Roextended Project

Introduction

Using Google Sheets, I’ve created calculators that will help you find the correct FOV and multimon settings for any monitor setup. This post will act as documentation, going over how the calculators work and what each parameter means.

For more information about FOV and a step by step guide on tuning your own setup, see my other post. Link: viewtopic.php?f=23&t=2125



General Information

The multimon_config.sii file provides the user with extensive control over the game’s camera. Up to 4 different camera views can be manipulated, changing the FOV, rotation, position, and cropping of each view. It also controls where on your screen the resulting views will appear.

The objective of the calculators is to provide the settings that match your specific setup as closely as possible. To do this, the calculator needs to know the position and orientation of your monitors relative to your head position. Your job is to enter in the requested measurements.

All distance values you enter must be in the same units. Which unit doesn’t matter (in, cm, mm), just don’t mix and match. Any angles you enter will be in degrees. I’ve tried to choose the easiest measurements that will give the calculator everything it needs to recreate your setup.

Included in the calculators are visualization diagrams that I’ve made out of graphs. They show what the setup you’ve entered looks like, so you can make sure it matches your actual setup.

To use the calculator, you must "Make A Copy". Do not request permission to edit.

• On desktop, go to File >> Make a copy.
• On mobile, tap the three dots to see more options, then it’s Share and Export >> Make a Copy.

I can’t allow edit access, since everyone’s edits will be visible to everyone else. That’s just how Google Drive works. I wish they made the “make a copy” option more obvious.

Calculator Link: https://docs.google.com/spreadsheets/d/ ... sp=sharing



Landing Page

The landing page contains general information and links to various related resources. Of note is the Color Legend, which shows what the cell colors mean. It should be self explanatory, just follow the rules.



Basic Calculator

Formerly named Horizontal Calculator, this calculator is designed to be simple and straightforward to use. For the majority of common setups, this is all you need to get the correct settings.


Capabilities

• Allows up to three monitors total
• Fixed center monitor plus a left and a right monitor
• Can shift monitors vertically

Input Parameters

> Monitor Angle:

• how angled the side monitors are compared to the center
• 0 is parallel, 90 is perpendicular, facing inward
• must be between 0 and 90, not inclusive

> Screen Width:

• width of the screen without bezels

> Screen Height:

• height of the screen without bezels

> Bezel Widths:

• width of the bezel on one side of the monitor
• just used to create a gap between screens, can be whatever distance you desire, even negative
• distance is applied parallel to the screen

> Perpendicular Eye Distance:

• distance from eye to screen, when your look direction is perpendicular to the screen’s surface
• when measuring, just go from your eyes to the screen in a straight line, don’t overthink
• as indicated by the colors, only enter eye distance for the center screen, the others are auto-calculated

> Vertical Offset:

• shift the monitor up or down
• requires screen height to function
• monitor moves up with positive values, down with negative values

> Auto Vertical Alignment:

• adds the appropriate offset to align the side monitor with the center monitor
• requires screen height of side monitor and center monitor to function
• can be used together with vertical offset to precisely tweak alignment

Helper Values

The column labeled “Normalized Eye Level Offset” shows the deviation of the eye level from screen center as a percentage of the screen height. If 0, the eye level is centered; if positive, eye level is above center; if negative, eye level is below center. Increasing vertical offset decreases eye level offset, and vice versa.

There are also potentially useful values worth mentioning. The cell labeled “Approximate Total hFOV” calculates the horizontal view angle from the left-most edge to the right-most edge of your setup. The reason it is approximate is because it counts the bezels as part of the FOV.

The higher the number, the more can be seen at once. This lets you quickly judge how practical the settings will be to use, and may be useful for those wanting to optimize their setup, as you can easily compare different options.

There are also cells labeled “Midpoint Between Center & Side Monitor”. This is referring to the eye distance where both the side monitor and center monitor are facing you directly. There are separate values for the left and right monitor.

This can be useful if you do not want to measure a specific eye position, and just want to sit in the midpoint between your monitors. To use it, copy the value to the center monitor’s perpendicular eye distance. You could also copy the formula if you want the value to continuously update.


Calculation Method

The situations this calculator applies to are relatively static, so I am simply doing some trigonometry to find the angles and distances I need.

