Equation of a 2D 'helix' I need to write some code to draw a 2D helix. Not a spiral, but more like the 2D projection of a normal helix. This would be like the representation of the gluon particle in a Feynman Diagram. This is shown in the image. ![enter image description here]( What would the equation of this shape look like?

You can indeed use the projection of a 3D helix.

The parametric equations of an horizontal helix can be written

$$\begin{cases}x=r\cos t,\\\y=r\sin t,\\\z=at.\end{cases}$$

Then rotating by an horizontal angle $\theta$ and dropping the $z$ coordinate,

$$\begin{cases}x'=r\cos t\cos\theta-at\sin\theta,\\\y'=r\sin t\end{cases}.$$

These are cycloids.

![enter image description here](