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Formulations of curves and surfaces for aesthetic design based on variational principle and investigations of their performances

Research Project

Project/Area Number 25289021
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Design engineering/Machine functional elements/Tribology
Research InstitutionShizuoka University

Principal Investigator

Miura Kenjiro T.  静岡大学, 工学部, 教授 (50254066)

Co-Investigator(Kenkyū-buntansha) MASUDA Hiroshi  電気通信大学, 大学院工学研究科, 教授 (40302757)
USUKI Shin  静岡大学, 電子工学研究所, 准教授 (60508191)
FUJISAWA Makoto  筑波大学, 図書館情報メディア研究科, 助教 (90508409)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥13,390,000 (Direct Cost: ¥10,300,000、Indirect Cost: ¥3,090,000)
Fiscal Year 2015: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2014: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2013: ¥7,670,000 (Direct Cost: ¥5,900,000、Indirect Cost: ¥1,770,000)
Keywords変分原理 / 対数型美的曲線 / 対数型美的曲面 / 対数型美的曲面フィッティング / SPH / ガウス曲率 / 平均曲率 / 意匠デザイン / 相似幾何 / 対数型美的流れ / 一般化対数型美的曲線 / リバースエンジニアリング / 自由曲線・曲面モデル / 高品質モデル / 3次元計測 / B-Spline / 美的B-spline / 形状モデリング / 美的曲線・曲面理論 / 極座標型美的曲線 / 美的空間
Outline of Final Research Achievements

The log-aesthetic curve is expected to be utilized for the field of aesthetic design because of its good properties. However, it is very difficult to extend it to surfaces and the existing formulas have some problems that they cannot use arbitrary boundary curves. In this research, we propose a new formula for the log-aesthetic surface whose isoparametric curves can be expressed by log-aesthetic curves. Based on variational principle our method can generate surfaces by minimizing the objective function newly proposed in the paper for given arbitrary boundary curves.
The mechanical performance of the log-aesthetic surface extended from the log-aesthetic curve has not been evaluated yet. In this research we target at the ship hull whose performance is greatly affected by its surface shape. In order to evaluate the mechanical performance of the log-aesthetic surface, we generate geometric models of the ship hull with smooth curvature distribution by use of the log-aesthetic surface.

Report

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

    (51 results)

All 2016 2015 2014 2013 Other

All Int'l Joint Research (4 results) Journal Article (17 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 17 results,  Acknowledgement Compliant: 3 results,  Open Access: 8 results) Presentation (25 results) (of which Int'l Joint Research: 2 results,  Invited: 1 results) Book (1 results) Remarks (2 results) Patent(Industrial Property Rights) (2 results)

  • [Int'l Joint Research] マレーシア大学トレンガヌ校(マレーシア)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] ファティ大学(トルコ)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] 啓明大学/国立清華大学(韓国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] カーネギーメロン大学/ケンタッキー大学(米国)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Structure Analysis with 2D Quadrilateral Meshes Generated by a Label-Driven Subdivision2016

    • Author(s)
      Bo Liu, Kenjiro T. Miura and Shin Usuki
    • Journal Title

      International Journal of Automation Technology

      Volume: 10 Issue: 2 Pages: 187-194

    • DOI

      10.20965/ijat.2016.p0187

    • NAID

      130007673876

    • ISSN
      1881-7629, 1883-8022
    • Year and Date
      2016-03-05
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Digital Grain Generation Method Suitable for Geometric Textures2016

    • Author(s)
      Ryoji Miyachi, Shin Usuki, and Kenjiro T. Miura
    • Journal Title

      International Journal of Automation Technology

      Volume: 10 Issue: 2 Pages: 209-213

    • DOI

      10.20965/ijat.2016.p0209

    • NAID

      130007674007

    • ISSN
      1881-7629, 1883-8022
    • Year and Date
      2016-03-05
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] An Efficient Boundary Handling with a Modified Density Calculation for SPH2015

