Angsizing Formula 2.0

[Kulf_Boba]

While trying to create a new angsizing formula for more accurate results, I discovered that Google Earth provides the distance from the camera to the ground and also includes scale lines indicating the length of objects on the screen. Using this information, I set out to develop a new formula. In the end, I modified the original formula to match the field of view used by the Google Earth camera.

I’d like to hear your thoughts on whether this formula could be implemented. I recalculated some cases using this new version and found that the distances were more than double those calculated with the original formula, which seems to be more accurate in most cases.

Angsizing Formula 2.0

vsbattles.fandom.com

Examples
N°1

• 70deg: 12742 * 1080/(1411 * 2 * tan(70deg/2)) = 6,964 km
• 35deg: 12742 * 1080 / [1411 * 2 * tan (35deg/2)] = 15,466 km (-Radius = 9.095 km)

N°2

• Distance to Fire Flame 70deg: 0.2275 * 667 /(56 * 2 * tan(70deg/2)) = 1.93m
• Distance to Fire Flame 35deg: 0.2275 * 667 / [56 * 2 * tan (35deg/2)] = 4.29m

N°3

• Distance to Electro 70deg: 0.225 * 370 /(24 * 2 * tan(70deg/2)) = 2.47m
• Distance to Electro 35deg: 0.225 * 370 / [24 * 2 * tan (35deg/2)] = 5.5m

 

[Floxy178]

Large Objects: Angsizing doesn’t account for the radius of large objects like planets, so it’s unclear whether the calculated distance is to the planet's center or surface, which isn’t ideal for certain analyses.

It will be distance to its center actually. In fact changing angle can't affect something like that, if you measure its diameter you get distance to its center in both cases.

Decreasing the angle simply requires the viewing point to be further away so that the object occupies the same portion of the screen. So it won't change context.

 

[Kulf_Boba]

It will be distance to its center actually. In fact changing angle can't affect something like that, if you measure its diameter you get distance to its center in both cases.

Decreasing the angle simply requires the viewing point to be further away so that the object occupies the same portion of the screen. So it won't change context.

Ok, anyway 35 degrees seems to give a more accurate distance to the surface .

For example in the case of Invincible, with 70deg it tells you that the distance to the center of the planet is 6964 km so the distance from Invincible to the surface of the planet is (6964-6371) = 593 km, that distance does not fit with how the planet looks on the screen.

This is what the Earth looks like from an altitude of 500 km.

And this is what the Earth looks like from an altitude of 9000 km.

 

[Antvasima]

@DontTalkDT @Executor_N0 @Spinosaurus75DinosaurFan @Mr. Bambu @Therefir @Ugarik @DMUA @Damage3245 @TheRustyOne @DemonGodMitchAubin @Jasonsith @Wokistan @Armorchompy @Migue79 @Psychomaster35 @CloverDragon03 @Dark-Carioca @AbaddonTheDisappointment @Aguywhodoesthings @Agnaa @Dalesean027 @DemiiPowa @Flashlight237 @SeijiSetto @SunDaGamer

What do you think about this?

 

[Dark-Carioca]

Google Earth provides the distance from the camera to the ground and also indicates the length of objects on the screen

Are you referring to the distance-measuring tool? If not I'd like to see what you mean, to see an example of that.

 

[Kulf_Boba]

Are you referring to the distance-measuring tool? If not I'd like to see what you mean, to see an example of that.

https://static.wikia.nocookie.net/vsbattles/images/8/8e/Screenshot_No.5.png

No, it's the main section, which in the bottom right corner shows the elevation of the camera relative to the ground, and on the sides, it also indicates the proportions on the screen using the scale lines.

For example, here the distance from the camera to the ground is 1447 m and the scale line measures 200 m.

 

[Kulf_Boba]

Bump.

 

[Flashlight237]

1. Maybe try replacing "static" with "vignette."
2. I'm not exactly sure about this. Our current angsizing formula is based on the vertical field of view (70°). I did the hand thing for angular size and the representation of 40 degrees (two outstretched hands put together) did not cover my entire field of view (in fact, it was just a little over half that). It's more in favor of keeping our current angular sizing formula the way it is.

