get front face of polygon based on rotation

[sacha_sk]

I've got a cylinder with 9 radial segments, resulting in 9 faces, representing f.
Each face shows a number, representing n.

I can rotate this cylinder on it's X-axis to show a different face. To get this rotation I use the following formula:
[math]r = ((360/f*n) - (360/f/2)) / 180*\pi[/math]
So when e.g. f = 9 and n = 1 we get r = 0.35

Now say f = 9 and r = 1.75, how would be get the value of n?

Any help is appreciated, thanks

 

[sacha_sk]

I solved this in the following way:

We can get the rotation in degrees from r
[math]rDeg = r * 180/\pi[/math]
we can then put this back in range of 0-360
[math]rDeg360 = rDeg - (360 * floor(rDeg / 360))[/math]
now we know rDeg360 we can calculate n=? like this
[math]n = (rDeg360 + (360 / f / 2)) / 2 / (360 / f / 2)[/math]

It is very likely that this could be solved in a cleaner way or at least, written down in a cleaner way. Feel free to suggest other solutions, I'm here to learn.

 

[Dr.Peterson]

Work is much easier if you simplify first, rather than writing everything in the most complicated way you can think of. (For example, why write 360/f/2 rather than 180/f?)

The formula simplifies to [math]r=\frac{360}{f}\left(n-\frac{1}{2}\right)\frac{\pi}{180} = \frac{(2n-1)\pi}{f}[/math].

To solve this for n, just multiply by f, divide by pi, add 1, and divide by 2. Then, for f = 9 and r = 1.75, I get n = 3.