Spline approximation of planar discrete data

平面离散数据的样条近似

• 批准号: 12640134
• 负责人: SAKAI Manabu
• 金额: $ 1.86万
• 依托单位: Kagoshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640134/
• 关键词: curve fitting; spline; interpolation; curvature; spiral; Mathematica; rational; スプライン関数; 形状保存; 変曲点; 特異点

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.

螺旋线有几个优点，既不包含拐点，奇点，也不曲率极值。在视觉上令人愉悦的曲线设计中，这种曲线对于现有曲线的延伸和现有曲线之间的过渡是有用的。这种由三次样条组成的三次螺旋线，即仅在指定位置具有曲率极值的曲率连续曲线，对于高速公路或铁路路线或移动的机器人的轨迹或数控切割机械的切割路径的设计等应用是理想的。首先给出了对给定数据在每个子区间上可使用T-三次或弧/T-三次时，控制点处的单位切向量的条件。其次，我们提出了平面三次样条曲线的等距曲线的三次样条逼近算法，并导出了三次样条逼近算法的一个易于计算的算法和等距长度存在的一个充分条件。第三，我们证明了，如果光滑螺线上的两个插值点足够接近，则插值到从螺线上取的G^2 Hermite数据的两点三次样条也是螺线。

项目成果

M.Sakai: "Osuculatory Interpolation"Proceeding of SciCADE 2001, Vancouver, Jul.29-Aug.3. 92 (2001)

M.Sakai：“Osuculatoratory Interpolation”SciCADE 2001 论文集，温哥华，7 月 29 日至 8 月 3 日。

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).

Zulfiqar Habib，Manabu Sakai：“平面螺旋的Aspiral interpolation”，京都大学数学科学研究所（待发表）。

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

Z.Habit，M.Sakai：“高精度有理三次曲线”Scientiae Mathematicae Japonicae。

M.Sakai: "Osculatory Interpolation"Comp. Aided Geometric Design. 18. 739-750 (2001)

M.Sakai：“接触插值”Comp。

Habib,Zulfiqar & Sakai,Manabu: "G^2 two point Hermite rational cubic interpolation")accepted for) pubication in Inter. J. Computer Math..

哈比卜·佐勒菲卡尔