[Affected]

So recently I attended a lecture by Zbig Rybczinski on what he called "diseases of the image", and he addressed the problems with linear perspective in some length. I'd known about it before, but hadn't really bothered with it before. Just now I was pointed to this site:
http://www.treeshark.com/Persptut.html

and I started wondering, is there a program that would let you input FOV , grid density and image width+ height and would then create a suitable grid for drawing reference. You could just make an image like seen on that site once in vectors but scalability of grid density is pretty important too.

[cheney]

I would think it would more easy than most would consider. Try using a warped horizon line, but don't warp your depth to compensate for the change in horizon. Then when you draw your perspective line it should work out correctly.

What makes this complicated is that this is easy to plan for in terms of individual objects, but overall composition is a whole other ball of wax.
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http://prettydiff.com/

[Affected]

uum, I'm not sure I get what you're trying to say. But the horizon would pretty much be the one line that would not get warped under any circumstances.

[jfrancis]

Some related stuff I've put together:

http://www.digitalartform.com/archives/2004/10/nodal_point_pan_1.html

http://www.digitalartform.com/archives/2004/10/nodal_point_pan.html

if you only read one, read this third one:

http://www.digitalartform.com/archives/2004/11/nodal_point_pan_2.html

I would invite the guy with the treeshark web site who has a hard time imagining how to stitch the train tracks together to take a look at my third web page above. I'd be curious to hear what he thinks about it.

[cheney]

[Affected]

jfrancis: that's interesting, but in the last article ofyours it does look like there's still some distortion going on.

you might be interested in rybczinski's tinkerings:
http://www.zbigvision.com/
see the "concepts" page, there's something on perspective there, though the images are sadly small.

[Affected]

cheney: care to draw an example? maybe I'm stupid, but I fail to see how warping the horizon alone would even affect the geometry at all, except maybe in making vanishing points move a bit.

[treeshark]

Hi all, there are several sorts of panoramic perspectives. One is cylindrical this has 4 vanishing points. East South North West. Spherical has these and adds one up and one down. Until they invent spherical immersive bubbles we will be stuck with the problem of how to get a curved image onto a flat surface. Mercator was the first to wrestle with this when he tried to print a spherical map of the world onto a rectangular bit of paper. Joseph what you are doing is similar to taking photos in a circle and stitching the middle bits together which will work fine the more angles you take the the thinner the slices and the better the end result. A few 3d programs do this automaticaly Bryce and Form.z spring to mind.
As for horizons they are always at the same height as your eyes or veiwpoint unless you are high enough for the curve of the earth to have an effect.
Here's a guy who paints true spherical perspective on the outside of spheres.
http://www.termespheres.com/
Rob

[jfrancis]

The horizon will only be straight if the camera is level. There is, however, no particular reason why a camera should be level. Have you tried developing panoramas as if the camera is tilted? That would be interesting to see.

Linear perspectives stitch perfectly, as long as you stitch them in 3-space -- it's kind of like the alien puzzle in the movie "Contact." You only need lots of thin ones (or curved lines) if you are trying to stitch them all in 2D. You could see in my third link that I took to images that had no hope of stitching in 2D space and stitched them flawlessly by embedding them in 3D space. Affected -- if you're feeling "distortion" it's the same distortion you'd feel in a movie when the camera pans. That's why it's possible to use this technique to do set extensions with matte paintings on pan and tilt shots.

If you trace what you see through a window onto that window (without moving) I think you'll see that linear perspective is what you'll get. If you rotate the camera (by panning or tilting it, or by looking around) you'll not get straight lines, but then again, that's cheating. If you are going to rotate your camera during the recording process, why stop there? Why not drive it down the street and around the corner?

If you DO move the camera (or the subject) around during the recording process, you'll find you've stumbled across "slit scanning". It looks like Zbig Rybczynski is using slit scanning to twist the figures in his 1988 film, "The Fourth Dimension". I used to work at R/Greenberg Associates in NY; we did a lot of slit-scanning there. Here's a frame from a 1982 Renault commercial



You can see the commercial at rga.com if you can navigate the flash interface. It's in the history section, I believe.

Some panoramic cameras do a kind of slit-scanning as they rotate around. The original slit scan process was I think invented by Douglas Trumbull and used in the Kubrick film 2001 to do the weird trip through hyperspace.