By knowing the eye distance to the center monitor and the width of the screen, it creates an isosceles triangle that I can solve. The angles allow me to find the FOV for the center monitor.

For the side monitors, I can once again use triangles to find the distances and angles. I just need the screen width, bezel widths, and monitor angle, along with the measurements from the center monitor. This old post I made shows the general process. Link: viewtopic.php?f=23&t=2125&p=45056#p45056

The helper values in my calculator actually represent variables from the third diagram. From left to right, the helper values represent “a”, “c”, “e”, and “f”. The only difference in the formulas is how I deal with bezels.

This method is flawed though, since as the monitor angle approaches 90°, “a” and “c” approach infinity, and the formula breaks. However, since it’s quite rare for a setup to have side monitors at 90°, I haven’t bothered fixing it. If you need this capability, use the Hybrid Calculator instead.

Finally, if there is any eye level offset to apply, it uses the screen height and perpendicular eye distance to create more right triangles that are solvable. This other post shows the formulas I used. Link: viewtopic.php?f=23&t=2125&p=45057#p45057



Hybrid Calculator

This newest calculator combines aspects from all my previous calculators. It provides the full range of options all in one place and can accommodate almost any setup, while still being fairly easy to use.

Use this Hybrid Calculator if the Basic Calculator isn’t enough to recreate your setup, or if you want to access the extra features. These include auto width/height from aspect ratio, LHD/RHD offset, curve compensation options, additional FOV info, virtual screen space/UI adjustment, and console script output.


Capabilities

• Allows up to four monitors total (max for the game)
• Adjustable center monitor plus left, right, up, or down monitors
• Can add multiple monitors to one side (ex. 2 right monitors)
• Can shift monitors horizontally or vertically
• Can yaw or pitch any monitor
• Has options for curved monitors
• Full virtual screen space control

Parameters

> Add Monitor to:

• choose from the drop-down in which direction this monitor should be added, relative to previous monitors
• for center monitor, choose whether monitor angle represents yaw or pitch

> Monitor Angle:

• how angled the monitor is compared to the previous adjacent monitor
• for center monitor, positive angle means back of monitor is facing right (if yaw) or up (if pitch)
• for center monitor, negative angle means back of monitor is facing left (if yaw) or down (if pitch)
• for other monitors, positive angle means angling inwards, negative angle means angling outwards
• LIMITATION: if a monitor is split horizontally, resulting pitch will always be 0

> Screen Width:

• width of screen without bezels
• typing “Auto” into the cell will have the width auto-calculated based on height, aspect ratio, and curvature
• cannot have both width and height be auto

> Screen Height:

• height of screen without bezels
• typing “Auto” into the cell will have the height auto-calculated based on width, aspect ratio, and curvature
• cannot have both width and height be auto

> Bezel Widths:

• width of the bezel on one side of the monitor
• just used to create a gap between screens, can be whatever distance you desire, even negative
• distance is applied parallel to the screen
• not all bezel widths are needed; if there is no adjacent monitor, it will not affect the result, so the cell will be grayed out

> Lateral Offset:

• move entire monitor horizontally by this distance
• positive values move to the right, negative values move to the left
• unused if left or right monitor, use bezels to perform lateral offset instead

> Vertical Offset:

• move entire monitor vertically by this distance
• positive values move up, negative values move down
• unused if up or down monitor, use bezels to perform vertical offset instead

> Auto Alignment:

• for center monitor, choose LHD or RHD to add the appropriate lateral offset for an LHD/RHD setup
• for left/right monitor, choose Center, Top, or Bottom to add the appropriate vertical offset to align with the center monitor
• for up/down monitor, choose Center, Left, or Right to add the appropriate lateral offset to align with the center monitor
• can be used together with lateral or vertical offset to precisely tweak alignment

> Curvature Radius:

• the curvature specification of the monitor, listed as the radius of a circle in millimeters (e.g. 1800R)
• convert to the same units used in your other distance measurements
• assumes curvature is along width for landscape aspect ratios and along height for portrait aspect ratios

> Split Into How Many Views:

• how many views the monitor should be evenly divided into
• the more views, the more accurate the approximation to the curve
• total number of views is limited to 4
• splits horizontally for landscape aspect ratios, and splits vertically for portrait aspect ratios

> Screen Width (Pixels):

• pixel width of screen

> Screen Height (Pixels):