    • Author(s)
      Makoto Fujisawa and Kenjiro T. Miura
    • Journal Title

      Computer Graphics Forum (Proc. Pacific Graphics 2015)

      Volume: 34(7) Issue: 7 Pages: 155-162

    • DOI

      10.1111/cgf.12754

    • NAID

      120007135934

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Development of Multi-resolution Microscopy Image Processing System2015

    • Author(s)
      T. Suzuki, S. Usuki and K. T. Miura
    • Journal Title

      Journal of Imaging Science and Technology

      Volume: 59 Pages: 1-11

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reformulation of Generalized Log-aesthetic Curves with Bernoulli Equations2015

    • Author(s)
      Kenjiro T. Miura, R.U. Gobithaasan, Sho Suzuki, Shin Usuki
    • Journal Title

      Computer-Aided Design and Applications

      Volume: 13 Issue: 2 Pages: 265-269

    • DOI

      10.1080/16864360.2015.1084200

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The Polar-aesthetic Curve and Its Applications to Scissors Design2015

    • Author(s)
      Kenjiro T. Miura, R.U. Gobithaasan, Shin Usuki
    • Journal Title

      Computer-Aided Design and Applications

      Volume: 12 Issue: 4 Pages: 431-438

    • DOI

      10.1080/16864360.2014.997639

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Logarithmic Curvature Graph as a Shape Interrogation Tool2014

    • Author(s)
      R. U. Gobithaasan, Kenjiro T. Miura
    • Journal Title

      Applied Mathematical Sciences

      Volume: 8 Pages: 755-765

    • Related Report
      2014 Annual Research Report 2013 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Velocity calculation of 2D geometric objects by use of surface interpolation in 3D2014

    • Author(s)
      Yojiro Mandachi, Shin Usuki, Kenjiro T. Miura
    • Journal Title

      Journal of Advanced Mechanical Design, Systems, and Manufacturing

      Volume: 8 Issue: 2 Pages: JAMDSM0012-JAMDSM0012

    • DOI

      10.1299/jamdsm.2014jamdsm0012

    • NAID

      130004495247

    • ISSN
      1881-3054
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Log-Aesthetic Curves for Shape Completion Problem2014

    • Author(s)
      R. U. Gobithaasan, Yip Siew Wei, Kenjiro T. Miura
    • Journal Title

      Journal of Applied Mathematics

      Volume: 2014 Pages: 1-10

    • DOI

      10.1155/2014/960302

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Generation of Log-aesthetic curves using adaptive Runge-Kutta methods2014

    • Author(s)
      R.U. Gobithaasan, Y.M. Teh, A.R.M. Piah, Kenjiro T. Miura
    • Journal Title

      Applied Mathematics and Computation

      Volume: 2014 Pages: 257-262

    • DOI

      10.1016/j.amc.2014.08.032

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Log-aesthetic Magnetic Curves and its application for CAD systems2014

    • Author(s)
      Mei Seen Wo, R. U. Gobithaasan, Kenjiro T. Miura
    • Journal Title

      Mathematical Problems in Engineering

      Volume: 2014 Pages: 1-16

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] MC-curves and aesthetic measurements for pseudospiral curve segments2013

    • Author(s)
      Rushan Ziatdinov, Rifkat I. Nabiyev, Kenjiro T. Miura
    • Journal Title

      Mathematical Design & Technical Aesthetics

      Volume: Vol.1, No.1 Pages: 6-17

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On some families of planar curves with monotonic curvature function, their aesthetic measures and applications in industrial design2013

    • Author(s)
      Rushan Ziatdinov, Rifkat I. Nabiyev, Kenjiro T. Miura
    • Journal Title

      Bulletin of Moscow Aviation Institute

      Volume: 20(2) Pages: 209-218

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Designing Log-aesthetic Splines with G2 Continuity2013

    • Author(s)
      Kenjiro T. Miura, Dai Shibuya, R.U. Gobithaasan, Shin Usuki
    • Journal Title