 

[DontTalkDT]

I'm also in favor of keeping our current value.

To be clear: There is no such thing as an absolutely right angle. There is a range of values that for a human looks natural and our standard angle is one of those. That is why angsizing is generally considered a scaling method to avoid when possible. In principle, comics could use any of the range, but in lack of real reason to use any different one, the one we use seems fine.

If one would like a more accurate value, I would suggest to use the fact that, if one knows distance and size to something, one can calculate the angle. That can come in handy if one has a decent estimate of the distance to something in the image (say, the hand of some character or something), so that one can figure out the FoV angle before angsizing a different object.

 

[Kulf_Boba]

1. Maybe try replacing "static" with "vignette."
2. I'm not exactly sure about this. Our current angsizing formula is based on the vertical field of view (70°). I did the hand thing for angular size and the representation of 40 degrees (two outstretched hands put together) did not cover my entire field of view (in fact, it was just a little over half that). It's more in favor of keeping our current angular sizing formula the way it is.

Isn't the 70 degree field of view supposed to be based on the cameras? Why are you making the comparison to your field of view which exceeds 100 degrees?

anyway I would like you to check the results to see which one seems to be more accurate, as in the case of Invincible where the estimated distance with the 70 degrees does not seem to coincide with how the Earth would be seen from that distance.

 

[Kulf_Boba]

I'm also in favor of keeping our current value.

To be clear: There is no such thing as an absolutely right angle. There is a range of values that for a human looks natural and our standard angle is one of those. That is why angsizing is generally considered a scaling method to avoid when possible. In principle, comics could use any of the range, but in lack of real reason to use any different one, the one we use seems fine.

Wouldn't it be reason enough that a 35-degree field of view results in somewhat more realistic distances compared to a 70-degree FoV?

For example, look at these two cases:

Case 1

VS Battles Wiki

The VS Battles Wiki is the world's most comprehensive and popular index of statistics and powers for characters and items from all of popular fiction.

vsbattles.fandom.com

• A-Train's head: 154.6px | 0.193 m.
• Hughie's father's head: 94px | 0.19 m.
• Panel height: 657px

70deg

• Distance from the Panel to Hughie's Father: 0.94m
• Distance from the Panel to A-Train: 0.58m
• Distance from A-Train to Hughie's Father: 0.36m | 36 cm

35deg

• Distance from the Panel to Hughie's Father: 2.1m
• Distance from the Panel to A-Train: 1.3m
• Distance from A-Train to Hughie's Father: 0.8m | 80 cm

Case 2

Homelander head: 325px | 0.22 m.
Panel height: 804px

70deg

• Distance from panel to Homelander: 0.38m | 38cm

35deg

• Distance from panel to Homelander: 0.86m | 86cm

Look at the image below about the “behind the scenes” of that scene, the camera is definitely not 38 centimeters away.

 

[Flashlight237]

Okay, Buster Brown, if you're gonna be that way..!

Here's a setup I deliberately made to show why assuming 35 degrees as a field of view is a problem. The setup involves my phone's camera lens being exactly one foot away from the notepad here, which has a height of 8.5 cm. The ruler has markings of which, while the metric ones are a bit too blurry to read, the imperial markings remain legible. All photos taken are 3072 pixels tall.

At this distance and under six sig-figs, the notepad would be 15.8758 degrees while the imperial markings of the ruler is 53.1301 degrees. However, our angular sizing formula's a bit wonkier than this, as it's written as such:

Distance from point of view to object = object size * panel height in pixels/[object height in pixels*2*tan(70deg/2)]

Working back the wiki's formula, this time replacing "tan(70deg/2)" with x, here's what I got.:

0.085*3072/(818*2*x)=0.3048
0.085*3072/1636x=0.3048
261.12/1636x=0.3048
0.159608802/x=0.3048
0.3048x=0.159608802
0.159608802/0.3048=0.5236509291
x=0.5236509291

tan^-1(0.5236509291)=27.63884432 degrees
27.63884432*2=55.27768864

That is NOWHERE near 35 degrees. And to make sure you know I'm not messing around... I. Repeated. It.