• pixel height of screen

> Lateral Offset (Pixels):

• move entire screen horizontally by this many pixels
• positive values move right, negative values move left

> Vertical Offset (Pixels):

• move entire screen vertically by this many pixels
• positive values move down, negative values move up

> Should Display UI:

• whether the game’s UI should display on this screen
• if none are checked, UI will display across all screens

> FOV Adjustment Method:

• eye distance and FOV are directly related; choose your preferred adjustment method
• no matter what you choose, an eye distance to screen center value will be calculated and used for the rest of the calculations

> Value (for Center Monitor):

• the eye distance or target FOV for the center monitor
• for Eye Distance to Screen Center, measure directly to center point of screen, even if at an angle
• for Perpendicular Eye Distance, measure in the direction perpendicular to the surface of the screen
• for Target Horizontal FOV or Target Vertical FOV, simply choose a desired value in degrees

> Invert Normalized Y:

• in recent game updates, the normalized y parameter was changed to specify the top edge of the monitor rather than the bottom
• this checkbox fixes that, uncheck it if you play on an older version before the change

Helper Values

The curvature angle helper value refers to how much of a circle the monitor should look like. For example, if it were 180, the monitor would look like a half circle. If it were 90, it would be a quarter circle.

The curvature depth helper value refers to the depth the screen has due to the curve. So if you were to draw a straight line from edge to edge of the curved monitor, how far the center of the screen would be from that line is the curvature depth.

These helper values can help you tweak the curvature radius input if you don’t know the curvature specification of your monitor, or if your monitor is not curved like a cylinder.

Apparent lateral and vertical skew attempts to quantify how far off center the view is on each monitor. Positive means the right or top of the monitor appears skewed, negative means it’s the left or bottom. A value of 1 means the center of the camera view is exactly at the edge of the screen.

Normally, this skew is just an inherent part of a mathematically correct view, you will not notice it as long as you’re in the correct head position. But if you don’t/can’t use that head position, this helper value can quantify how much apparent skew you can expect. Then you can figure out which settings will reduce skew, if that’s what you want.

Will add more to this section later


Calculation Method

The calculations here are a combination of the previous Physical and Virtual Calculators, reworked to integrate curve compensation and the new features. All the previous curve compensation splitting logic was rewritten to improve functionality and consistency. Repetitive operations were also converted to named functions for better readability.

Overall, it’s a two stage process. In the first stage, any relative inputs are converted into absolute inputs, and useful values related to curvature are calculated. The physical measurements determine the 3D vector position of each monitor, using a 3D coordinate space where the head position is the origin point.

More specifically, the 3D position of the center monitor can be calculated from “eye distance to screen center”, “lateral offset”, and “vertical offset”. Then, the positions of each additional monitor can be found using their widths/heights, bezels, angles, and offsets. The math is mostly vector addition and rotation.

The virtual 2D positions of each monitor are also calculated in this stage. With the center monitor being at the origin, the other monitor positions are simple to calculate using their pixel widths/heights and offsets; it’s all just addition or subtraction.

In the second stage, monitors are split into the appropriate number of views. Each view is treated as a separate monitor, with adjusted angles, dimensions, and 3D vector positions based on the curvature. The math involves trigonometry and more vector addition and rotation. The 2D virtual coordinates and pixel dimensions are also adjusted accordingly.

Perpendicular eye distance and angle to edge values are then calculated, which provides the measurements for the right triangles used for FOV calculations. These values are obtained by rotating the 3D position vector of each monitor by their negative yaw and pitch values, which “realigns” the monitor to the axes.

Finally, the rest of the multimon parameters are calculated. The “normalized” variables use the pixel values, simply normalizing each value to the combined size of the screens. For the UI, see the calculation method section of the Standalone Virtual Calculator for the explanation, it works exactly the same.

You can easily look at the formulas in each cell if you’re interested in delving deeper. I will gladly answer any questions about the calculations if you have any.



Standalone Physical Calculator

Formerly named Quad Calculator or Advanced Calculator, this is an enhanced version of the Basic Calculator. It does the same job, dealing with the parameters related to physical dimensions, but can accommodate more setup types. It uses absolute inputs for consistency, which might make it less intuitive to use.

