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How do I create the effect of a viewer looking at the interior of a flat parabolic surface that seems to stretch off into infinity? Please see the following image for an illustration of the idea.

enter image description here

The best idea I had so far was to use the vanishing point tool in Photoshop with several perspective planes at different angles but that's not working.

EDIT

This is close to what I want:

enter image description here

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This actually might be a good question for physics.se purely on the math involved, lol. –  OghmaOsiris Feb 19 '13 at 23:46
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My initial reaction is map an image to a 3D surface. –  Scott Feb 20 '13 at 1:02
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Also worth noting that if you want a point at a distance of inifity away from a subject, the sides of the curve will be straight and not curved. –  OghmaOsiris Feb 21 '13 at 1:46
    
@OghmaOsiris Yeah, that occurred to me a few minutes after I posted the original question. –  Rodrick Chapman Feb 21 '13 at 2:45
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3 Answers

up vote 2 down vote accepted

You can just about do it for that shape, but it's not very flexible. This is in Illustrator: Photoshop's 3D tools (which I don't know well) are much more sophisticated but based on similar principles.

1- Prepare a flat image as if it was going to be wallpaper on the flat wall. Drag it into the Symbols panel (Window > Symbols)

enter image description here

2- Make a vertical line. Revolve (Effects > 3D > Revolve) it 180 degrees with an offset, forming a curved wall.

enter image description here

3- Map Art the wallpaper onto the appropriate face of the wall.

enter image description here

Changing the shape of the wall from a circle to something longer and thinner isn't easy in Illustrator (might be easier in PS). One way is to simply expand the effect, then scale the thing so it's thinner. If you're doing this, make a note of the numeric scaling value, then create a variant of your wallpaper fattened by 1 over that value as a decimal so you end up with non-distorted wallpaper (e.g. if you're going to make it 80% width, 1 / 0.8 = 1.25 so stretch the wallpaper 125% width).

Here's a low-res example with 800% / 12.5% scaling:

enter image description here

No infinity, but up the perspective and increase the scaling until the end point gets close to being less than 1px or one dot on a printed page, then just let it disappear.

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+1 because it's a great answer, but also because that t-shirt is awesome. –  Yisela Feb 20 '13 at 19:29
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I'm guessing you're wanting something similar to an endless hallway: enter image description here

This is what's called recursion. You simply copy the outer scene into itself to form a seemingly endless image.

If you want it to make it seem like the sample you provided, you can add a gradient to white so it fades off into the distance.

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I would just use the perspective plane in the Vanishing Point filter to get the first perspective right. I would then convert it to a smart object to preserve the quality. I think after that you might be able to use the Warp tool and curve the top of the image (top left & top right) to match that perspective curve in your example.

I haven't tried this — so I could be mistaken. . Just as a heads up.... :)

It reminds me of my own interest in mapping 2D images from Illustrator into PS in order to mock up a design on a mug or other curved surface. The options in the Vanishing Point filter seem a little janky for something so (seemingly) simple.

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