This time, painstakingly having made sure the edge of the notepad and the camera lens lined up with the ends of the ruler's Imperial markings. Here's the math from that.:
0.085*3072/(878*2*x)=0.3048
0.085*3072/1756x=0.3048
0.1487015945/x=0.3048
0.1487015945=0.3048x
0.1487015945/.3048=0.4878661238
x=0.4878661238

tan^-1(0.4878661238)=26.00618039
26.00618039*2=52.01236078

Still nowhere near 35 degrees. If anything, it's closer to a range of 52 to 55 degrees. And just to make sure I am on the money... I repeated it! From two feet!:

And here are the results...

0.085*3072/(416*2*x)=0.6096
0.085*3072/832x=0.6096
0.3138461538/x=0.6096
0.3138461538=0.6096x
0.3138461538/0.6096=0.5148394912
x=0.5148394912

tan^-1(0.5148394912)=27.2411983
27.2411983*2=54.48239661

If anyone wants to repeat my experiment with a 16:9 camera (as my phone uses a 4:3 camera), grab yourself the following:

1. A stack of pallet notes. Something else uniform in size that can hold itself up firmly works too.
2. A ruler or tape measure.
3. A thick book to hold the object up and make it fully visible at the same time.
4. A camera
5. A floor (duh!)
6. Lots of patience and careful adjustment.

For now, I'll put up my experimental angular sizing formula:

• Distance from point of view to object (low end)= object size * panel height in pixels/[object height in pixels*2*tan(55deg/2)]
• Distance from point of view to object (high end)= object size * panel height in pixels/[object height in pixels*2*tan(52deg/2)]

Although with how my experiments went, I wouldn't be surprised if the angular size formula got reduced down to this:

• Distance from point of view to object = object size*panel height in pixels/object height in pixels

 

[Kulf_Boba]

Okay, Buster Brown, if you're gonna be that way..!

Thanks, Grandpa. So, what's your nickname from the '50s?

Here's a setup I deliberately made to show why assuming 35 degrees as a field of view is a problem. The setup involves my phone's camera lens being exactly one foot away from the notepad here, which has a height of 8.5 cm. The ruler has markings of which, while the metric ones are a bit too blurry to read, the imperial markings remain legible. All photos taken are 3072 pixels tall.

At this distance and under six sig-figs, the notepad would be 15.8758 degrees while the imperial markings of the ruler is 53.1301 degrees. However, our angular sizing formula's a bit wonkier than this, as it's written as such:

Distance from point of view to object = object size * panel height in pixels/[object height in pixels*2*tan(70deg/2)]

Working back the wiki's formula, this time replacing "tan(70deg/2)" with x, here's what I got.:

0.085*3072/(818*2*x)=0.3048
0.085*3072/1636x=0.3048
261.12/1636x=0.3048
0.159608802/x=0.3048
0.3048x=0.159608802
0.159608802/0.3048=0.5236509291
x=0.5236509291

tan^-1(0.5236509291)=27.63884432 degrees
27.63884432*2=55.27768864

That is NOWHERE near 35 degrees. And to make sure you know I'm not messing around... I. Repeated. It.

This time, painstakingly having made sure the edge of the notepad and the camera lens lined up with the ends of the ruler's Imperial markings. Here's the math from that.:
0.085*3072/(878*2*x)=0.3048
0.085*3072/1756x=0.3048
0.1487015945/x=0.3048
0.1487015945=0.3048x
0.1487015945/.3048=0.4878661238
x=0.4878661238

tan^-1(0.4878661238)=26.00618039
26.00618039*2=52.01236078

Still nowhere near 35 degrees. If anything, it's closer to a range of 52 to 55 degrees. And just to make sure I am on the money... I repeated it! From two feet!:


And here are the results...

