Cycloid of Ceva - going from polar to parametric curve

Question

Ceva Cycloid polar coordinates form is: $$ r = 1 + 2\cos(2\phi) $$

I found that the relation between polar and Cartesian coordinates can be expressed:

$$ x = r\cos\phi, y = r\sin\phi $$

I need to express Ceva Curve as a parametric equation of the form: $$ a(t) = (f(t), g(t)) $$

The purpose is that I can draw Ceva Curve as a raster image, programmatically. $a(t)$ could be treated as function of time.

I'd be very grateful for instructions.

Cycloid of Ceva:

Answer 1

Note that it should be $r = 1 + {\color{red}2}\cos(2\phi)$. Simply take $$ a(t)=(r(t)\cos t,r(t)\sin t), $$ with $$ r(t)=1 + 2\cos(2t). $$