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

Moduli space of motions of geometric objects

Research Project

Project/Area Number 23654054
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionKyushu University

Principal Investigator

OCHIAI Hiroyuki  九州大学, マス・フォア・インダストリ研究所, 教授 (90214163)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords変形 / リー群 / 補間 / 運動群 / 離散微分幾何 / 映像 / 曲面 / 曲線 / 変形空間 / モジュライ / セミノルム / 関数空間 / 群
Research Abstract

Computer Graphics produces a scene. It is a collection of large data, depending on the time variable.
In this research, we study the structure of the space of scenes, in terms of geometry and Lie theory. The groups acting on the objects are the central role of this study. The example of such groups are Euclidean motion groups, orthogonal groups, rotation groups, and affine transformation groups. We give an interpretation of these groups into several subgroups or the matrix exponential image of subspaces as a basic tool of interpolation and blend in the graphics, such as SLERP (spherical linear interpolation) and ARAP (as rigid as possible). This analysis enables us to understand the previous method as well as to generalize and to improve the quality and speed of the interpolation.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (62 results)

All 2014 2013 2012 2011 Other

All Journal Article (21 results) (of which Peer Reviewed: 9 results) Presentation (37 results) (of which Invited: 9 results) Book (2 results) Remarks (2 results)

  • [Journal Article] Values of twisted tensor L-functions of automorphic forms over imaginary quadratic fields2014

    • Author(s)
      Dominic Lanphier and Howard Skogman, Appendix by Hiroyuki Ochiai
    • Journal Title

      Canadian J. Math

      Volume: 66 Issue: 5 Pages: 1078-1109

    • DOI

      10.4153/cjm-2013-047-5

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] Zeros of Witten zeta functions and absolute limit2013

    • Author(s)
      Nobushige Kurokawa and Hiroyuki Ochiai
    • Journal Title

      Kodai Math. J

      Volume: 36, no.3 Pages: 440-454

    • NAID

      130004496191

    • Related Report
      2013 Final Research Report
  • [Journal Article] Non-commutative harmonic oscillators. Symmetries, integrable systems and representations2013

    • Author(s)
      Hiroyuki Ochiai
    • Journal Title

      Springer Proc. Math. Stat

      Volume: 40 Pages: 483-490

    • Related Report
      2013 Final Research Report
  • [Journal Article] A generalized hypergeometric system2013

    • Author(s)
      Hiroyuki Ochiai and Uuganbayar Zunderiya
    • Journal Title

      J. Math. Sci. Univ. Tokyo

      Volume: 20, no.2 Pages: 285-315

    • NAID

      120006906115

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] On orbits in double flag varieties for symmetric pairs2013

    • Author(s)
      Xuhua He, Hiroyuki Ochiai, Kyo Nishiyama and Yoshiki Oshima
    • Journal Title

      Transform. Groups

      Volume: 18, no.4 Pages: 1091-1136

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] Dualities for absolute zeta functions and multiple gamma functions2013

    • Author(s)
      Nobushige Kurokawa and Hiroyuki Ochiai
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci

      Volume: 89, no.7 Pages: 75-79

    • NAID

      40019725109

    • Related Report
      2013 Final Research Report
  • [Journal Article] Alpha-determinant for rank-two matrices2013

    • Author(s)
      Hiroyuki Ochiai
    • Journal Title

      Geometry, Number Theory and Representation Theory

      Pages: 93-112

    • Related Report
      2013 Final Research Report
  • [Journal Article] A Lie theoretic parameterization of affine transformation, Mathematical Progress in Expressive Image Synthesis2013

    • Author(s)
      Shizuo Kaji, Sampei Hirose, Hiroyuki Ochiai and Ken Anjyo
    • Journal Title

      MI Lecture Note

      Volume: Vol.50 Pages: 134-140

    • Related Report
      2013 Final Research Report
  • [Journal Article] Anti-commutative dual complex numbers and 2D rigid transformation, Mathematical Progress in Expressive Image Synthesis2013

    • Author(s)
      Genki Matsuda, Shizuo Kaji and Hiroyiki Ochiai
    • Journal Title

      MI Lecture Note

      Volume: Vol.50 Pages: 128-133

    • Related Report
      2013 Final Research Report
  • [Journal Article] Mathematical formulation of motion/deformation and its applications, Mathematical Progress in Expressive Image Synthesis2013

    • Author(s)
      Hiroyuki Ochiai and Ken Anjyo
    • Journal Title

      MI Lecture Note

      Volume: Vol.50 Pages: 100-103

    • Related Report
      2013 Final Research Report
  • [Journal Article] Zeros of Witten zeta functions and absolute limit2013

    • Author(s)
      Nobushige Kurokawa and Hiroyuki Ochiai
    • Journal Title

      Kodai Mathematical Journal

      Volume: 36

    • NAID

      130004496191

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-commutative harmonic oscillators. in Symmetries, integrable systems and representations2013

    • Author(s)
      Hiroyuki Ochiai
    • Journal Title

      Springer Proc. Math. Stat.

