| Project/Area Number |
09640281
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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 Tsuyosi 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) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1998: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | curve fitting / shape preserving / curvature / singularity / inflection points / Mathematica / spline / spiral / 平面データ / スパライラル / スパイラル / 計算の手間 |
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| Research Abstract |
In this project, first we have obtained the distribution of inflection points and singularities on a parametric rational cubic curve segment with aid of Mathematica(A System for Doing Mathematics by Computer). The reciprocal numbers of the magnitudes of the end slopes determine the occurrence of inflection points and singularities on the segment Its use enables us to check whether the segment has inflection points ora singularity (a loop or a cusp) and to get an idea how to place control vertices and how to choose weights for the rational Bezier cubic curve segment to preserve the fair shape. Spiral segments have several advantages of containing neither inflection points, singularities nor curvature extrema. Next, we have given (i) an easy to use condition for a planar T- cubic .segment to be a spiral in terms of the reciprocal numbers of the magnitudes of the end slopes, (ii) the explicit form of the T-cubic spiral, and (iii) simple algorithms for forming a T-cubic spiral and an arc/T-cubic spiral. We have also discussed which spirals should be used according to the angles of the tangent vectors at the data points. These results are useful for generating planar "visually pleasing", "shape preserving" approximations to a set of planar data points.
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