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Tiling Engineering: Computation of Tiles Close to Desired Figures

Research Project

Project/Area Number 24360039
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Engineering fundamentals
Research InstitutionMeiji University

Principal Investigator

SUGIHARA KOKICHI  明治大学, 研究・知財戦略機構, 教授 (40144117)

Co-Investigator(Kenkyū-buntansha) IMAHORI SHINJI  中央大学, 理工学部, 教授 (90396789)
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥17,550,000 (Direct Cost: ¥13,500,000、Indirect Cost: ¥4,050,000)
Fiscal Year 2015: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2014: ¥5,850,000 (Direct Cost: ¥4,500,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2013: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Keywords数理工学 / タイル貼り / 図地反転 / 錯視アート / エッシャー / タイル / 図地反転アート / エッシャー化 / ロバスト幾何計算 / 錯視効果 / 多義立体 / フットステップ錯視 / 単一タイルアート / タイリング可能条件 / 格子パターン
Outline of Final Research Achievements

Algorithms for creating tiling patterns were constructed for two types of artistic styles of tiling proposed by Dutch artist Escher. The first style is a regular subdivision of the plane. An existing algorithm for finding a tilable pattern closest to an input figure was improved so that the important features of the input figure are preserved in finding the closeset tilable pattern. The second style is a figure-ground reversal in Escher's artpiece "Sky and Water".
The figure-ground interaction of two figures was extended to the interaction of three figures. Moreover, the figure-ground reversal was extended to the reversal depending on the view directions, while Eshcer's original style is the reversal depending on the locations. The resulting algorithms can be used by non-specialists to create artistic patterns automatically.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (36 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (7 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 7 results,  Open Access: 2 results,  Acknowledgement Compliant: 3 results) Presentation (24 results) (of which Int'l Joint Research: 8 results,  Invited: 4 results) Book (2 results) Remarks (1 results) Patent(Industrial Property Rights) (2 results)

  • [Journal Article] Approximation of fruit skin patterns using spherical Voronoi diagrams2016

    • Author(s)
      S. Chaidee and K. Sugihara
    • Journal Title

      Pattern Analysis and Applications, Online version

      Volume: 21 Issue: 3 Pages: 783-795

    • DOI

      10.1007/s10044-016-0534-2

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Escher-like Tilings with Weights2016

    • Author(s)
      S. Imahori, S. Kawade, Y. Yamakata
    • Journal Title

      Post-Conference Proceedings of JCDCG^2 2015, LNCS

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Height reversal generated by rotation around a vertical axis2015

    • Author(s)
      K. Sugihara
    • Journal Title

      Journal of Mathematical Psychology

      Volume: 68-69 Pages: 7-12

    • DOI

      10.1016/j.jmp.2015.07.001

    • NAID

      120006552169

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Ambiguous cylinders: A new class of impossible objects2015

    • Author(s)
      K. Sugihara
    • Journal Title

      Computer Aided Drafting, Design and manufacturing

      Volume: 25

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A single solid that can generate two impossible motion illusions2014

    • Author(s)
      K. Sugihara
    • Journal Title

      Perception

      Volume: 43 Issue: 9 Pages: 1001-1005

    • DOI

      10.1068/p7700

    • NAID

      120006552168

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] フットステップ錯視アートの設計法2013

    • Author(s)
      小野隼,友枝明保,杉原厚吉
    • Journal Title

      日本応用数理学会論文誌

      Volume: 23 Pages: 585-600

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Local-Search Based Algorithm for the Escherization Problem2012

    • Author(s)
      S. Imahori, S. Sakai
    • Journal Title

      Proceedings of the IEEE International Conference on Industrial Engineering and Engineering Management

      Volume: (Outstanding Conference Paper Award) Pages: 151-155

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] How Does Human Interpret Images? --- Week Points of Our Visual Systems Learned by Mathematical Study of Optical Illusion2015

    • Author(s)
      K. Sugihara
    • Organizer
      the 25th International Conference on Artificial Reality and Telexistence and the 20th Eurographics Symposium on Virtual Environments (ICAT-EGVE 2015)
    • Place of Presentation
      Kyoto
    • Year and Date
      2015-10-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Fragility of visual media culture suggested by mathematical modeling of depth perception2015

