TITLE: Equation of a 2D 'helix'
QUESTION [5 upvotes]: 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. 

What would the equation of this shape look like?

REPLY [4 votes]: 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.