The flawed math behind curved monitors

Opinions on curved monitors vary a lot: some people claim it's the greatest thing ever, others say it's just a fad. But so far I haven't seen anyone who actually tried to verify the main claim of curved monitors. Manufacturers claim that the curvature ensures that all pixels on the screen are the more or less the same distance away from your eyes, which supposedly avoids the distortion often seen close to the edges of screens. This claim is wrong. If you do the math, you will find that a curved screen actually makes the distortion worse.

The short explanation is that virtually all cameras have flat image sensors. These sensors do indeed distort the image - objects close to the edges will appear stretched. The thing is, the distortion caused by the flat sensor is canceled out exactly by the distortion of the flat screen. It really doesn't matter that the pixels near the edges of the screen are further away from your eyes, as long as the screen has the same shape as the camera sensor (and the same field of view). If you want a more complete explanation, and some actual proof, read on.

The test image

I made a simple test image in Blender. It's a simple rendering of a grid of spheres. Each of the spheres is perfectly round, but you can clearly see that the spheres close to the edges appear stretched. I'm intentionally using a very wide field of view (roughly 90 degrees) to make the effect more obvious. You can download the original source files at the end of this post.

Flat monitor

Let's see what happens when the test image is displayed on an ordinary flat monitor. This is a model of a basic 16:9 monitor (64cm x 36cm, roughly 29"):

This is what it would look like when you're sitting directly in front of it:

The spheres near the center look fine, but those closer to the edges are stretched. But watch what happens when you rotate the camera towards one of the corners:

Somehow, the spheres in the corner now look normal whereas the spheres in the center are stretched! No, I didn't mess with that image, there's no Photoshopping/compositing/whatever going on here. All I did was rotate the camera. How is this possible? Simple: when the camera faces the corner of the screen instead of the center, the screen tilted relative to the camera. This tilt compensates the distortion that we saw earlier.

Does this also work in real life? Of course! You just have to sit in the right spot, so your field of view matches that of the camera. Since I used a very wide field of view for the test image (90 degrees), you need to sit very close to see it properly. For example, if your screen is 50cm wide, your eyes should be 25cm away from the screen to watch the test image. Ideally your eyes should be in the center, but you obviously can't have both of your eyes in the center at the same time. In order to get a perfect result, you should close one eye and make sure that your other eye right in the center of the screen. Now open the test image in your browser, make it fullscreen (press F11 - this is important), and watch. You shouldn't be able to see any distortion at all, no matter where you look.

Curved monitor

Now let's try this again with a curved monitor. I couldn't find any actual specs regarding the amount of curvature used by real monitors, so I just used a screenshot of Linus' LG 34U97 unboxing video to get some numbers. The 34U97 is 83cm wide, and based on the unboxing video, it looks like the center is recessed about 2.5cm compared to the corners (which is far less than the photos on the product page suggest - typical marketing I guess). This corresponds to the curvature of a circle with a 7m diameter, which means the 'sweet spot' is located 3.5m away from the center of the screen (makes sense for a TV, but rather strange for a computer monitor IMO). Anyway, I took the model that I used earlier and gave it the same curvature as the 34U97, and this is the result:

You can clearly see the curvature when you're sitting right in front of it, but does it actually make the image better? Not at all. The edges are closer to you, which means the spheres near the edges appear even larger than they were already! Now let's rotate the camera again:

It's still more or less okay, but it's not as 'perfect' as with the ordinary flat monitor.

Highly curved monitor

Let's try this again with a monitor with a higher curvature, just to see what will happen. The 'sweet spot' for this monitor is just 1m away from the center (instead of 3.5m).

It just gets worse. Here's a comparison of the three cases. I've overlaid a green circle on top of the spheres to show you the distortion:

In the case of the flat monitor, the distortion is canceled out almost perfectly, resulting in a near-perfect circle. In the other two cases, not so much.

So why do movie theaters use curved screens?

Because the projectors used in movie theaters contain lenses, which adds lens distortion. The screen is curved to cancel out the lens distortion. Monitors do not use lenses, so there's no reason to make them curved.

Don't cameras have lenses too?

There are many different types of camera lenses and they all have a unique distortion pattern. To make things even worse, the distortion pattern depends on zoom and focus as well. There's no way you can compensate all those different distortion patterns just by using a slightly curved screen. Only the camera crew can properly correct lens distortion, since only they know what lenses were used to capture the footage.

As far as I can tell, this claim is actually correct. For example, the edges of the 34U97 are tilted about 7 degrees compared to a flat monitor. This should effectively increase the maximum viewing angle by 7 degrees. So if you're willing to accept a small amount of distortion to get a better maximum viewing angle, a curved monitor makes sense. There's some good news though: as Linus correctly pointed out, the curvature has little effect when you are sitting further away from the screen. And you get the best possible viewing angle when you're sitting in the 'sweet spot', which is 3.5m away from the screen. So a curved screen could actually make sense for a TV, but not for a computer monitor. Of course the distortion increases once you move away from the center, but you still get most of the benefit of the improved viewing angle.

What do you think? Would you still buy a curved monitor to improve the maximum viewing angle, even if the image becomes slightly distorted?

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The short explanation is that virtually all cameras have flat image sensors.

Finally someone with the right explanation. Thank you.

.

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Wow, really interesting and informational. Best first post ever!

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Wow, really interesting and informational. Best first post ever!

Yep, and I did some checking, seems like its total OC also!

Great job man!

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The award for best first post goes to......

Seriously, very interesting stuff. I'll probably refer people to this thread if I get into a conversation about curved monitors, well done.