      Volume: 40

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dualities for absolute zeta functions and multiple gamma functions2013

    • Author(s)
      Nobushige Kurokawa and Hiroyuki Ochiai
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci.

      Volume: 89

    • NAID

      40019725109

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Alpha-determinant for rank-two matrices2013

    • Author(s)
      Hiroyuki Ochiai
    • Journal Title

      in Geometry, Number Theory and Representation Theory

      Pages: 93-112

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-commutative harmonic oscillators2013

    • Author(s)
      Hiroyuki Ochiai
    • Journal Title

      Proceeding of the International Conference on Geometry, Number Theory and Representation Theory

      Pages: 95-112

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Zeros of Witten zeta functions and absolute limit2013

    • Author(s)
      Nobushige Kurokawa, Hiroyuki Ochiai
    • Journal Title

      Kodai Mathematical Journal

    • NAID

      130004496191

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Closed orbits on partial flag varieties and double flag variety of finite type2013

    • Author(s)
      Kensuke Kondo, Kyo Nishiyama, Hiroyuki Ochiai, Kenji Taniguchi
    • Journal Title

      Kyushu Journal of Mathematics

    • NAID

      130004941519

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Computer Graphics における運動の記述2013

    • Author(s)
      落合啓之
    • Journal Title

      「数学モデリングの基礎と展開」COE Lecture Note

      Volume: 46 Pages: 1-10

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Holonomic system of Gegenbauer type polynomials2012

    • Author(s)
      Tomoyoshi Ibukiyama, Takako Kuzumaki, Hiroyuki Ochiai
    • Journal Title

      Journal of Mathematical Society of Japan

      Volume: 64 Pages: 273-316

    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Journal Article] Holonomic systems of Gegenbauer type polynomials of matrix arguments related with Siegel modular forms2012

    • Author(s)
      伊吹山知義、葛巻孝子、落合啓之
    • Journal Title

      Journal of Mathematical Society of Japan

      Volume: 64 Pages: 273-316

    • NAID

      10030740141

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Double flag varieties for a symmetric pair and finiteness of orbits2011

    • Author(s)
      Kyo Nishiyama and Hiroyuki Ochiai
    • Journal Title

      Journal of Lie Theory

      Volume: 21 Pages: 79-99

    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Presentation] チーム発表1「安生チーム」2014

    • Author(s)
      落合啓之
    • Organizer
      第1回 JST CREST「数学」領域横断若手合宿~冬の学校@指宿~
    • URL

      http://www.wpi-aimr.tohoku.ac.jp/~nakano/cmyrc/2013/

    • Related Report
      2013 Final Research Report
  • [Presentation] math for CG, 映像制作に使われる数学2013

    • Author(s)
      落合啓之
    • Organizer
      城西大学理学部数学科講演会
    • Place of Presentation
      学部3年生対象
    • Year and Date
      2013-12-18
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] CG を用いた映像制作に使われる数学技術2013

    • Author(s)
      落合啓之
    • Organizer
      応用数理学会
    • URL

      http://www.jsiam.org/annualmeeting/2013/

    • Place of Presentation
      正会員主催OS : 数学テクノロジーのフロンティア, アクロス福岡
    • Year and Date
      2013-09-09
    • Related Report
      2013 Final Research Report
  • [Presentation] 行列の数理と運動の記述2013

    • Author(s)
      落合啓之
    • Organizer
      Computer Entertainment Developer Conference, CEDEC 2013
    • Place of Presentation
      パシフィコ横浜
    • Year and Date
      2013-08-21
    • Related Report
      2013 Final Research Report
  • [Presentation] ユニタリ表現の分類はそろそろできるだろうか?, 企画特別講演2013

    • Author(s)
      落合啓之
    • Organizer
      2013年度日本数学会年会
    • Place of Presentation
      京都大学
    • Year and Date
      2013-03-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Mathematical Description of Motion and Deformation --- From Basics to Graphics Applications ---2013

