Help identifying the function

Question

I plotted some raw data and it looks like it's almost a perfect circle (the first half of it).

From point H till point F we can see a nice circular curve.

What's the relationship between H and F? In other words, if there was a function of $x$, what would it be?

Answer 1

Let the point $R$ have coordinates $(r_1,r_2)$ then $H,G,A,B,C,D$ and $E$ would have coordinates of the form $$\big(\cos(x+r_1)+r_2,\sin(x+r_1)+r_2\big)$$

It seems though for me as $F$ is not on the circle.

Answer 2

The implicit equation for a circle is $(x-a)^2+(y-b)^2=r^2$, where $(a,b)$ is the center of the circle and $r$ is the radius. You need the lower half of the circle, so you can rearrange it to get $y=-\sqrt{r^2-(x-a)^2}+b$.