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Visualization of 4D space by VR and complex dynamics

Research Project

Project/Area Number 18K18722
Research Category

Grant-in-Aid for Challenging Research (Exploratory)

Allocation TypeMulti-year Fund
Review Section Medium-sized Section 12:Analysis, applied mathematics, and related fields
Research InstitutionKyushu University

Principal Investigator

Ishii Yutaka  九州大学, 数理学研究院, 教授 (20304727)

Co-Investigator(Kenkyū-buntansha) 稲生 啓行  京都大学, 理学研究科, 准教授 (00362434)
荒井 迅  中部大学, 創発学術院, 教授 (80362432)
寺尾 将彦  山口大学, 時間学研究所, 講師 (50772357)
鍛冶 静雄  九州大学, マス・フォア・インダストリ研究所, 教授 (00509656)
松本 啓吾  東京大学, 大学院情報理工学系研究科, 助教 (20909527)
Project Period (FY) 2018-06-29 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2020: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2019: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2018: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Keywordsバーチャル・リアリティ / ジュリア集合 / 高次元可視化 / virtual reality / 4次元回転 / 4次元可視化 / 複素力学系 / 4次元空間 / バーチャルリアリティ / Polyvision / 可視化
Outline of Final Research Achievements

Visualization of higher dimensional objects attracts great interest from mathematics, physics and data science, etc. The purpose of this project is to visualize mathematical objects in 4 dimensional space such as the Julia sets by using virtual reality system. As a consequence, we succeeded a system called Polyvision which is a higher dimensional analogue of CAD (computer aided design) by using the idea of multi-projections. This system has been accepted to SIGGRAPH ASIA, one of the top conferences in computer graphics. We also started psychological test based on this system.

Academic Significance and Societal Importance of the Research Achievements

今回の研究成果の中で最も重要なものは Polyvision の開発に成功したことである。科学における研究対象物は高次元空間内のデータセットとして与えられることが多く、その形状の特性を抽出することが重要である。本研究の具体的な意義として、このような幾何的形状の抽出を容易にすることで、数学、地質学、材料工学への応用の道を切り開いた点が挙げられる。具体的には、数学においては複素力学系のパラメータ集合における奇妙な「穴」を稲生が発見し、現在その厳密な証明に取り組んでいる。また材料工学への応用として、素材の亀裂を生み出す「トリガー」の発見に Polyvision を応用する研究も進んだ。

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (10 results)

All 2022 2021 2019

All Journal Article (2 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 1 results) Presentation (8 results) (of which Int'l Joint Research: 1 results,  Invited: 7 results)

  • [Journal Article] バーチャル・リアリティを用いた4次元可視化プロジェクト2022

    • Author(s)
      石井豊
    • Journal Title

      数学通信

      Volume: 3 Pages: 49-54

    • Related Report
      2022 Annual Research Report
  • [Journal Article] Polyvision: 4D Space Manipulation through Multiple Projections2019

    • Author(s)
      Matsumoto Keigo、Ogawa Nami、Inou Hiroyuki、Kaji Shizuo、Ishii Yutaka、Hirose Michitaka
    • Journal Title

      SA '19: SIGGRAPH Asia 2019 Emerging Technologies

      Volume: November Pages: 36-37

    • DOI

      10.1145/3355049.3360518

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Visualization in complex dynamics in dimension two2022

    • Author(s)
      Hiroyuki Inou
    • Organizer
      Interactive recognition of higher-dimensional spaces with virtual reality 2
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Capturing the fourth dimension2022

    • Author(s)
      Shizuo Kaji
    • Organizer
      Interactive recognition of higher-dimensional spaces with virtual reality 2
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Walking the Mobius Strip: Extending Redirected Walking into the 3rd Dimension2022

    • Author(s)
      Keigo Matsumoto
    • Organizer
      Interactive recognition of higher-dimensional spaces with virtual reality 2
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Complex dynamics, rigorous numerics and 4D visualization2022

    • Author(s)
      Yutaka Ishii
    • Organizer
      Topology and computer
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] 4次元可視化プロジェクト2021

    • Author(s)
      石井豊
    • Organizer
      VRを用いたインタラクティブな高次元認識
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 4 次元の回転とVR における操作2021

    • Author(s)
      稲生啓行
    • Organizer
      VRを用いたインタラクティブな高次元認識
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] シンプルな4次元パストレーサーによるレンダリング2021

    • Author(s)
      鍛冶静雄
    • Organizer
      VRを用いたインタラクティブな高次元認識
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Polyvision: 4D space manipulation through multiple projections2019

    • Author(s)
      Keigo Matsumoto, Nami Ogawa, Hiroyuki Inou, Shizuo Kaji, Yutaka Ishii, Michitaka Hirose
    • Organizer
      SIGGRAPH Asia 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research

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Published: 2018-07-25   Modified: 2024-01-30  

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