    • Author(s)
      Hiroyuki Ochiai and Ken Anjyo
    • Organizer
      SIGGRAPH Asia 2013 Course
    • Place of Presentation
      Hong Kong Convention and Exhibition Center
    • Related Report
      2013 Final Research Report
  • [Presentation] Mathematical Formulation of Motion/Deformation and its Applications2013

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      研究集会「Mathematical Progress in Expressive Image Synthesis」
    • URL

      http://mcg.imi.kyushu-u.ac.jp/meis2013/

    • Place of Presentation
      九州大学百年記念講堂
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] 非可換調和振動子とホインの微分方程式2013

    • Author(s)
      落合啓之
    • Organizer
      Workshop on Accessory Paramaters
    • Place of Presentation
      東京大学玉原国際セミナーハウス, 群馬県沼田市
    • Related Report
      2013 Final Research Report
  • [Presentation] 行列の数理と運動の記述2013

    • Author(s)
      落合啓之
    • Organizer
      文科省共催 SMART 研究会「応用現代幾何学」
    • URL

      http://www.dais.is.tohoku.ac.jp/~amf/information/

    • Place of Presentation
      東北大学情報科学研究科
    • Related Report
      2013 Final Research Report
  • [Presentation] Covariant differential operators and Heckman-Opdam hypergeometric systems2013

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      JSPS-NWO Seminar, Analysis, Geometry and Group Representations for Homogeneous Spaces
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Related Report
      2013 Final Research Report
  • [Presentation] Hypergeometric Functions2013

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      CIMPA Research School "Hypergeometric Functions and Representation Theory"
    • Place of Presentation
      Ulaanbaatar, Mongolia
    • Related Report
      2013 Final Research Report
  • [Presentation] On orbits in double flag varieties for symmetric pairs2013

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      The second Pacific Rim Mathematical Association Congress
    • Place of Presentation
      上海交通大学, 中国
    • Related Report
      2013 Final Research Report
  • [Presentation] 特殊関数の活用について2013

    • Author(s)
      落合啓之
    • Organizer
      第6回多重ゼータミニセミナー
    • Place of Presentation
      九州大学大学院数理学研究院
    • Related Report
      2013 Final Research Report
  • [Presentation] On orbits in double flag varieties for symmetric pairs2013

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      The second Pacific Rim Mathematical Association Congress
    • Place of Presentation
      上海交通大学、中国
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Hypergeometric Functions2013

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      CIMPA Research School ``Hypergeometric Functions and Representation Theory''
    • Place of Presentation
      Ulaanbaatar, Mongolia
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 行列の数理と運動の記述2013

    • Author(s)
      落合啓之
    • Organizer
      Computer Entertainment Developer Conference 2013
    • Place of Presentation
      パシフィコ横浜
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Covariant differential operators and Heckman-Opdam hypergeometric systems2013

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      JSPS-NWO Seminar, Analysis, Geometry and Group Representations for Homogeneous Spaces,
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] CGを用いた映像制作に使われる数学技術2013

    • Author(s)
      落合啓之
    • Organizer
      応用数理学会、 正会員主催OS: 数学テクノロジーのフロンティア
    • Place of Presentation
      アクロス福岡
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Mathematical Description of Motion and Deformation --- From Basics to Graphics Applications ---2013

    • Author(s)
      Hiroyuki Ochiai and Ken Anjyo
    • Organizer
      SIGGRAPH ASIA 2013
    • Place of Presentation
      Hong Kong Convention and Exhibition Center
    • Related Report
      2013 Annual Research Report
  • [Presentation] 特殊関数の活用について2013

    • Author(s)
      落合啓之
    • Organizer
      第6回多重ゼータミニセミナー
    • Place of Presentation
      九州大学大学院数理学研究院
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] ユニタリ表現の分類はそろそろできるだろうか?2013

    • Author(s)
      落合啓之
    • Organizer
      2013年度日本数学会年会企画特別講演
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Double flag variety for a symmetric pair and finiteness of orbits2012

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      Representation Theory of Chevalley Groups and Related Topics
    • Place of Presentation
      名古屋大学大学院多元数理科学研究科
    • Year and Date
      2012-03-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Non-commutative harmonic oscillators and the connection problem for the Heun differential equation2012

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      Workshop on "Avoided Crossing of Eigenvalue Curves" -- Non-commutative Harmonic Oscillator, Special Functions and Number Theory--
    • Place of Presentation
      稲盛ホール, 九州大学
    • Year and Date
      2012-03-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Positivity of alpha determinant2012

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      Geometric Analysis on Euclidean Homogeneous Spaces
    • Place of Presentation
      Tufts university
    • Year and Date
      2012-01-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Alpha-determinant for rank-two matrices2012