0.085*3072/(416*2*x)=0.6096
0.085*3072/832x=0.6096
0.3138461538/x=0.6096
0.3138461538=0.6096x
0.3138461538/0.6096=0.5148394912
x=0.5148394912

tan^-1(0.5148394912)=27.2411983
27.2411983*2=54.48239661

If anyone wants to repeat my experiment with a 16:9 camera (as my phone uses a 4:3 camera), grab yourself the following:

1. A stack of pallet notes. Something else uniform in size that can hold itself up firmly works too.
2. A ruler or tape measure.
3. A thick book to hold the object up and make it fully visible at the same time.
4. A camera
5. A floor (duh!)
6. Lots of patience and careful adjustment.

For now, I'll put up my experimental angular sizing formula:

• Distance from point of view to object (low end)= object size * panel height in pixels/[object height in pixels*2*tan(55deg/2)]
• Distance from point of view to object (high end)= object size * panel height in pixels/[object height in pixels*2*tan(52deg/2)]

Good job, I had already thought of the same approach to develop a new formula. Too bad I don't have a camera right now.

Still, I don't think it's a serious problem; 35 degrees is well within the lower limit for natural-looking photos. At less than that angle, images start to look too compressed. I also saw that this is a common angle on telephoto cameras I think.

Although with how my experiments went, I wouldn't be surprised if the angular size formula got reduced down to this:

• Distance from point of view to object = object size*panel height in pixels/object height in pixels

I had also seen this formula.

I think we should test various values to determine which one provides the most accurate results for what we would typically estimate at a glance.

In my opinion, 35 degrees yields better results than 70 degrees. However, there might be an angle that better balances different situations, such as photos, movies, and comics. It may not provide exact results but could offer a more balanced approach

 

[DontTalkDT]

Isn't the 70 degree field of view supposed to be based on the cameras? Why are you making the comparison to your field of view which exceeds 100 degrees?

Cameras also use various different values. IIRC phone cameras are on the wider side, while traditional ones tend to be narrower. I believe photographers actually switch between various angles based on what suits the shot. Angles between 30° to 70° are pretty common in use. Things close to 40° have widely be considered to look most "natural" (according to "how to" by Randall Munroe)

I'm not making a comparison to human FoV, I'm talking about which angles look natural for a human in a picture.

anyway I would like you to check the results to see which one seems to be more accurate, as in the case of Invincible where the estimated distance with the 70 degrees does not seem to coincide with how the Earth would be seen from that distance.

You can't use Google Earth as ground truth, as that as well has just chosen some kind of FoV more or less arbitrarily.

 

[Kulf_Boba]

Cameras also use various different values. IIRC phone cameras are on the wider side, while traditional ones tend to be narrower. I believe photographers actually switch between various angles based on what suits the shot. Angles between 30° to 70° are pretty common in use. Things close to 40° have widely be considered to look most "natural" (according to "how to" by Randall Munroe)

Why not choose an angle between 30 and 40 degrees, which would provide objectively more realistic results than 70 degrees, especially when considering comic panels and movies?

I'm not making a comparison to human FoV, I'm talking about which angles look natural for a human in a picture.

That response was directed at the other user.

You can't use Google Earth as ground truth, as that as well has just chosen some kind of FoV more or less arbitrarily.

They are not arbitrary; they are the angles used by specialized cameras on aircraft and satellites.

 

[Dark-Carioca]

https://static.wikia.nocookie.net/vsbattles/images/8/8e/Screenshot_No.5.png

No, it's the main section, which in the bottom right corner shows the elevation of the camera relative to the ground, and on the sides, it also indicates the proportions on the screen using the scale lines.

For example, here the distance from the camera to the ground is 1447 m and the scale line measures 200 m.

This screenshot is very small, by the way... I know what you mean but this is not good proof.

Overall I'm not entirely sure the change is necessary. I don't think I've ever encountered issues with my angsizing calcs in regards to believable distances, I can calculate those decently well with the naked eye myself and the current angsizing formula (while perhaps not perfect) is serviceable enough.

 

[Floxy178]

Can't we keep existing 70 degree as standart value and, for example if someone gets inconsistent results, he can use calculated FOV from another scene?

Maybe it won't work in comics panels but in Homelander example we can find distance from behind the scenes and calculate FOV which would likely be same in other scenes too.