    • Author(s)
      K. Sugihara
    • Organizer
      JST CREST-PRESTO Symposium 2015: Mathematics for the 22nd Century
    • Place of Presentation
      Tokyo
    • Year and Date
      2015-09-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Visual Media Culture Supported by Human Depth Illusion2015

    • Author(s)
      K. Sugihara
    • Organizer
      Mathematical Progress in Expressive Image Synthesis 2015 (MEIS2015)
    • Place of Presentation
      Fukuoka
    • Year and Date
      2015-09-25
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Fitting Spherical Laguerre Voronoi Diagrams to Real World Tessellations Using Planar Photographic Images2015

    • Author(s)
      S. Chaidee and K. Sugihara
    • Organizer
      JCDCG^2 2015
    • Place of Presentation
      Kyoto
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Escher-Like Tilings with Weights2015

    • Author(s)
      S. Imahori, S. Kawade, Y. Yamakata
    • Organizer
      18th Japan Conference on Discrete and Computational Geometry and Graphs
    • Place of Presentation
      Kyoto
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Design of ambiguous cylinders2015

    • Author(s)
      K. Sugihara
    • Organizer
      Asian Forum on Graphic Science
    • Place of Presentation
      Bangkok, Thailand
    • Year and Date
      2015-08-05
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical fitting of planar photographic images with spherical Voronoi diagrams2015

    • Author(s)
      S. Chaidee and K. Sugihara
    • Organizer
      Asian Forum on Graphic Science
    • Place of Presentation
      Bangkok, Thailand
    • Year and Date
      2015-08-05
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Impossible objects as a tool for understanding the human vision systems2015

    • Author(s)
      K. Sugihara
    • Organizer
      Asian Forum on Graphic Science (AFGS 2015)
    • Place of Presentation
      Bangkok, Thailand
    • Year and Date
      2015-08-05
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A method for fitting real world tessellations with Voronoi diagrams2015

    • Author(s)
      S. Chaidee and K. Sugihara
    • Organizer
      31st European Workshop on Computational Geometry
    • Place of Presentation
      Ljubljana, Slovenia
    • Year and Date
      2015-03-15 – 2015-03-18
    • Related Report
      2014 Annual Research Report
  • [Presentation] 重み付きプロクラステス距離を用いたエッシャー風タイリング生成2014

    • Author(s)
      川出静,西澤慶亮,宮田考史,今堀慎治
    • Organizer
      NICOGRAPH 2014
    • Place of Presentation
      愛知
    • Year and Date
      2014-11-03 – 2014-11-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] Mathematical modeling approach to creation of anomalous motion illusions2014

    • Author(s)
      K. Sugihara
    • Organizer
      the Fourth IIEEJ International Workshop on Image Electronics and Visual Computing
    • Place of Presentation
      Koh Samui, Thailand
    • Year and Date
      2014-10-07 – 2014-10-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] 2種類の図形によるタイリング生成における図形の選択方法2014

    • Author(s)
      川出静,今堀慎治
    • Organizer
      RIMS研究集会「最適化アルゴリズムの進展:理論・応用・実装 」
    • Place of Presentation
      京都
    • Year and Date
      2014-09-24 – 2014-09-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] Comparison between curved-surface tessellations and the Voronoi diagrams using planar photographic images2014

    • Author(s)
      S. Chaidee and K. Sugihara
    • Organizer
      The 17th Japan Conference on Discrete and Computational Geometry and Graphs
    • Place of Presentation
      Tokyo
    • Year and Date
      2014-09-15 – 2014-09-16
    • Related Report
      2014 Annual Research Report
  • [Presentation] 最適化手法を用いた芸術的なタイリング生成2014

    • Author(s)
      今堀慎治
    • Organizer
      明治大学 錯覚と数理の融合研究セミナー
    • Place of Presentation
      東京
    • Year and Date
      2014-07-22
    • Related Report
      2014 Annual Research Report
  • [Presentation] バクテリアの時空パターンとモアレ錯視2013

    • Author(s)
      小林奈央樹, 脇田順一, 森山修, 山崎義弘, 杉原厚吉, 松下貢
    • Organizer
      日本物理学会大会
    • Place of Presentation
      東広島市
    • Year and Date
      2013-03-28
    • Related Report
      2012 Annual Research Report
  • [Presentation] 2種類の図形によるタイリング生成2013

