| Project/Area Number |
18560130
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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 |
Design engineering/Machine functional elements/Tribology
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| Research Institution | Shizuoka University |
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Principal Investigator |
MIURA Kenjiro Shizuoka University, Graduate School of Science and Technology, Professor (50254066)
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| Co-Investigator(Kenkyū-buntansha) |
YAMASHITA Atsushi Shizuoka University, Dep. of Mech. Engi, Associate Professor (30334957)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,810,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥2,900,000 (Direct Cost: ¥2,900,000)
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| Keywords | log-aesthetic curve / inflection point / G2 continuity / logarithmic curvature graph / compound-rhythm curve / logaritbmic spiral / clothoid curve / Nielsen's spiral / 美しい曲線の一般式 / 美的曲線 / 曲率対数分布図 / 自己アフィン性 / フルネー・セレーの公式 / ねじれ率 / B-spline曲線 / 共役勾配法 |
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| Research Abstract |
The curve is the most basic design element to determine shapes and silhouettes of industrial products and works for shape designers and it is inevitable fir them to make it aesthetic and attractive to improve the total quality of the shape design. If we can find equations of the aesthetic curves, it is expected that the quality of the curve design improves drastically because we can use them as standards to generate, evaluate, and deform the curves The authors have proposed the general equations of aesthetic curves as such a standard. The log-aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral thorn of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design However, their input method proposed so fir by use of three so-called control points can generate only an aesthetic curve segment with monotonic curvature variation and can not create a curve with the curvature-extremal point or the inflection point Hence at first we propose a technique to input a log-aesthetic curve segment with an inflection point at its end. Then we propose a method to generate a log-aesthetic curve with G2 continuity from a sequence of 2D points input with, for example, a liquid crystal pen tablet.
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