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# How to: calculating angles to position Eyefinity/Surround monitors

How to: identify geometric angles and approximate lengths to position triple-monitor setups in order to achieve a desired viewing angle

UPDATE 7/10/2011:
Or if you want to do the math, continue reading...

Note that this guide will probably only be useful to those who have not yet purchased their displays. Or for those who already own three displays and are simply OCD (me) to verify/reassess the geometric configuration of said monitors.

First off, let me explain what you can identify using these calculations:
1) The length between you and your side monitors
2) The viewing angle on your side monitors
3) The angle between your two side monitors
And you can manipulate these values to determine any angle (more than likely the angle between your side monitors and your center monitor) to set up your new triple-monitor configuration.

Refer to the below photo:

In the steps below I will outline the method to identify angle x, or the angle between your two side monitors (since this is more than likely the only important detail you would want to know). However, like any mathematical formula, this can be manipulated so you can identify different values if need be.

Step 1: Identifying your display's horizontal size
Use the Pythagorean Thereom to identify the a and b values of the monitor given c, the diagonal size of the monitor. To determine the a:b ratio (the aspect ratio), divide the horizontal number of pixels by the vertical number of pixels. In my case it would be 1920:1080, or 16:9. This tells me there are 16 units of length for every 9 units of height.
We can determine the a and b values by first isolating a variable a:b proportion and then using substitution and plugging it in to the Pythagorean theoream in order to work with a single variable.
After determining the value of b, we can use substitution again and plug b into the Pythagorean Theorem to determine value a, the horizontal screen size.

However, since manufacturer screen size specifications do not compensate for the bezel length, we'll add 1 inch to the horizontal screen size, thus making it 21.5 inches.

Step 2: Begin determining approximate lengths
With the above knowledge of the horizontal screen size, we can further implement this by using the Pythagorean Theorem again to determine approximate lengths between you and your monitor. The only variable in this step is the length between you and your center monitor (assuming you are looking straight at it towards the center of your center monitor). In my case it will be 30 inches.
Here are the values we know thus far:

And since you are looking directly at the center of your center monitor, we can assume the values to the left and right of the 90 degree angle are the same. And as such we can also assume the same lengths apply to your side monitors (assuming you have three identical monitors):

We can use the Pythagorean Theorem to determine the length between you and the bezel of your two monitors, and we can further use that length to determine the length between you and the center of your side monitors.
Note that you can only determine the length between you and your center monitors if the viewing angle is assumed to be 90 degrees. If it is not, we will get to that later.

Step 3: Determining approximate angles
With the above knowledge we can begin using basic trigonometric formulas to determine approximate angles. We can first determine the angle between the side monitor and you. But remember since that angle is only half of the entire obtuse angle, we must multiply that value by 2.

And as such we can determine the angle between two side monitors, assuming you wanted the viewing angle to be a perfect perpendiclar angle:

If the viewing angle between your two monitors is not perfectly perpendicular...
Since the Pythagoream Theoream only applies to right triangles, this makes things slightly more difficult.
First, you must determine the desired viewing angle, or the angle between you and the center of your side monitor. I'm going to use 40:

And we can thus use the trigonometric cosine function to determine the length of the smaller triangle on the C₂ length (z). We can also determine value y in order to determine angle x for calculating the longer length on C₂.
EDIT 7/10/2011: An easier way to calculate C₂ is using the Pythagorean Theorem knowing the value of y (using trigonometric functions) and the length of C₁, then adding the value of z. Man, it's been a while since I've done any trig...
Thanks to mike.mg for pointing this out

Knowing these values allow us to find the angle of between the two side monitors by using more simple trigonometric functions:

And we translate these values into a view that is slightly easier to see:

It was my mistake to have chosen 40 as a degree--it is impossible to achieve that angle when the monitors are facing in, thus throwing my results off. Choosing a more realistic number would give you accurate results.
EDIT 7/10/2011: In order for all of this to work properly, you must choose an angle greater than 55 degrees.

Edited by kiwiasian - 7/10/11 at 7:40am
wow man nice post , didnt understand a thing but cool none the less .

Might bend my outside monitors in abit .
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couldnt we just move them in different angles until we like the way they are positioned, my way sounds alot easier then yours
You deserve rep for all that trig. Gawd I hated trig.
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Quote:
Originally Posted by pmrballer123;14077921
couldnt we just move them in different angles until we like the way they are positioned, my way sounds alot easier then yours

Yeah I kind of realized that when I was half way done writing this guide.

Hence why I added the following:
Quote:
Originally Posted by kiwiasian;14077885
Note that this guide will probably only be useful to those who have not yet purchased their displays. Or for those who already own three displays and are simply OCD (me) to verify/reassess the geometric configuration of said monitors.

Admittedly, before I bought my monitors I did at least 20 calculations like this to make sure everything was perfect.
Bump, pretty sure someone will benefit from this.
Lol bump again, everyone hates math
What is this, i don't even.......

Man i am impressed with the Napkin math and the time and effort you went for this, so totaly repping this.
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Lol thanks.
So apparently no one actually finds this useful.
wooooow that is ALOT of work
and just to show a little appreciation I did all what you did but in an excel sheet and i attached it (it was more fun than studying for my CE3400"mechanics of materials" mid-term on Monday:p )

and btw you had a lil mistake with your calculations where you used 21.5 instead of 21.05 for the monitor length

and to find C2 you didn't need to find the angle X. instead you can use the Pythagorean Theorem because you already have Y and C1, and that will save you an extra step

thanx again

Edited by mike.mg - 12/28/12 at 10:20am
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