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How do I plot the Cornu parametric spiral in 3D with Mathematica. The 2D is quite easy. For more details, you need to be familiar with the Cornu statement.

$$\begin{cases} x(t)=\int_{0}^{t}\cos(u^{2})du&\\ y(t)=\int_{0}^{t}\sin(u^{2})du& \end{cases}$$

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body[t_] = Integrate[#[u^2], {u, 0, t}] & /@ {Cos, Sin}

enter image description here

ParametricPlot3D[body[t]~Join~{t}, {t, -2 Pi, 2 Pi}, 
 BoxRatios -> 1, SphericalRegion -> True]

enter image description here

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    $\begingroup$ I hope folks will help you get Reversal badge :) $\endgroup$ – Kuba Apr 3 '14 at 18:26

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