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When I think about a simple 2D projection on a screen with vertical-cylinder curvature and of viewing positions away from the "sweet spot" it seems to me pretty obvious that there would be geometrical distortions of the image and a correspondingly worse viewing experience (unless it was mild enough to get used to and ignore after a while). But what about 3D? Would that too be worse in every way or could the curvature actually improve something specific about the 3D projection? (Still thinking about viewers sitting away from the "sweet spot", which will typically be most of the people in the theater.)

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2D image distortions translate directly to images in 3D scenes: thinner image, shallower depth.
Curved screen is better for both 2D and 3D in terms of worst view angle.

Technologies that produce 3D image in cinemas nowadays use screen image as a basis. So all distortions that are seen on 2D images will translate into image distortions in 3D scene

I used a figure from patent 7106411 to compare curved and plane screens in terms of incidence angle viewing from bad seat (between view direction and screen normal):

  • for plane screen, back row worst incidence angle is 37$^{\circ}$
  • for curved screen, back row worst incidence angle is 29$^{\circ}$

P.P.S. Interesting fact for unfortunate sideways seater in curved screen cinema: if we compare equivalent plane (non-curved) screen sizes for "sweet spot" and sideways seat they are almost the same.

Update 1
after asked for "specific kinds of distortions ... (in) the left and right 2D image differences":

The specific distortion for curved screen is non-linear angle change when scanning screen across (e.g. left-to-right). Incidence angle changes not only due to view direction change but also due to screen normal direction change. But this is a second order effect, so to speak, with lower impact than incident angle difference itself.

And as for 3D, these effects will translate into both image and depth distortions: thinner image, shallower depth. That will still be more pronounced for plane screen, compared to curved screen.

Update 2
more accurate estimation of viewing angle change:

In case of flat screen viewing angle changes linearly from 0$^{\circ}$ (ideal front view for nearest screen point) to 39$^{\circ}$ (farthest point)

In case of curved screen viewing angle changes nonlinearly (as screen normal changes its direction) from 19$^{\circ}$ (farthest screen point) to 29$^{\circ}$ (nearest point)

And less angle change causes the fact that "the loss of 3D depth is uniform/constant for the curved screen but non-uniform/progressive for the flat screen" as mentioned in Don Joe's comment.

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  • $\begingroup$ I don't think it's that simple. 2D on-screen image distortions do translate 1:1 into distortions in the 2D images that reach your left and right retinas respectively, but those images have significant differences in content, differences that are meant to be further processed by your brain to merge them into a 3D image or perception. The question was whether the specific kinds of distortions introduced by a curved screen into the left and right 2D image differences can improve the brain-merged 3D result in any way, when the projection is viewed from a lateral seat. $\endgroup$ – Don Joe Sep 30 '16 at 11:18
  • $\begingroup$ All I see in your recent edit in terms of addressing my question directly is your last paragraph, where you talk about loss of depth being an effect of side-seat viewing without explaining how such an effect would be produced by the geometrical changes, and then you go on to assert that this effect is still worse for flat screens, again without supporting your claim in any way. So I'm still not seeing a real answer here. $\endgroup$ – Don Joe Nov 5 '16 at 0:22
  • $\begingroup$ I've thought about it some more and I think I understand why you think there'd be a loss of depth and why it would be worse for a flat screen, and indeed it all has to do with incident viewing angles and how much they deviate from the normal. For the flat screen you start with 0 deviation at "your" edge of the screen and progress to 37 degrees at the far edge, while for the curved screen the deviation is about the same (29-ish degrees) across the whole screen. This means the loss of 3D depth is uniform/constant for the curved screen but non-uniform/progressive for the flat screen. $\endgroup$ – Don Joe Nov 5 '16 at 10:32

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