    • Author(s)
      川出静, 今堀慎治
    • Organizer
      愛知OR研究交流会
    • Place of Presentation
      名古屋
    • Year and Date
      2013-03-13
    • Related Report
      2012 Annual Research Report
  • [Presentation] Footstep illusion art: apparent rotation generated by pure translation2013

    • Author(s)
      J. Ono, A. Tomoeda and K. Sugihara
    • Organizer
      36th European Conference on Visual Perception
    • Place of Presentation
      Bremen, Germany
    • Related Report
      2013 Annual Research Report
  • [Presentation] フットステップ錯視アート2012

    • Author(s)
      小野隼, 友枝明保, 杉原厚吉
    • Organizer
      NICOGRAPH
    • Place of Presentation
      京都
    • Year and Date
      2012-11-17
    • Related Report
      2012 Annual Research Report
  • [Presentation] Footstep Illusionを利用した錯視アートの試み2012

    • Author(s)
      小野隼, 友枝明保, 杉原厚吉
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      稚内, 北海道
    • Year and Date
      2012-08-29
    • Related Report
      2012 Annual Research Report
  • [Presentation] An Improved Method for the Escherization Problem2012

    • Author(s)
      S. Sakai, S. Imahori
    • Organizer
      The 15th Japan-Korea Joint Workshop on Algorithms and Computation
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2012-07-11
    • Related Report
      2012 Annual Research Report
  • [Presentation] フットステップ錯視アート:キックバック錯視とアースワーム錯視

    • Author(s)
      小野隼,友枝明保,杉原厚吉
    • Organizer
      日本応用数理学会平成25年度年会
    • Place of Presentation
      福岡
    • Related Report
      2013 Annual Research Report
  • [Presentation] エッシャー風タイリング問題に対する局所探索法

    • Author(s)
      今堀慎治,酒井翔平
    • Organizer
      情報処理学会 第144回 アルゴリズム研究会
    • Place of Presentation
      函館市,北海道
    • Related Report
      2013 Annual Research Report
  • [Presentation] 2種類の図形によるタイリング生成 -図形の接合を用いたアルゴリズムの構築-

    • Author(s)
      川出静,今堀慎治
    • Organizer
      日本オペレーションズリサーチ学会秋季研究発表会
    • Place of Presentation
      徳島市,徳島県
    • Related Report
      2013 Annual Research Report
  • [Presentation] Local Search Algorithms for Escherization

    • Author(s)
      S. Imahori, S. Kawade, S. Sakai
    • Organizer
      16th Japan Conference on Discrete and Computational Geometry and Graphs
    • Place of Presentation
      Tokyo, Japan
    • Related Report
      2013 Annual Research Report
  • [Book] 計算幾何学2013

    • Author(s)
      杉原厚吉
    • Total Pages
      205
    • Publisher
      朝倉書店
    • Related Report
      2013 Annual Research Report
  • [Book] 錯視図鑑2012

    • Author(s)
      杉原厚吉
    • Total Pages
      199
    • Publisher
      誠文堂新光社
    • Related Report
      2012 Annual Research Report
  • [Remarks] Mathematics and the Arts

    • URL

      http://home.mims.meiji.ac.jp/~sugihara/project/mathart/MathematicsandArts(English).pdf

    • Related Report
      2014 Annual Research Report
  • [Patent(Industrial Property Rights)] 時計装置及び時計プログラム2013

    • Inventor(s)
      杉原厚吉,友枝明保,小野隼
    • Industrial Property Rights Holder
      明治大学
    • Industrial Property Rights Type
      特許
    • Industrial Property Number
      2013-110085
    • Filing Date
      2013-05-24
    • Related Report
      2013 Annual Research Report
  • [Patent(Industrial Property Rights)] 時計装置及び時計プログラム2012

    • Inventor(s)
      小野隼, 友枝明保, 杉原厚吉
    • Industrial Property Rights Holder
      明治大学
    • Industrial Property Number
      2012-173418
    • Filing Date
      2012-08-03
    • Related Report
      2012 Annual Research Report

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Published: 2012-04-24   Modified: 2019-07-29  

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