= Euler spiral
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{wiki}
= Cornu spiral
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{synonym}
The <Euler spiral> is the planar <curve> parametrized by the <Fresnel integrals>. In the optical convention,
$$
C(u)+iS(u)=\int_0^u e^{i\pi t^2/2}\,dt.
$$
The tangent has unit length and argument $\pi u^2/2$, so its signed <curvature> is $\pi u$, proportional to signed <arc length>. In <Fresnel diffraction>, an interval integral is the directed chord joining its endpoint parameters on the <Cornu spiral>. Chord length gives the interval factor's <modulus>, while chord direction gives its <complex argument>.
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