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Spirals and Thier Applications in CAGD

Research Project

Project/Area Number 14540130
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKagoshima University

Principal Investigator

SAKAI Manabu  Kagoshima Univ., Fac.of Sci., Prof., 理学部, 教授 (60037281)

Co-Investigator(Kenkyū-buntansha) NAKASHIMA Masaharu  Kagoshima Univ., Fac.of Sci., Prof., 理学部, 教授 (40041230)
ATSUMI Tsuyosi  Kagoshima Univ., Fac.of Sci., Prof., 理学部, 教授 (20041238)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2004: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsspirals / cubic / guintic / transition curves / Mathematica / rational / geometric / Hermite interpolation / 曲線の当てはめ / スプライン / 補間 / 曲率 / スプライン関数 / スパイラル関数 / Mathemaica / 幾何学的連続度 / スパイラル / 数式処理言語 / マテマチカ / メイプル
Research Abstract

Geometric Modeling plays a significant role in the construction, design and manufacture of various objects. In addition to its critical importance in the traditional fields of automobile and aircraft manufacturing, shipbuilding, and general product design, geomtric modeling methoda have also proven to be indispensable in a variety of modern industries, includind copmputer vision, robotics, medal imaing, visualization textile, designing, painting, and other media. The research aims to study spirals and their applications to geometric modeling. Spirals have several advantages of containing neither inflection points, singularities nor curvature extrema. Such curves are useful for extension of an existing curve and transition between existing ones in the design of visually pleasing curves. Such cubic spirals composed of cubic splines, i.e., curvature continuous curves with curvature extrema only at specified locations are desirable for applications as the design of highway or railway routes or the trajectories of mobile robots or the cutting paths for numerically controlled cutting machinery. The benifit of using such curves in the design of surfaces, in particular surfaces of evolution and swept surfaces, is the control of unwanted flat spots and undulations. First we have obtained the cubic spiral condition for the given data on each subintervals. Secondly, we have proposed an algorithm for a cubic spline approximation of the given data and derived an easier to calculate algorithm. Thirdly, we have explored the use of such spiral segments for CAD.

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (60 results)

All 2005 2004 2003 2002 Other

All Journal Article (49 results) Publications (11 results)

  • [Journal Article] Spiral Transition Curves and their Applications2005

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Scientiae Mathematice Japonicae 61

      Pages: 251-263

    • NAID

      10015447707

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Simplified and Flexible Spiral Transitions for use in Computer Graphics and Geometric Modelling2005

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Computers & Graphics 29(印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Simplified and Flexible Spiral Transitions for use in Computer Graphics and Geometric Modelling2005

    • Author(s)
      Z.Habib, M.Sakai, M.Sarfraz
    • Journal Title

      Science Mathematicae Japonicae 61

      Pages: 263-273

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Spiral Transition Curves and their Applications2005

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Scientiae Mathematicae Japonicae 61

      Pages: 251-263

    • NAID

      10015447707

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Simplified and Flexible Spiral Transitions for use in Computer Graphics and Geometric Modelling2005

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Scientiae Mathematicae Japonicae 61

      Pages: 263-273

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Reachable Regions for spiral Segments and applications in Geometric Modelling2004

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of IEEE International Conference on Computer Graphics, Imaging and Visualization, CGIV04-Malaysia,(IEEE Computer Society Press)

      Pages: 21-26

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Interactive Shape Control with Rational Cubic Splines2004

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Computer-Aided Design & Applications 1

      Pages: 709-718

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Spiral conditions for spline s and their applications to curve design2004

    • Author(s)
      Z.Habib, M.Sakai, M.Sarfraz
    • Journal Title

      Kokyuroku (ComputerAlgebra-Algorithms, Implementations and Applications) 1362

      Pages: 235-243

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Constrained guided spiral transition curves2004

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      Kokyuroku (ComputerAlgebra-Algorithms, Implementations and Applications) 1395

      Pages: 164-170

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Shapes of Bezier Conic Segments2004

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      Workshop on Applied Maths, 2004, Dec.20-22, Ryukoku Univ.