 

[Flashlight237]

You can't use Google Earth as ground truth, as that as well has just chosen some kind of FoV more or less arbitrarily.

That's what I considered saying. Google Earth is a map simulation and, putting it frankly, cartography as a whole isn't exactly reality so much as it is just a representation of what a piece of land looks like. I basically used a camera and a tricky setup just to provide a more realistic approach to angular sizing. The photos I've taken are 4:3, by the way.

Cameras also use various different values. IIRC phone cameras are on the wider side, while traditional ones tend to be narrower. I believe photographers actually switch between various angles based on what suits the shot. Angles between 30° to 70° are pretty common in use. Things close to 40° have widely be considered to look most "natural" (according to "how to" by Randall Munroe)

If there is a range with 70° being the "high end" of said range, wouldn't using said range provide a better picture of how angular sizing works? Also, I would highly recommend that you provide a citation for that 40° figure mentioned here.

 

[DontTalkDT]

If there is a range with 70° being the "high end" of said range, wouldn't using said range provide a better picture of how angular sizing works?

70° isn't necessarily the absolute high end of it. That's just what I had the impression was common.
I would rather keep it to the existing standard value.

Also, I would highly recommend that you provide a citation for that 40° figure mentioned here.

according to "how to" by Randall Munroe

Or do you mean the exact text? If so:

 

[Flashlight237]

70° isn't necessarily the absolute high end of it. That's just what I had the impression was common.
I would rather keep it to the existing standard value.


Or do you mean the exact text? If so:

Oh hey! A citation..! Thanks!

And in response to your first statement, honestly, me too, but everything we've posted in this thread so far isn't doing that standard any favors unfortunately.

 

[Flashlight237]

I'll remain neutral to any decisions made to angular sizing, whether it's to keep it the same (as me and DontTalk wanted) or change it (as things are starting to look that way).

 

[Kulf_Boba]

I'll remain neutral to any decisions made to angular sizing, whether it's to keep it the same (as me and DontTalk wanted) or change it (as things are starting to look that way).

Upon further reflection, it doesn’t make sense to use the height of the screen for angsizing calculations in series and movies that use the common 16:9 format. This is because if you assume a vertical field of view (FOV) of 70 degrees, the resulting horizontal FOV would be about 102°. With such a wide FOV, the image should appear distorted, which is not the case in these productions.

For this reason, in cases where I used a vertical FOV of 35 degrees to analyze scenes from series like The Boys and Invincible, the results have been more realistic. This is because, with a vertical FOV of 35 degrees in a 16:9 aspect ratio, the horizontal FOV would be around 58.9°, which is more consistent with what we see on screen.

 

[Kulf_Boba]

Applying a horizontal FOV of 70 degrees (for the length of the screen) in movies and TV shows makes much more sense, as it provides more accurate results and matches the standard FOV commonly used in video games. The next step is to determine what FOV can be used for comic book and manga panels.

 

[Kulf_Boba]

bump.

 

[Antvasima]

I trust DontTalk's sense of judgement here.

 

[Kulf_Boba]

Then it would be good if you could give your opinion regarding this:

Upon further reflection, it doesn’t make sense to use the height of the screen for angsizing calculations in series and movies that use the common 16:9 format. This is because if you assume a vertical field of view (FOV) of 70 degrees, the resulting horizontal FOV would be about 102°. With such a wide FOV, the image should appear distorted, which is not the case in these productions.

For this reason, in cases where I used a vertical FOV of 35 degrees to analyze scenes from series like The Boys and Invincible, the results have been more realistic. This is because, with a vertical FOV of 35 degrees in a 16:9 aspect ratio, the horizontal FOV would be around 58.9°, which is more consistent with what we see on screen.

Applying a horizontal FOV of 70 degrees (for the length of the screen) in movies and TV shows makes much more sense, as it provides more accurate results and matches the standard FOV commonly used in video games. The next step is to determine what FOV can be used for comic book and manga panels.

 

[Antvasima]

@DontTalkDT @Executor_N0 @Ugarik

It seems like your help is needed here.

