I’ve been working on a color wheel for the past few hours, and have really great progress so far:

I’m successfully able to, given the X and Y of the mouse in the local space of the wheel, solve for the Hue and Saturation as follows:

```
-- mid = midpoint of the circle (also the radius)
-- dist = distance from the mouse to the midpoint
local hue = (math.pi - math.atan2(y - mid, x - mid)) / (math.pi * 2)
local sat = dist / mid
```

This works super well, my issue comes in that I now have to go the reverse way: Solve for an X and Y given a Hue and Saturation.

Here are my algebra steps to solve down the original hue equation for the angle:

`.1) h = (π - arctan(a)) / (2π)`

`.2) 2πh = π - arctan(a)`

`.3) 2πh - π = -arctan(a)`

`.4) π - 2πh = arctan(a)`

So I’ve arrived at where I would reverse the `arctan`

, and normally I would take the `tan`

of both sides. I tried this and got really undesirable numbers.

I believe I’m left with two options, either my algebra is wrong (which is totally possible), or the `atan2`

function does more under the hood than just an `arctan`

which I need to account for in my equation, which I think is the more likely option but I don’t really know. So now I ask for help, how should I solve for `a`

? And overall, what else should I know to solve for `x`

and `y`

given `a`

?