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I can see the curve making stuff like movies look weird through this effect, but for games I think it'd work a lot better. I definitely want one of the 1440p 21:9 monitors, but whether I want the curve or not is still up for debate.

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Great Post! @LinusTech please feature this on the Wan show, because it is really interesting.

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Thanks .

I can see the curve making stuff like movies look weird through this effect, but for games I think it'd work a lot better. I definitely want one of the 1440p 21:9 monitors, but whether I want the curve or not is still up for debate.

Games is one of those use cases where you may actually care more about the viewing angle than the distortion, especially for ultra-widescreen. Besides, if you are playing games with a high FOV setting (probably for tactical reasons), the perspective will already be distorted anyway (unless you're sitting really close to the screen).

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Great first post. Welcome to the forum.

One comment is that from a quick read it seems like you're assuming all the content we consume on our monitor will have been shot by a camera at some point. Anything that wasn't (text/productivity applications for example) shouldn't have any inherent distortion.

This post gave me a better understanding of why LG went with such a subtle curve on the monitor we reviewed recently though, and validates my "feeling" like I couldn't really see the curve (since it wasn't making much difference to the image distortion anyway) and the image just "looked more natural" which could have been the improved viewing angles and perceived panel uniformity (due to looking at it more directly) .

Again, great post.

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@Maarten Baert, thanks for taking the time to write up such a long but thoroughly informative post about curved screens. I will definitely save this thread of yours and refer others to it if they're thinking about purchasing a curved display. You're good value mate (Aussy saying). You quite clearly did a lot of research on this for the benefit of others.

How long did all this take you (including the 3D models)?

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@Maarten Baert, thanks for taking the time to write up such a long but thoroughly informative post about curved screens. I will definitely save this thread of yours and refer others to it if they're thinking about purchasing a curved display. You're good value mate (Aussy saying). You quite clearly did a lot of research on this for the benefit of others.

How long did all this take you (including the 3D models)?

Thanks . It took a few hours. The models are pretty simple and you can do things pretty fast in Blender once you're used to it.

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Thanks . It took a few hours. The models are pretty simple and you can do things pretty fast in Blender once you're used to it.

No worries! You did a good job mate. That's some pure dedication right there . Good work!

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• 8 months later...

Thanks for this post, mate.

Dat First Post

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• 8 months later...

Gah. Linus beat me to it by like.. a year...

I agree that curved TVs are silly for many reasons, but there are a couple problems with this post:

1) Curved monitors generally come with a subtle curve, and only in the 21:9 variety where the distance from the center to the edge is much greater than a 16:9.

2) You've made the assumption that all (or most) of a computer monitor experience is watching something shot on a camera, which in my case (and likely almost everyone elses case) is the opposite. When I move icons around on my desktop, or move text from one side of the screen to the other, it doesn't change based on its location on the screen. Another big one is gaming, where the image is rendered and not shot by a camera. I would say that a good 90% of what I look at on my screen was not shot by a camera, and when it is, it is normally 16:9 content that is not really affected by the subtle curve.

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On 9/24/2014 at 6:30 PM, LinusTech said:

Great first post. Welcome to the forum.

One comment is that from a quick read it seems like you're assuming all the content we consume on our monitor will have been shot by a camera at some point. Anything that wasn't (text/productivity applications for example) shouldn't have any inherent distortion.

This post gave me a better understanding of why LG went with such a subtle curve on the monitor we reviewed recently though, and validates my "feeling" like I couldn't really see the curve (since it wasn't making much difference to the image distortion anyway) and the image just "looked more natural" which could have been the improved viewing angles and perceived panel uniformity (due to looking at it more directly) .

Again, great post.

Your also ignoring the vertical axis...  how many people have a monitor that is not centered on eye level (I do).   If you sit up in your chair a little or slouch down does the image change?? Technically yes, realistically no our brains are amazing and things like that go unnoticed

In addition the befits of a flat screen would only be visible when the viewer is recreating the viewing angle.  By this I mean that the image being reproduced is centered on the persons eye.  Anyone who does content creation where the picture is pushed to a corner,zoomed in to do detailed work, or even a monitor that is not raised to a proper height is going to introduce a similar level distortion that you described.

Simply that a perfect viewing angle is rarely achieved, and a minor issue that our brains and eyes filter out.  It is amazing the things that you will never notice because our brain corrects it subconsciously.  HOWEVER a curved monitor is something that your brain will notice and that it will register, most of us see this as a WOW where distortion is filtered out subconsciously and all that is left is the experience.

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• 1 year later...
On 2/21/2016 at 2:57 PM, -BirdiE- said:

Gah. Linus beat me to it by like.. a year...

I agree that curved TVs are silly for many reasons, but there are a couple problems with this post:

1) Curved monitors generally come with a subtle curve, and only in the 21:9 variety where the distance from the center to the edge is much greater than a 16:9.

2) You've made the assumption that all (or most) of a computer monitor experience is watching something shot on a camera, which in my case (and likely almost everyone elses case) is the opposite. When I move icons around on my desktop, or move text from one side of the screen to the other, it doesn't change based on its location on the screen. Another big one is gaming, where the image is rendered and not shot by a camera. I would say that a good 90% of what I look at on my screen was not shot by a camera, and when it is, it is normally 16:9 content that is not really affected by the subtle curve.

One thing needs to be added here and since we're already answering with a year delay (plus it was quite high in google results - grats!)... As far as I know most games are projected on a flat surface which causes distortion similar to cameras (except lens effects) and thus is corrected by flatness of the screen. Exceptions that I know of are some racing games which make software corrections for triple monitor setups and card manufacturers projecting on more than one plane which is essential for VR.