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      International Conference on Geometry, Number Theory and Representation Theory
    • Place of Presentation
      Inha University, Korea
    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Presentation] Double flag variety for a symmetric pair and spherical actions2012

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      Summer School and Workshop on Representation Theory and Harmonic Analysis
    • Place of Presentation
      Chern Institute of Mathematics, Nankai University, China
    • Related Report
      2013 Final Research Report
  • [Presentation] Double flag variety for a symmetric pair and spherical actions2012

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      Summer School and Workshop on Representation Theory and Harmonic Analysis
    • Place of Presentation
      Chern Institute of Mathematics, Nankai University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Positivity of alpha determinant2012

    • Author(s)
      落合啓之
    • Organizer
      Geometric Analysis on Euclidean and Homogeneous Spaces(招待講演)
    • Place of Presentation
      Tufts University, ボストン市, USA
    • Related Report
      2011 Research-status Report
  • [Presentation] Double flag variety for a symmetric pair and finiteness of orbits2012

    • Author(s)
      落合啓之
    • Organizer
      Representation Theory of Chevalley Groups and Related Topics(招待講演)
    • Place of Presentation
      名古屋大学大学院多元数理科学研究科、愛知県名古屋市千種区
    • Related Report
      2011 Research-status Report
  • [Presentation] 対称対の有限型二重旗多様体2011

    • Author(s)
      落合啓之
    • Organizer
      2011年度表現論シンポジウム
    • Place of Presentation
      国民宿舎紀州路みなべ
    • Year and Date
      2011-11-10
    • Related Report
      2013 Final Research Report
  • [Presentation] On Sekiguchi correspondence, Topics in the Theory of Weyl Groups and Root Systems2011

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      関口次郎還暦研究集会
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2011-09-21
    • Related Report
      2013 Final Research Report
  • [Presentation] On non-commutative harmonic oscillators2011

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      Infinite Analysis 11
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2011-07-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Mathematical consideration on visualization of complex objects2011

    • Author(s)
      Hiroyuki Ochiai
    • Organizer
      International Symposium on Plasma Turbulence, Imaging and Synergy
    • Place of Presentation
      伊藤極限プラズマ研究連携センター
    • Year and Date
      2011-06-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Mathematical consideration on visualization of complex objects2011

    • Author(s)
      落合啓之
    • Organizer
      International Symposium on Plasma Turbulence, Imaging and Synergy(招待講演)
    • Place of Presentation
      伊藤極限プラズマ研究連携センター、春日市
    • Related Report
      2011 Research-status Report
  • [Presentation] On non-commutative harmonic oscillators2011

    • Author(s)
      落合啓之
    • Organizer
      Infinite Analysis 11(招待講演)
    • Place of Presentation
      東京大学大学院数理科学研究科、東京都渋谷区
    • Related Report
      2011 Research-status Report
  • [Presentation] On Sekiguchi correspondence2011

    • Author(s)
      落合啓之
    • Organizer
      Topics in the Theory of Weyl Groups and Root Systems(招待講演)
    • Place of Presentation
      東京大学大学院数理科学研究科、東京都渋谷区
    • Related Report
      2011 Research-status Report
  • [Presentation] 対称対の有限型二重旗多様体2011

    • Author(s)
      落合啓之
    • Organizer
      2011年度表現論シンポジウム(招待講演)
    • Place of Presentation
      国民宿舎 紀州路みなべ、和歌山県日高郡みなべ町
    • Related Report
      2011 Research-status Report
  • [Book] Mathematical formulation of motion and deformation and its applications. In : Mathematical Progress in Expressive Image Synthesis I, K. Anjyo ed., Mathematics for Industry 42014

    • Author(s)
      Hiroyuki Ochiai and Ken Anjyo
    • Publisher
      Springer-Verlag, Berline, Germany
    • Related Report
      2013 Final Research Report
  • [Book] Mathematics --- as an infrastructure of technology and science, In : Mathematics for Industry, Vol 5, Nishii et al(Eds) : A Mathematical Approach to Research Problems of Science and Technology2014

    • Author(s)
      Hiroyuki Ochiai
    • Publisher
      Springer-Verlag, Berline, Germany
    • Related Report
      2013 Final Research Report
  • [Remarks]

    • URL

      http://user.math.kyushu-u.ac.jp/index.php?ochiai

    • Related Report
      2013 Final Research Report
  • [Remarks]

    • URL

      http://user.math.kyushu-u.ac.jp/index.php?ochiai

    • Related Report
      2011 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi