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词汇 Cornu Spiral
分类 英语词汇 英语翻译词典
释义

Cornu Spiral

中文百科

羊角螺线 Euler spiral

（重定向自Cornu Spiral）
双头欧拉螺线

羊角螺线（clothoid），又称欧拉螺线（Euler spiral），是形式为

x = C(t)
y = S(t)

的曲线，其中 C(t)、S(t) 为 Fresnel积分：

S(x)=\int_0^x \sin(t^2)\,dt=\sum_{n=0}^{\infin}(-1)^n\frac{x^{4n+3}}{(4n+3)(2n+1)!},
C(x)=\int_0^x \cos(t^2)\,dt=\sum_{n=0}^{\infin}(-1)^n\frac{x^{4n+1}}{(4n+1)(2n)!}.

上面参数方程的参数t，也是螺线于该点的曲率：\kappa(t) = t。

两个螺线的中心位于\pm ( \sqrt{\pi} / 2 , \sqrt{\pi} / 2)

由于此螺线的曲率与长度成正比，故常用于公路工程或铁路工程，以缓和直路线与圆曲路线之间的曲率变化（向心力变化）。

在光学上，近场绕射（Fresnel绕射）中会应用Fresnel积分。

英语百科

Euler spiral 羊角螺线

（重定向自Cornu Spiral）
A double-end Euler spiral. The curve continues to converge to the points marked, as t tends to positive or negative infinity.
Animation depicting evolution of a Cornu spiral with the tangential circle with the same radius of curvature as its tip (click on thumbnail to observe).

An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred to as spiros, clothoids, or Cornu spirals.

Euler spirals have applications to diffraction computations. They are also widely used as transition curve in railroad engineering/highway engineering for connecting and transiting the geometry between a tangent and a circular curve. The principle of linear variation of the curvature of the transition curve between a tangent and a circular curve defines the geometry of the Euler spiral:

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