With the new Hybrid Calculator that combines all the different options into one place, there’s little reason to use this standalone calculator. It’s just another way to do the calculations, as the formulas are slightly different. I’ve since removed it from the main calculator to reduce clutter, but if you still want to use it for some reason, let me know.


Capabilities

• Allows up to four monitors total (max for the game)
• Adjustable center monitor plus left, right, up, or down monitors
• Can add multiple monitors to one side (ex. 2 right monitors)
• Can shift monitors horizontally or vertically
• Can yaw and pitch any monitor

Parameters

> Add Monitor to:

• choose from the drop-down in which direction this monitor should be added, relative to previous monitors

> Lateral Angle / Yaw:

• horizontal facing angle of monitor relative to forward look direction
• 0 means pointing directly forward (horizontally)
• negative angle means back of monitor is facing left
• positive angle means back of monitor is facing right

> Vertical Angle / Pitch:

• vertical facing angle of monitor relative to forward look direction
• 0 means pointing directly forward (vertically)
• negative angle means back of monitor is facing down
• positive angle means back of monitor is facing up

> Screen Width:

• width of screen without bezels

> Screen Height:

• height of screen without bezels

> Eye Distance to Screen Center:

• distance from eyes to center of monitor
• this is different from perpendicular eye distance, it does not need to be perpendicular
• as indicated by the colors, only enter eye distance for the center screen, the others are auto-calculated

> Bezel Widths:

• width of the bezel on one side of the monitor
• just used to create a gap between screens, can be whatever distance you desire, even negative
• distance is applied parallel to the screen
• not all bezel widths are needed; if there is no adjacent monitor, it will not affect the result, so the cell will be grayed out

> Lateral Offset:

• move entire monitor horizontally by this distance
• positive values move to the right, negative values move to the left
• unused if left or right monitor, use bezels to perform lateral offset instead

> Vertical Offset:

• move entire monitor vertically by this distance
• positive values move up, negative values move down
• unused if up or down monitor, use bezels to perform vertical offset instead

Calculation Method

The calculations here are much more complex than in the Basic Calculator. Since any monitor, including the center, can yaw and pitch, it’s a lot trickier to create the right triangles that I used to calculate the values before.

The way I did it is using 3D vectors in a 3D coordinate space, with the head position as the origin point. Starting with the center monitor, I could figure out the position vector of the center point using “eye distance to screen center”, “lateral offset”, and “vertical offset”.

Then, the position vector was projected onto the monitor’s normal direction, which is perpendicular to the surface of the monitor, found using the yaw and pitch. That gives me the perpendicular eye distance.

Next, the original position vector is rotated using matrix multiplication to “realign” the monitor to the axes. Finally, using the new coordinates along with the screen width/height and perpendicular eye distance, I can create my right triangles and find the angles that correspond to FOV.

For the other monitors, the process is similar, but I need to calculate their positions relative to the center monitor. Using the width, bezel, and angle measurements, this is not too difficult, just some trigonometry involved. Once I get the 3D position vector of the center point, the rest of the process is the same.

There’s definitely more efficient ways to do all of this, but I like using 3D vectors so I can visualize it in my head.



Standalone Virtual Calculator

This calculator is for the multimon parameters that pertain to the virtual screen space. These parameters only need to be tweaked for specific setups with mismatched monitor sizes, most setups will not need this. Its capabilities are similar to the Standalone Physical Calculator.

With the new Hybrid Calculator that combines all the different options into one place, there’s little reason to use this standalone calculator. It’s just a way to calculate these parameters separately. I’ve since removed it from the main calculator to reduce clutter, but if you still want to use it for some reason, let me know.


Capabilities

• Allows up to four monitors total (max for the game)
• Adjustable center monitor plus left, right, up, or down monitors
• Can add multiple monitors to one side (ex. 2 right monitors)
• Can shift monitors horizontally or vertically

Parameters

> Add Monitor to:

• choose from the drop-down in which direction this monitor should be added, relative to previous monitors

> Screen Width:

• pixel width of screen

> Screen Height:

• pixel height of screen

> Lateral Offset:

• move entire screen horizontally by this many pixels
• positive values move right, negative values move left

> Vertical Offset:

• move entire screen vertically by this many pixels
• positive values move down, negative values move up

> Should Display UI:

• whether the game’s UI should display on this screen
• if none are checked, UI will display across all screens

You will notice that there are two outputs for normalized ui x and width, either with or without aspect ratio compensation. The reason is that, since we can’t control the height or y values of the UI, it can sometimes get cut off on the top or bottom on certain setups.