      Computer-Aided Design & Applications

      Volume: 10(6) Pages: 1021-1032

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Shape Analysis of Generalized Log-Aesthetic Curves2013

    • Author(s)
      R. U. Gobithaasan, R. Karpagavalli, Kenjiro T. Miura
    • Journal Title

      International Journal of Mathematical Analysis

      Volume: 7(36) Pages: 1751-1759

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Calculation of Velocity on an Implicit Surface by Curvature Invariance2013

    • Author(s)
      Makoto Fujisawa, Yojiro Mandachi, Kenjiro T. Miura
    • Journal Title

      Journal of Information Processing

      Volume: 21(4) Pages: 674-680

    • NAID

      130003384026

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Drawable Region of the Generalized Log Aesthetic Curves2013

    • Author(s)
      R.U. Gobithaasan, R. Karpagavalli & Kenjiro T. Miura
    • Journal Title

      Journal of Applied Mathematics

      Volume: 2013 Pages: 1-7

    • DOI

      10.1155/2013/732457

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Presentation] 変分原理に基づく対数型美的曲面の生成 -等パラメトリック曲線の対数型美的曲線化-,"2016

    • Author(s)
      鈴木晶, 臼杵深, 三浦憲二郎, Salvi Peter
    • Organizer
      2016年度精密工学会春季大会学術講演会
    • Place of Presentation
      千葉県野田市東京理科大学
    • Year and Date
      2016-03-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] 対数型美的曲線に関する研究-LA流れと熱伝導方程式,相似幾何による空間曲線の定式化,LCGの傾き-2016

    • Author(s)
      三浦憲二郎, 鈴木晶, 臼杵深, R.U. Gobithaasan
    • Organizer
      2016年度精密工学会春季大会学術講演会
    • Place of Presentation
      千葉県野田市東京理科大学
    • Year and Date
      2016-03-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] 二次元曲線軌道上の最短時間駆動2016

    • Author(s)
      蘭 豊礼, 三浦憲二郎, 玉井博文, 牧野洋,
    • Organizer
      2016年度精密工学会春季大会学術講演会
    • Place of Presentation
      千葉県野田市東京理科大学
    • Year and Date
      2016-03-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] 2 次元頂点ラベル付けにより細分割された4 角形メッシュによる構造解析2016

    • Author(s)
      劉波, 三浦憲二郎, 臼杵深
    • Organizer
      2016年度精密工学会春季大会学術講演会
    • Place of Presentation
      千葉県野田市東京理科大学
    • Year and Date
      2016-03-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] Generation of the Log-aesthetic Curve and Surface with Variational Principle2015

    • Author(s)
      Sho Suzuki, Shin Usuki, Kenjiro Miura and R.U. Gobithaasan
    • Organizer
      Asian Conference on Design and Digital Engineering (ACDDE2015)
    • Place of Presentation
      福岡県北九州市Kitakyushu International Conference Center, Kitakyushu
    • Year and Date
      2015-11-04
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Aesthetic Design with Log-aesthetic Curves and Surfaces2015

    • Author(s)
      Kenjiro T. Miura
    • Organizer
      Symposium MEIS2015 : Mathematical Progress in Expressive Image Synthesis,
    • Place of Presentation
      福岡県福岡市Kyushuu University, Fukuoka, Fukuoka
    • Year and Date
      2015-09-25
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 対数型美的曲面フィッティングによる船舶幾何モデルの生成2015

    • Author(s)
      山本哲也, 鈴木晶, 臼杵深, 三浦憲二郎
    • Organizer
      2015年度精密工学会秋季大会学術講演会
    • Place of Presentation
      宮城県仙台市東北大学
    • Year and Date
      2015-09-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] 対数型美的流れ2015

    • Author(s)
      三浦憲二郎, 鈴木晶, R.U. Gobithaasan, 臼杵深
    • Organizer
      2015年度精密工学会秋季大会学術講演会
    • Place of Presentation
      宮城県仙台市東北大学
    • Year and Date
      2015-09-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] リバースエンジニアリングに基づく対数型美的曲線・曲面の生成2015

