Definition:Cornu Spiral

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The Cornu spiral is the locus $C$ of the equation expressed in intrinsic coordinates as:

$s = a^2 \kappa$


$s$ denotes the length of arc at a point of $C$ from the origin
$\kappa$ denotes the curvature of $C$ at that point.


Also presented as

The Cornu spiral can also be presented in the form:

$s = a^2 \dfrac {\d \psi} {\d s}$

where $\psi$ is the turning angle of $C$ at the point where the length of arc from the origin is $s$.

Also known as

Other names for the Cornu spiral include:

Euler spiral (for Leonhard Paul Euler)
klothoid or clothoid

Also see

Source of Name

This entry was named for Marie Alfred Cornu.

Historical Note

The Cornu spiral is used primarily for:

analysis of intensities of diffraction patterns
designing curves on railway lines and roller coasters so as to provide a smooth curvature transition