Pages: 99-105

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Computational Illusion-Toward Escher and Beyond Escher2009

    • Author(s)
      Kokichi Sugihara
    • Journal Title

      The Joint Conference of ASCM (Asian Symposium on Computer Mathematics) 2009 and MACIS (Mathematical Aspects of Computer And Information Sciences)

      Pages: 6-12

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Generation of cutter paths for hand matelial in wire EDM2008

    • Author(s)
      S. Imahori, M. Kushiya, T. Nakashima and K. Sugihara
    • Journal Title

      Journal of Material Processing Technology 206

      Pages: 453-461

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An energy efficient routing approach for wireless sensor network2008

    • Author(s)
      B. Haider and K. Sugihara
    • Journal Title

      Advances in Computer Science and Engineering 34

      Pages: 261-276

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Constructing centroidal Voronoi tessellations on surface meshes2008

    • Author(s)
      M. Moroguchi and k. Sugihara
    • Journal Title

      Generalized Voronoi Diagrams -A Geometry- Based Approach to Computational lntelligence

      Pages: 235-245

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sliver-free perturbation for the Delaunay tetrahedrization2007

    • Author(s)
      Kokichi Sugihara
    • Journal Title

      Computer-Aided Design 39

      Pages: 87-94

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 頂点追加による2次元DistMeshの等方性向上2007

    • Author(s)
      長井超慧, 杉原厚吉, 鈴木宏正
    • Journal Title

      日本応用数理学会論文誌 17

      Pages: 195-217

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 滑らかな境界を表現する等方的四面体メッシュ生成法2007

    • Author(s)
      長井超慧, 杉原厚吉
    • Journal Title

      日本応用数理学会論文誌 17

      Pages: 347-361

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Why is geometric computation difficult, and how can we overcome?2010

    • Author(s)
      Kokichi Sugihara
    • Organizer
      International Workshop on Numerical Verification and Its Applications (Invited)
    • Place of Presentation
      Hachijo Island, Japan
    • Year and Date
      2010-03-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] Selective perturbation in geometric computation2009

    • Author(s)
      Kokichi Sugihara
    • Organizer
      Canada-Japan Conference on Discrete and Computational Geoemtry (Invited)
    • Place of Presentation
      Tokyo, Japan
    • Related Report
      2009 Annual Research Report
  • [Presentation] 幾何計算駆け込み寺住職体験記2009

    • Author(s)
      杉原厚吉
    • Organizer
      第21回RAMPシンポジウム(招待講演)
    • Place of Presentation
      松江
    • Related Report
      2009 Annual Research Report
  • [Presentation] 錯視は,足りない情報を補おうとして失敗したときに生じる~「だまし絵」から「勘違い」まで2009

    • Author(s)
      杉原厚吉
    • Organizer
      錯視ワークショップ
    • Place of Presentation
      東京
    • Related Report
      2009 Annual Research Report
  • [Presentation] Computer aided design system for Escher-like tilings2009

    • Author(s)
      H. Koizumi and K. Sugihara
    • Organizer
      25th European Workshop on Computational Geometry
    • Place of Presentation
      ブリュッセル,ベルギー
    • Related Report
      2008 Annual Research Report
  • [Presentation] Discrete Voronoi diagrams on surface triangulations and a sampling condition for topological guarantee2008

    • Author(s)
      Masaki Moriguchi and Kokichi Sugihara
    • Organizer
      24th European Workshop on Computational Geometry (Euro CG' 08)
    • Place of Presentation
      フランス,ナンシー市
    • Year and Date
      2008-03-20
    • Related Report
      2007 Annual Research Report
  • [Presentation] Precision necessary for d-dimensional sphere Voronoi diagrams2008

    • Author(s)
      T. Nishida and K. Sugihara
    • Organizer
      the 5th lnternatiolal Symposium on Voronoi Diagrams in Science and Engineering
    • Place of Presentation
      キエフ,ウクライナ
    • Related Report
      2008 Annual Research Report
  • [Presentation] Toward superrobust geometric computation2008

    • Author(s)
      K. Sugihara
    • Organizer
      ACM Solid and Physical Modeling Symposium
    • Place of Presentation
      ニューヨーク
    • Related Report
      2008 Annual Research Report
  • [Presentation] Unsolved problems in robustness of geometric algorithms2008

    • Author(s)
      K. Sugihara
    • Organizer
      RIMS Workshop on Computational Geometry and Discrete Mathematics
    • Place of Presentation
      京都大学
    • Related Report
      2008 Annual Research Report
  • [Presentation] Restricted edge contractions in triangulations of the sphere with boundary2007

    • Author(s)
      Masaki Moriguchi and Kokichi Sugihara
    • Organizer
      The 19th Canadian Conference on Computational Geometry (CCCG2007)
    • Place of Presentation
      Ottawa, Canada
    • Year and Date
      2007-08-21
    • Related Report
      2007 Annual Research Report
  • [Book] 縄張りの数理モデル~ボロノイ図からの数理工学入門2009

    • Author(s)
      杉原厚吉
    • Total Pages
      166
    • Publisher
      共立出版
    • Related Report
      2009 Annual Research Report
  • [Book] タイリング描法の基本テクニック2009

    • Author(s)
      杉原厚吉
    • Total Pages
      143
    • Publisher
      誠文堂新光社
    • Related Report
      2009 Annual Research Report
  • [Book] なわばりの数理モデル-ボロノイ図からの数理工学入門2009

    • Author(s)
      杉原厚吉
    • Total Pages
      166
    • Publisher
      共立出版
    • Related Report
      2008 Annual Research Report
  • [Book] だまし絵の描き方入門2008

    • Author(s)
      杉原厚吉
    • Total Pages
      142
    • Publisher
      誠文堂新光社
    • Related Report
      2008 Annual Research Report
  • [Book] へんな立体2007

    • Author(s)
      杉原厚吉
    • Total Pages
      143
    • Publisher
      誠文堂新光社
    • Related Report
      2007 Annual Research Report
  • [Patent(Industrial Property Rights)] United States Patent2009

    • Inventor(s)
      Kokichi Sugihara, Masayoshi Sawai, Kohki Nagakura
    • Industrial Property Rights Holder
      Yazaki Corporation
    • Acquisition Date
      2009-08-18
    • Related Report
      2009 Annual Research Report
    • Overseas

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi