2001 Fiscal Year Final Research Report Summary
Spline approximation of planar discrete data
| Project/Area Number |
12640134
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kagoshima University |
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Principal Investigator |
SAKAI Manabu Kagoshima Univ., Fac. of Sci., Prof., 理学部, 教授 (60037281)
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| 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)
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| Project Period (FY) |
2000 – 2001
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| Keywords | curve fitting / spline / interpolation / curvature / spiral / Mathematica / rational |
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| 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.
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