 

[Kulf_Boba]

For example, in the film industry, it is common to use 35 mm and 28 mm lenses, which offer a diagonal field of view of 63° and 75°, respectively.

 

[Flashlight237]

For example, in the film industry, it is common to use 35 mm and 28 mm lenses, which offer a diagonal field of view of 63° and 75°, respectively.

As much as I really appreciate the effort put into your side the argument here, this kinda leans more towards the 70° standard we have here, although the "Normal" section (which equates to run-of-the-mill cameras) in the infographic would equate to a median focal angle of 40°, which is kinda what DontTalkDT brought up despite his stance to keep the 70-degree standard:

Or do you mean the exact text? If so:

Imo, if a change in our Angular Sizing formula were to materialize, a 40-70 degree range would basically meet both sides of the argument here rather than angular sizing having a set value.

 

[Kulf_Boba]

As much as I really appreciate the effort put into your side the argument here, this kinda leans more towards the 70° standard we have here, although the "Normal" section (which equates to run-of-the-mill cameras) in the infographic would equate to a median focal angle of 40°, which is kinda what DontTalkDT brought up despite his stance to keep the 70-degree standard:

I need you to comment regarding this, please, because I am not advocating at this time to fix a 35° FOV:

Upon further reflection, it doesn’t make sense to use the height of the screen for angsizing calculations in series and movies that use the common 16:9 format. This is because if you assume a vertical field of view (FOV) of 70 degrees, the resulting horizontal FOV would be about 102°. With such a wide FOV, the image should appear distorted, which is not the case in these productions.

For this reason, in cases where I used a vertical FOV of 35 degrees to analyze scenes from series like The Boys and Invincible, the results have been more realistic. This is because, with a vertical FOV of 35 degrees in a 16:9 aspect ratio, the horizontal FOV would be around 58.9°, which is more consistent with what we see on screen.

Applying a horizontal FOV of 70 degrees (for the length of the screen) in movies and TV shows makes much more sense, as it provides more accurate results and matches the standard FOV commonly used in video games. The next step is to determine what FOV can be used for comic book and manga panels.

Imo, if a change in our Angular Sizing formula were to materialize, a 40-70 degree range would basically meet both sides of the argument here rather than angular sizing having a set value.

40° could be used for the height of comic and manga panels.

For example, for panels such as these:

And for panels like these that appear to have a film aspect ratio, 70° could be used for panel length.

 

[Flashlight237]

I need you to comment regarding this, please, because I am not advocating at this time to fix a 35° FOV:




40° could be used for the height of comic and manga panels.

For example, for panels such as these:

And for panels like these that appear to have a film aspect ratio, 70° could be used for panel length.

My opinion doesn't change from what I wrote before.

 

[Kulf_Boba]

My opinion doesn't change from what I wrote before.

However, I have provided a rationale to explain why the 70° angle should apply to the length of the panel, not its height. and you have not commented on it.

 

[Kulf_Boba]

Bump.

 

[Kulf_Boba]

People, please pay attention to this, as it impacts hundreds of calculations using the angsizing method, affecting many works. I would appreciate more input from experienced users:

Upon further reflection, it doesn’t make sense to use the height of the screen for angsizing calculations in series and movies that use the common 16:9 format. This is because if you assume a vertical field of view (FOV) of 70 degrees, the resulting horizontal FOV would be about 102°. With such a wide FOV, the image should appear distorted, which is not the case in these productions.

For this reason, in cases where I used a vertical FOV of 35 degrees to analyze scenes from series like The Boys and Invincible, the results have been more realistic. This is because, with a vertical FOV of 35 degrees in a 16:9 aspect ratio, the horizontal FOV would be around 58.9°, which is more consistent with what we see on screen.

Applying a horizontal FOV of 70 degrees (across the screen) in movies and TV shows makes much more sense, as it provides more accurate results and aligns with the standard FOV commonly used in films and video games. The next step is to determine what FOV can be used for comic book and manga panels.

 

[Kulf_Boba]

40° could be used for the height of comic and manga panels.

For example, for panels such as these:

And for panels like these that appear to have a film aspect ratio, 70° could be used for panel length.