The compensated values attempt to shrink the UI to make sure nothing is cut off. However, that means the UI won’t fill the screen all the way horizontally. You can see the difference in the visualization diagram if you toggle the UI Display Compensation checkmark.

For most normal setups though, the values with or without compensation will be the same, indicating that there’s no clipping.


Calculation Method

This one is quite simple. All positions and distances are on a 2D coordinate grid, so I simply add the appropriate distances together to find the points I’m interested in. Normalize to the combined size of the screens to get the values for the multimon parameters. No trigonometry or 3D vectors involved.

For the UI compensation, first we need to understand how the UI works. When we set its horizontal position and width, it will automatically try to fill the game window vertically as much as it can. However, it has a maximum height; it cannot exceed a 16:10 aspect ratio. Additionally, the UI always centers itself vertically within the game window.

So I look at the top and bottom edges of the monitors to see if the UI would exceed those bounds. If so, the UI width is reduced so that the height is in bounds. It will display 0 if there’s no way for it to keep the UI in bounds. This method is far from perfect, as it doesn’t take into account any horizontal position or vertically stacked monitors, so it may overcorrect in some cases.



Visualization Diagrams

Each of the calculators have visualization diagrams. Use them to check whether you've entered everything correctly. It should match what your setup looks like, with accurate proportions and positions.


Parameters

> X-Axis Margin Scalar:

• adjust the x-axis margins of the diagram
• 0 means no margins, diagram can touch the side of graph
• positive values leaves more space on the sides
• negative values allow the diagram to go out of bounds on the side

> Y-Axis Margin Scalar:

• adjust the y-axis margins of the diagram
• 0 means no margins, diagram can touch the top or bottom of graph
• positive values leaves more space on the top and bottom
• negative values allow the diagram to go out of bounds on the top or bottom

Calculation Method

The diagrams are made from line charts. I specify the x and y values of points, that then form lines representing the monitors. The points are calculated from the measurements that have been entered into the calculator. They are all multiplied by the scale factor.

The scale factor is automatically calculated to keep the entire diagram within the bounds of the graph. The margin scalar values adjust the scale factor, which effectively lets you zoom in or out. You could even just overwrite the scale factor value and set it to whatever you want.



Conclusion

Hopefully, these calculators will cover everyone’s setups. Let me know if you find any mistakes or weird behaviours. If you have questions, check the guide linked at the top first, you may find your answer there. If not, feel free to ask down below.

Changelog

Horizontal V1

• First iteration

Horizontal V2

• Added visualization graph, top down view
• Minor visual adjustments
• HOTFIX: subrect x value for right monitor was incorrect, it is now corrected

Horizontal V3

• Added monitor height input
• Added eye level offset input
• Added visualization graph, front view
• Repositioned sections
• Minor visual adjustments

Quad V1

• Added support for fourth monitor
• Monitors can be added in any direction (left, right, up, down)
• Added top and bottom bezels input
• Certain cells dynamically change color depending on if they matter
• Calculation methods improved (angle at 90 doesn't break things anymore)
• Added adjustable margin scalar values for visualization diagrams
• Visual adjustments and more

Quad V2

• Separated monitor angle into yaw and pitch
• Angles can now be applied to center monitor
• Added lateral offset value, works for center and vertical monitors
• Replaced normalized eye level offset with vertical offset
• Eye distance to center is now separate from perpendicular eye distance
• Checkmark for left/right swapped for better consistency
• Most inputs are now absolute rather than relative to adjacent monitor
• Calculation methods improved (uses 3D vectors, more consistent formulas)
• Visual adjustments and more

Major Update (08/15/23)

• All calculators are on the same file now
• Added Landing Page with general information
• Renamed Horizontal Calculator to Basic Physical Calculator
• Renamed Quad Calculator to Advanced Physical Calculator
• Added Virtual Calculator
• Added Curve Compensation Calculators (Physical and Virtual)
• Added LHD / RHD Offset Calculator
• Added Normalized Eye Level Offset / Vertical Offset Converter
• Added Eye Distance Calculator