[treeshark]

The horizon is always straight though I don't object to it curving for artistic purpose
the horizon is always on the nodal point of any veiwing device. Remember that the camera back virtual or otherwise is a flat plane interrupting a spherical image. Your maya demo will work fine if the veiw is into the center of the face of an octagon with thew field of view set a 90 degrees. Try this: A straight chequerboard floor just on the flat( boring I know) Veiwing angle 270 degrees, that's seriously chicken eyed.
Does it still work? ( I don't know I'm just curious!)
rob

[jfrancis]

I don't think we are going to come to an agreement over terms. Angle of view is determined by size of film back and/or focal length. No focal length no matter how short, and no film back, no matter how large is going to give you an angle of view greater than 180 degrees.

Projection from 3D to 2D is a form of mapping. You are mapping 3-space to 2-space. Once you are talking about fields of view greater than 180 degrees you are talking about mappings from 3-space to 2-space other than that which the eye does.

There's nothing essentially wrong with other mappings. If you enjoy them, then by all means, dig in. I like them too. Funhouse mirrors, rippled shower glass, silvery gazing balls, and panoramic perspectives. It's all good.

My only point is that there's nothing essentially "righter" about them, either.

[treeshark]

[jfrancis]

Perspective has as much influence over the circle in perspective as it does over anything else. I think you are confusing the center of the circle with the center of the ellipse that the circle becomes in perspective. They are two different points. Enclose the circle in a square and you'll see what I mean.

http://www.digitalartform.com/archives/2004/11/how_to_draw_ell.html

The minor axis of the ellipse is normal to the plane in which the circle lies.

http://drawthrough.com/tutorials/ellipses.html

----

There is a very interesting short movie about the evolution of the eye to be found here

http://www.pbs.org/wgbh/evolution/library/01/1/l_011_01.html

According to current thinking, the eye started as a flat patch of light sensitive cells. All they conveyed was "dark" or "bright". The next useful change was for that patch to sag into a bowl shape. Now since parts of the bowl shaded other parts, a rudimentary sense of light source direction was born. Issues of lenses and fine focus had, according to this theorist, no bearing on the roundness of the eye. The roundness idea came first, and did nothing more than turn "on or off" into a tonal gradation. When lenses developed later, they worked with what was already there -- the roundness. If lenses could have evolved first, we'd probably have camera eyes with flat backs.

If you look at the first two links I originally provided, (particularly the second one) you'll see I start the explanation with the idea that we are inside a sphere, and I camera project the photography onto the inner surface of that sphere. Later I go to flat planes. It really doesn't matter which shape I use, since I am projecting and viewing from the same place. I could do the entire thing on the inner surface of a hollow chocolate Easter bunny and you'd never know the difference, since areas of the image projected onto close parts would project smaller, because the projection throw is shorter, yet LOOK bigger, because the projection landing area is closer, and close things look bigger. Conversely when parts of the image are projected into the distant reaches of the bunny ear tips they would project larger, because the projection throw distance is greater, yet they would LOOK smaller, by virtue of landing on such a distant spot. Those two effects: distantly projected things looking bigger, and distantly viewed objects looking smaller, would exactly counterbalance each other. End result? No clue that I was using a totally crazy shape as my projection screen.

You know how a movie ripples across a closed curtain? It only ripples because it is being projected from one place and viewed from another. If you could stick your eye where the projector is (and yet not block any light) you'd see no distortion of the shape of the movie, no matter how crazily the curtain was shaped or moved. (you'd see light falloff variation, but no shape variation)
----

Here's the thing, as I see it:

Anything fundamentally "true" about spherical or cylindrical screens is only true as long as the screen stays spherical or cylindrical, and as long as you view it from one special place. As soon as you leave that place or unwrap and flatten the screen, you've introduce one distortion -- or another. Choose your poison.

If you could be inside a Termesphere, you'd get a striking sense of being immersed in reality. You'd perceive no curved lines because each curved line is a great circle aiming straight at you in the center of the sphere. (Again, see my original links. Same thing -- and again, there's nothing magical about using a sphere -- it could be made to work equally well with a hollow Easter bunny)

Once you leave the center of the Termesphere, or unwrap it and present a flat representation of it, it becomes a charming objet d'art, but no fundamentally "truer" a representation of the world than anything else.

[treeshark]

[digitaldecoy]

@ treeshark:

Now, that�s exactly what jfrancis said here:

[treeshark]

[jfrancis]

I think we all agree that this is an intersting conversation, and speaking for myself, I have lots of things to think about here.

