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Spline approximation of planar discrete data

Research Project

Project/Area Number 12640134
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) ATSUMI Tsuyoshi  Kagoshima Univ., Fac. of Sci., Prof., 理学部, 教授 (20041238)
NAKASHIMA Masaharu  Kagoshima Univ., Fac. of Sci., Prof., 理学部, 教授 (40041230)
Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2000: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordscurve fitting / spline / interpolation / curvature / spiral / Mathematica / rational / スプライン関数 / 形状保存 / 変曲点 / 特異点
Research Abstract

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. First we have obtained the condition on the unit tangent vectors at the controlled points if T-cubic or arc"/ T-cubic can be used on each subintervals for the given data. Secondly, we have proposed an algorithm for a cubic spline approximation of an offset curve for a planar cubic spline and derived an easier to calculate algorithm for the cubic approximation method and a sufficient condition on an offset length for the existence. Thirdly, we have shown that that two-point cubic splines interpolating to the G^2 Hermite data taken from the spiral are also spirals if the two interpolation points on the smooth spiral are close enough.

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] Z.Habit, M.Sakai: "High accurate rational cubic curve"Scientiae Mathematicae Japonicae. 5. 341-346 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Sakai, Z.Habit: "Spiral cubic interpolation to a planar spiral"応用数学合同研究集会報告集. 247-252 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Sakai: "Osuculatory Interpolation"Proceeding of SciCADE 2001, Vancouver, Jul.29-Aug.3. 92 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Z.Habit, M.Sakai: "Spiral interpolation to a planar spiral"京都大学数理解析研究所講究録. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] K.Suenaga, M.Sakai: "Cubic spline approximation of offset curves of planar cubic splines"Inter. J. Computer Math. 178. 445-450 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Sakai: "Osculatory Interpolation"Comp. Aided Geometric Design. 18. 739-750 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Suenaga,Katsumasa and Sakai,Manabu: "How to join two circles with one circle inside the other"Rep. Fac. Sci., Kagoshima Univ.. 33. 47-54 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sakai,Manabu: "Osculatory Interpolation"Comp. Aided Geometric Design. 18. 739-750 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Suenaga,Katsumasa and Sakai,Manabu: "Cubic spline approximation of offset curves of planar cubic splines"Inter. J. Computer Math.. 178. 445-450 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Habib,Zulfiqar & Sakai,Manabu: "High accurate rational cubic curve"Scientiae Mathematicae Japonicae. 5. 341-346 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sakai,Manabu: "Osuculatory Interpolation"Proceedings of Inter. Conf. on Scientific Computation & Differntial. Eqs )Vancouver, Canada), Jul. 29-Aug. 3. 92 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Habib,Zulfiqar & Sakai,Manabu: "G^2 two point Hermite rational cubic interpolation")accepted for) pubication in Inter. J. Computer Math..

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Habib,Zulfiqar & Sakai,Manabu: "Quadratic and T-cubic spline approximation to a planar spiral")sumbitted to) Scientiae Mathematicae.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Habib,Zulfiqar & Sakai,Manabu: "T-cubic and arc/T-cubic spirals for Web-based visualization of planar data")accepted in) Proceedings of the Workshop at King Fahd Univ. of Petroleum & Minerals to be held in March, 2002.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sakai,Manabu & Habib,Zulfiqar: "G^2 Spiral cubic spline interpolation to a planar spiral")submitted to) Proceedings of the Syposium at Univ. of London to be held in July, 2002.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Zulfiqar Habib, Manabu Sakai: "High accurate rational cubic curve"Scientiae Mathematicae Japonicae. 5. 341-346 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Manabu Sakai, Zulfiqar Habib: "Spiral cubic interpolation to a planar spiral"応用数学合同研究集会報告集. 247-252 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Manabu Sakai: "Osuculatory Interpolation"Proceedings of SciCADE 2001, Vancouver, Jul.29-Aug.3. 92 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Zulfiqar Habib, Manabu Sakai: "Apiral interpolation to a planar spiral"京都大学数理解析研究所講究禄. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Katsumasa Suenaga, Manabu Sakai: "Cubic spline approximation of offset curves of planar cubic splines"Inter. J. Computer Math. 178. 445-450 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Manabu Sakai: "Osculatory Interpolation"Comp. Aided Geometric Design. 18. 739-750 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 酒井宦: "Planar cubic spirals"数理解析研究所講究録. 1145. 204-210 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 酒井宦,末永勝征: "Cubic spline approximation of offset curves of planar cubic splines"応用数学合同研究集会報告書. 127-132 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 末永勝征,酒井宦: "How to join two circles with one circle inside the other"鹿児島大学理学部紀要. 33. 47-54 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Suenaga & M.Sakai: "A cubic spline approximation of an offset curver of planar cubic spline"Intern.J.Computer Math.. (to appear).

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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