Changes to Basic Physical Calculator:

• Fixed error in formula for Frustum Subrect X
• Added Auto Vertical Alignment input
• Added Potentially Useful Values section
• Added adjustable Margin Scalars for visualization diagrams
• Various visual adjustments

Changes to Advanced Physical Calculator:

• Switched to using dropdowns instead of checkmarks for direction to add monitor to
• Various visual adjustments

Major Update (12/10/23)

• Added Hybrid Calculator
• Removed all helper calculators (all functionality now included in Hybrid Calculator)
• Renamed Basic Physical Calculator to Basic Calculator
• Renamed Advanced Physical Calculator to Standalone Physical Calculator
• Renamed Virtual Calculator to Standalone Virtual Calculator

Changes to Landing Page:

• Removed "Which Calculator(s) Do I Use?" section (no longer necessary)

Changes to Basic Calculator:

• Normalized Eye Level Offset input changed to Vertical Offset (easier to use for alignment)
• Added Horizontal FOV Relative Offset output (makes it clear that it must be set to 0)
• Minor visual adjustments

Changes to Standalone Physical Calculator:

• Added Horizontal/Vertical FOV Relative Offset output (makes it clear that it must be set to 0)

Minor Update (05/20/24)

• Removed standalone calculators (they were mostly redundant, but let me know if you want them back)

Changes to Hybrid Calculator:

• Added Invert Normalized Y checkbox (fix for v1.50+)
• Added "multimon reload" to Console Script Output (wasn't necessary in my testing, but also didn't seem to harm anything)

This is AWESOME!!!! Thank you very very much. Works like a charm!

@FormelLMS - You're welcome!

Hi, please could you tell me the units (cm / mm / inches).

I have followed the set up on three monitors (27” 2560x1440, 32” 3440x1440, 27” 2560x1440) using SWRE but the centre camera seems too far forward in relation to the side cameras.

Thank you in advance.

@Hansoloscorpse - The units for distance can be whatever you want, but keep them all the same. For example, measure everything in inches or everything in millimeters, just don't mix and match.

If the view doesn't look right, check the visualization diagrams and make sure it looks accurate. Double check the numbers in your multimon file match the calculator as well.

For your case, I suspect the problem is due to the center monitor being a different aspect ratio to your side ones. Post a picture of what you've entered into the calculator and maybe your multimon file as well, and I can help you further.

Hey!
First of all thank you for your tool :)
I am running into an issue, it seems my FOVs are way too low. All three screens look like they are zoomed in.
Do you have any idea how to solve this?
Thank you very much!

@domi27 - Hi, the FOV seeming low is normal, that is how a mathematically correct FOV looks. Imagine your monitors as windows into the game world, the calculated view is what you should be seeing when you're sitting at the distance you've specified. If you want to maintain realism, the only ways to increase FOV are to move closer to your monitors, or get bigger monitors.

However, if neither of those are options, there are a few other things you can try. If your problem is that you can't see the dashboard without looking down, try raising your eye level by increasing the "normalized eye level offset" value in the calculator. If you do too much, you might not be able to see traffic lights without looking up, so it's a bit of a tradeoff. Adjusting your seat position may also help.

If you have trouble seeing out the side, you can try the "Smooth Interior Camera" plugin, which lets you set hotkeys to smoothly look to the side, then return back to center on release. JHTrucker also has controls.sii tweaks that may be of interest, check his post for that. Another option is headtracking, which is not my cup of tea, but many people seem to enjoy it.

But if all that is too impractical (which is totally understandable) and you don't mind giving up some realism, just set the "perpendicular eye distance" value in the calculator to an arbitrary number. The smaller it is, the higher the FOV. All the angles and bezel corrections will still be correct.

Hey a1337cookie, thank you for creating this, I've received many hours of better immersion due to your FoV calculator.
Math is not my strong point, and I was curious if it would be possible to add calculations for a 4th monitor?
For example: (left, center1, center2, right), where "center1" is at "0" degrees to you as normal, and "center2" is off to your right, but also flat and inline with "center1".

Thank you so much.

@SpectralTiger - I suppose I can cook something up. I took a break from the game and I've actually ditched my quad monitor setup for a VR headset, but I don't mind working more on the calculator. It's great to know that people are getting good use out of it. Give me a few days to make the new version.