    • Author(s)
      鈴木晶,山本哲也, 臼杵深,三浦憲二郎
    • Organizer
      グラフィックスとCAD/Visual Computing合同シンポジウム2015
    • Place of Presentation
      兵庫県姫路市姫路市市民会館
    • Year and Date
      2015-06-28
    • Related Report
      2015 Annual Research Report
  • [Presentation] Bernoulli方程式による一般化対数型美的曲線の導出2015

    • Author(s)
      三浦憲二郎,R.U. Gobithaasan, 鈴木晶, 臼杵深
    • Organizer
      2015年度精密工学会春季大会学術講演会
    • Place of Presentation
      東洋大学, 東京都文京区白山5-28-20
    • Year and Date
      2015-03-17 – 2015-03-19
    • Related Report
      2014 Annual Research Report
  • [Presentation] エネルギ最小化による自由曲線の美的化2015

    • Author(s)
      鈴木晶, 臼杵深, 三浦憲二郎
    • Organizer
      2015年度精密工学会春季大会学術講演会
    • Place of Presentation
      東洋大学, 東京都文京区白山5-28-20
    • Year and Date
      2015-03-17 – 2015-03-19
    • Related Report
      2014 Annual Research Report
  • [Presentation] モーションキャプチャデータに基づく動きの評価2015

    • Author(s)
      荒浪太一, 鈴木晶, 三浦憲二郎, 小林祐一, 臼杵 深,
    • Organizer
      2015年度精密工学会春季大会学術講演会
    • Place of Presentation
      東洋大学, 東京都文京区白山5-28-20
    • Year and Date
      2015-03-17 – 2015-03-19
    • Related Report
      2014 Annual Research Report
  • [Presentation] 対数型美的曲線の汎関数のスケール不変化とα値の推定2014

    • Author(s)
      三浦憲二郎, 鈴木晶, 臼杵深
    • Organizer
      2014年度精密工学会秋季大会学術講演会
    • Place of Presentation
      鳥取大学, 鳥取県湖山町南4丁目101
    • Year and Date
      2014-09-17 – 2014-09-19
    • Related Report
      2014 Annual Research Report
  • [Presentation] リバースエンジニアリングのための対数型美的曲線・曲面フィッティング2014

    • Author(s)
      鈴木晶, 臼杵深, 三浦憲二郎
    • Organizer
      2014年度精密工学会秋季大会学術講演会
    • Place of Presentation
      鳥取大学, 鳥取県湖山町南4丁目101
    • Year and Date
      2014-09-17 – 2014-09-19
    • Related Report
      2014 Annual Research Report
  • [Presentation] Frenet-Serret式の一般解の導出2014

    • Author(s)
      澁谷大, 臼杵深, 三浦憲二郎
    • Organizer
      2014年度精密工学会春季大会学術講演会
    • Place of Presentation
      東京大学(東京都)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 変分原理に基づく対数型美的曲線・曲面の生成2014

    • Author(s)
      鈴木晶, 臼杵深, 三浦憲二郎
    • Organizer
      2014年度精密工学会春季大会学術講演会
    • Place of Presentation
      東京大学(東京都)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 離散積分曲線の生成法2014

    • Author(s)
      三浦憲二郎, 鈴木晶, 臼杵深
    • Organizer
      2014年度精密工学会春季大会学術講演会
    • Place of Presentation
      東京大学(東京都)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Designing Log-aesthetic Splines with G2 Continuity2013

    • Author(s)
      Kenjiro T. Miura, Dai Shibuya, R.U. Gobithaasan, Shin Usuki
    • Organizer
      2013 International CAD Conference and Exhibition
    • Place of Presentation
      University of Bergamo (Bergamo, Italy)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Robot Trajectory Generation with Smoothly Changing Curvature Using the Clothoid Spline2013

