2004 Fiscal Year Final Research Report Summary
Spirals and Thier Applications in CAGD
| Project/Area Number |
14540130
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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) |
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)
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| Project Period (FY) |
2002 – 2004
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| Keywords | spirals / cubic / guintic / transition curves / Mathematica / rational / geometric / Hermite interpolation |
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| 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.
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