      Pages: 153-158

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Simplified and Flexible Spiral Transitions for use in Computer Graphics and Geometric Modelling2004

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of IEEE International Conference on Image and Graphics, Dec.18-20, 2004, Hong Kong, China,(IEEE Society Press)

      Pages: 426-429

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Reachable Regions for Spiral Segments and Applications in Geometric Modelling2004

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of IEEE International Conference on Computer Graphics, Imaging and Visualization, CGIV04-Malaysia(IEEE Computer Society Press, USA)

      Pages: 21-26

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Interactive Shape Control with Rational Cubic Splines2004

    • Author(s)
      Z.Habib, M.Sakai, M.Sarfraz
    • Journal Title

      Proceedings of Inter.CAD Conference, CAD'04- Thailand (May,24-28,2004,Pattaya Beach, Thailand) Computer-Aided Design & Applications 1

      Pages: 709-718

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Spiral conditions for spline s and their applications to curve design2004

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      Kokyuroku (Computer Algebra-Algorithms, Implementations and Applications) 1362

      Pages: 235-243

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Constrained guided spiral transition curves2004

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Kokyuroku (Computer Algebra-Algorithms, Implementations and Applications) 1395

      Pages: 164-170

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Simplified and Flexible Spiral Transitions for use in Computer Graphics and Geometric Modelling2004

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of IEEE International Conference on Image andGraphics Dec.18-20,2004,Hong Kong, China(IEEE Computer Society Press, USA)

      Pages: 426-429

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Interactive Shape Control with Rational Cubic Splines2004

    • Author(s)
      Z.Habib, M.Sakai, M.Sarfraz
    • Journal Title

      Computer-Aides Design & Applications 1

      Pages: 709-718

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Spiral conditions for spline s and their applications to curve design2004

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      京都大学数理解析研究所講究録 1362

      Pages: 235-243

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Constrained guided spiral transition curves2004

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      京都大学数理解析研究所講究録 1395

      Pages: 164-170

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On Shapes of Bezier Conic Segments2004

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      応用数学合同研究集会報告集,2004年12月20日-12月22日,龍谷大学瀬田キャンパス,153-158

      Pages: 153-158

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Spiral Transition Curves and their Applications2004

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Scientiae Mathematicae Japonicae, Acceptance #30554 61・2(印刷中)

    • NAID

      10015447707

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Simplified and Flexible Spiral Transitions for use in Computer Graphics and Geometric Modeling2004

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Scientiae Mathematicae Japonicae, Acceptance #30562 61・2(印刷中)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] G2 Planar Cubic Transition Between Two Circles2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Inter.J.Computer Math. 80

      Pages: 959-967

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Shapes of Bezier Conic Segments2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Advances in Geometric Modeling, (Editor ; M.Sarfraz);(J ohn Wiley)

      Pages: 133-151

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Planar G2 Cubic Transition Curves Between Two Circles2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Kokyuroku (ComputerAlgebra-Algorithms, Implementations and Applications) 1335

      Pages: 68-75

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Shapes of planar cubic curves2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Scientiae Mathematicae Japonicae 59

      Pages: 133-138

    • NAID

      10012917268

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Family of G2 Cubic Transition Curves2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of IEEE Inter.Conference on Geometric Modeling and Graphics, GMAG03-UK(10-12 July,(IEEE Computer Society Press, USA)

      Pages: 118-122

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quadratic and T-cubic spline approximations to a planar spiral2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Scientiae Mathematicae Japonicae 56

      Pages: 149-156

    • NAID

      10011059526

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Family of cubic G2 Spiral Transition2003

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      Workshop on Appled Maths, 2003, Dec.18-20, Ryukoku Univ.

      Pages: 247-252

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] G^2 Planar Cubic Transition Between Two Circles2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Inter.J.Computer Math. 80

      Pages: 959-967

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Shapes of Bezier Conic Segments2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Advances in Geometric Modeling(Editor : M.Sarfraz)(John Wiley)

      Pages: 133-151

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Planar G^2 Cubic Transition Curves Between Two Circles2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Kokyuroku (Computer Algebra-Algorithms, Implementations and Applications) 1335

      Pages: 68-75

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Family of G^2 Cubic Transition Curves2003

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of IEEE Inter.Conference on Geometric Modeling and Graphics, GMAG03-UK(10-12 July,2003,London England)(IEEE Computer Society Press, USA)

      Pages: 118-122

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] T-Cubic and Arc/T-Cubic Spirals for Web-based Visualization of Planar Data2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of 4th KFUPM Workshop on Information & Computer Science : Internet Computing (WICS'2002), Saudi Arabia

      Pages: 267-278

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Quadratic and t-cubic spline approximations to a planar spiral2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Scientiae Mathematicae Japonicae 55