    • Author(s)
      Shibuya Dai, Shin Usuki, Kenjiro T. Miura
    • Organizer
      2013 Asian Conference on Design and Digital Engineering (ACDDE),
    • Place of Presentation
      Dongguk University (Seoul, Korea)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Bridging CAGD knowledge into CAD/CG applications2013

    • Author(s)
      R.U. Gobithaasan, Kenjiro T. Miura and Mohamad Nor Hassan
    • Organizer
      Simposium Kebangsaan Sains Matematik, SKSM21
    • Place of Presentation
      University Science Malaysia (Pulau Pinang, Malaysia)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Rendering Log Aesthetic Curves via Runge-Kutta Method2013

    • Author(s)
      R.U. Gobithaasan, Teh Yee Meng, A.R.M. Piah & Kenjiro T. Miura
    • Organizer
      Simposium Kebangsaan Sains Matematik, SKSM21
    • Place of Presentation
      University Science Malaysia (Pulau Pinang, Malaysia)
    • Related Report
      2013 Annual Research Report
  • [Presentation] GPU Acceleration of Runge Kutta-Fehlberg2013

    • Author(s)
      Wo Mei Seen , R.U. Gobithaasan and Kenjiro T. Miura
    • Organizer
      Simposium Kebangsaan Sains Matematik, SKSM21
    • Place of Presentation
      University Science Malaysia (Pulau Pinang, Malaysia)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Shape Reconstruction of Poles and Plates from Vehicle-Based Laser Scanning Data2013

    • Author(s)
      Hiroshi Masuda , Shogo Oguri, He Jun
    • Organizer
      The International Symposium on Mobile Mapping Technology
    • Place of Presentation
      National Cheng Kung University (Taipei, Taiwan)
    • Related Report
      2013 Annual Research Report
  • [Presentation] An Efficient Surface Generation Method for Vehicle-Based Mobile Mapping System2013

    • Author(s)
      Jun He, Hiroshi Masuda
    • Organizer
      The International Conference on Civil and Building Engineering Informatics
    • Place of Presentation
      Tokyo International Exchange Center (Tokyo, Japan)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 極座標型美的曲線2013

    • Author(s)
      三浦憲二郎, 臼杵深
    • Organizer
      2013年度精密工学会秋季大会学術講演会
    • Place of Presentation
      関西大学(大阪府)
    • Related Report
      2013 Annual Research Report
  • [Book] CGのための物理シミュレーションの基礎2013

    • Author(s)
      藤澤誠
    • Total Pages
      240
    • Publisher
      マイナビ
    • Related Report
      2013 Annual Research Report
  • [Remarks] 対数型美的曲線・曲面

    • URL

      http://ktm11.eng.shizuoka.ac.jp/profile/ktmiura/log-aesthetic.html

    • Related Report
      2015 Annual Research Report 2014 Annual Research Report
  • [Remarks] 対数型美的曲線・曲面

    • URL

      http://ktm11.eng.shizuoka.ac.jp/profile/ktmiura/log-aesthetic.html

    • Related Report
      2013 Annual Research Report
  • [Patent(Industrial Property Rights)] 表面加工データの作成方法および装置2013

    • Inventor(s)
      菊田守,三浦憲二郎, 宇津山大二郎,高橋賢治
    • Industrial Property Rights Holder
      菊田守,三浦憲二郎, 宇津山大二郎,高橋賢治
    • Industrial Property Rights Type
      特許
    • Filing Date
      2013-06-01
    • Acquisition Date
      2014-06-20
    • Related Report
      2014 Annual Research Report
  • [Patent(Industrial Property Rights)] 表面加工データの作成方法および装置、方法、及びプログラム2013

    • Inventor(s)
      菊田守,三浦憲二郎
    • Industrial Property Rights Holder
      菊田守,三浦憲二郎
    • Industrial Property Rights Type
      特許
    • Filing Date
      2013-06-01
    • Acquisition Date
      2014-06-20
    • Related Report
      2014 Annual Research Report

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Published: 2013-05-21   Modified: 2019-07-29  

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