      Pages: 107-114

    • NAID

      10011059526

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] High accurate rational cubic curve2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Scientiae Mathematicae Japonicae 55

      Pages: 479-484

    • NAID

      10010239216

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] G2 Planar Spiral Cubic Interpolation to a Spiral2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of EEE Computer International Confer. On Information Visualization, IV02-UK(10-12, July, 2002, London)(IEEE Society Press, USA)

      Pages: 51-56

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] G2 two point Hermite rational cubic interpolation2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Inter.J.Computer Math. 79

      Pages: 1225-1231

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Spiral Spline Interpolation to a Planar Spiral2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Kokyuroku (Computer Algebra-Algorithms, Implementations and Applications) 1295

      Pages: 102-108

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] G2 Planar Spiral Cubic Interpolation to a Spiral2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of EEE Computer International Confer. On Information Visualization, IV02-UK(10-12, July, 2002, London, England)(IEEE Society Press, USA)

      Pages: 51-56

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Planar G2 cubic transition curves between two circles2002

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      Workshop on Applied Maths, 2002, Dec.19-21, Ryukoku Univ.

      Pages: 247-252

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] T-Cubic and Arc/T-Cubic Spirals for Web-based Visualization of Planar Data2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of 4th KFUPM Workshop on Information & Computer Science : Internet Computing (WICS' 2002), Saudi Arabia

      Pages: 267-278

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] High accurate rational cubic curve, Scientiae2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Mathematicae Japonicae 55

      Pages: 479-484

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] G2 Planar Spiral Cubic Interpolation to a Spiral2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Proceedings of EEE Computer International Confer.On Information Visualization, IV02-UK(10-12,July,2002,London, England)(IEEE Society Press, USA)

      Pages: 51-56

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] G^2 two point Hermite rational cubic interpolation2002

    • Author(s)
      Z.Habib, M.Sakai
    • Journal Title

      Inter.J.Computer Math. 79

      Pages: 1225-1231

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Planar G^2 cubic transition curves between two circles

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      Workshop on Appled Maths, 2002,Dec.19-21(Ryukoku Univ.)

      Pages: 247-252

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Family of cubic G^2 Spiral Transition

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      Workshop on Appled Maths,2003,Dec.18-20(Ryukoku Univ.)

      Pages: 247-252

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Shapes of Bezier Conic Segments

    • Author(s)
      M.Sakai, Z.Habib
    • Journal Title

      Worshop on applied Maths,2004,Dec.20-22(Ryukoku Univ.)

      Pages: 153-158

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Rational cubic spline interpolation with shape control

    • Author(s)
      Z.Habib, M.Sarfraz, M.Sakai
    • Journal Title

      Computers & Graphics 29, no.4(Accepted for publication)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] Z.Habib, M.Sakai: "Family of G2 spiral transition"Inter.J.Computer Mathematics. 80. 959-967 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Z.Habib, M.Sakai: "Planar G2 cubic transition curves between two circles"京都大学数理解析研究所講究録. 1335. 68-75 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Z.Habib, M.Sakai: "Quadratic and T-cubic spline approximations to a planar spiral"Scientiae Mathematicae Japonicae. 56. 149-156 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Z.Habib.M.Sakai: "Family of G2 spiral transition between two circles"Advances in Geometric Modeling, John Wiley, Editor : M.Sarfraz. book chapter. 133-150 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Z.Habib, M.Sakai: "Shapes of parametric cubic curves"京都大学数理解析研究所講究録. 1335. 57-67 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Z.Habib, M.Sakai: "G2 planar spiral cubic interpolation to a spiral"Proceedings of Sixth International Conference on Information Visualization, 51-56,10-12 July 2003, London, England. 51-56 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Z.Habib, M.Sakai: "G^2 two point Hermite rational cubic interpolation"Inter.J.Computer Math.. 79. 1225-1231 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Z.Habib, M.Sakai: "Spiral cubic interpolation to a planar spiral"京都大学数理解析研究所講究録. 1295. 102-108 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Z.Habib, M.Sakai: "G^2 planar spiral cubic interpolation to a spiral"Proceedings of Sxith International Conference on Information Visualization. 51-56 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Z.Habib, M.Sakai: "High accurate rational cubic curve"Scientiae Mathematicae Japonicae. 55. 479-484 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Sakai, Z.Habib: "Planar G^2 cubic transition curves between two circles"応用数学合同研究集会報告集,2002年12月19-21日,龍谷大学瀬田キャンパスRECホール,6号館. 95-100 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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