When I was in college in the early 80's, I did a lot of 3D using my own software.

The usual perspective transformation from 3D X, Y, and Z points to 2D screen X' and Y' points (assuming the camera is at the origin and looking along the Z-axis) is to divide the X and Y values by Z. So usually it's . . .

X' = X / Z
Y' = Y / Z

One of the first things I wondered was what would happen if you divided X and Y by the true "as the crow flies" distance to the point (which I'll call D), instead of the camera Z distance to the point (Z)

When you use these equations:

X' = X / D
Y' = Y / D

You get what seemed to me to be a fisheye lens.

I just haven't had a lot of use for that kind of rendering since I'm normally trying to integrate CG into standard photography.

[balistic]

This thread makes my brain hurt but it is still AWESOME.
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brian.prince|light.comp.paint

[GordMacDonald]

This is a very facinating thread!

Gord
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Gord MacDonald: http://www.cg2020.com

[treeshark]

Yes it's a subject thats bound to get those braincells hopping about. I have just experimented with a spherical mapping of each image onto the sphere. With very unexpected (for me) results: the spherical perspective image is transformed into the straight perspective version when viewed from the center of the sphere. On the other hand the straight perspective version is transformed into the spherical version when veiwed from outside the same sphere.
Something for me to puzzle over.
I got into this sort of thing about 13 years ago developing images to be projected onto the planetarium dome at Madame Tussauds in London.
Here's an example: Don't laugh at the render quality it took as I recall 2days to render on an old Mac.

[a_sh]

treeshark:

i think you are making a mistake when you say this: " The simplest proof of this is that and circle placed on the floor in perspective always forms an elipse with its major and minor axia vertical and horizontal, try it, you will find that the properties of a circle mean that perspective has no effect. "
and then go on and say this: "he major axis of a circle distorted to an elipse is always parallel with the horizon."

While this is true for plates on the floor, all you need to do to realise they are not true for all circles, is to lean said plate agains something. Or more convieniently, look at the bottom of a bottle while rotating it around abit in your hand.

The major axis of a 2d ellipse is not always parallell to the the horizon. It is however always at a 90 degrees angle to the the minor axis. The minor axis is, as shown in previous links, parallell with the normal of the plane that the 3d circle occupies. So yes, the major axis would be parallell to the horizon for all circles placed on the floor or any other level surface. But ONLY those circles. (actually, even this is false. it would only be true as long as we look straight at the circle. if we were to look somewhere else, spherical perspective would tilt it.)
As soon as the 3d plane is tilted, so are the minor and major axises of the 2d ellipse.

To use your own words:
"For goodness sake get a plate lean it agains an object in a sorta 45degree angle and look at it."

The fact that a circle has no orientation is untrue. It has one, and that is its "up" direction. I.e. the normalt of the plane it occupies.

Very nice discussion! Long time since i thought about this.

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The horror...

[luggage]

[Affected]

by the way, treeshark, the spherical grid you used on that webpage is interesting, but it does make it impossible to make totally accurate perspective drawings, since you can no longer figure out foreshortening and shadows etc., as those require drawing straight lines through your geometry. Can't think of a way around it though, I guess it's time to learn to eyeball more.

[treeshark]

Sorry I thought I'd made this clear I am talking about circles lying on the ground plane. By orientation I mean in that plane. As a general guide if you extend the minor axis to where it crosses the horizon then that will be the vanishing point.
In constructed straight line perspective the major axis of a circle upon the ground plane tilts away from the horizontal as it moves left or right in the picture plane. It does not do this in reality. When perpective was first used in the 15th century it was noted that the bases of the columns in perspective drawings and paintings with the existing rules looked wrong, It is Brunelleschi the great renaissance architect who suggested that circles needed their own rule in order for them to look convincing.
Neither cameras or computers have taken this on board alas and still do them wrongly. So ladies and gentlemen if you want to look thin in a photo make sure you are in the middle of the frame cos at the edges you'll look fat!

[Lunatique]

I think although this stuff is cool for 3D image mapping or stitching photography panoramas, it's really not applicable to most 2D artworks, and you really shouldn't dwell on it too much. All this stuff assumes you want your picture to look like how it would if you TURNED your head both ways, instead of having one FIXED POV, which is what most static 2D images are. I really couldn't care less if my artwork looks like it was done with the consideration of how things would look if the viewer turned his head both ways.

[Affected]

lunatique: it isn't a matter of the POV moving: turning your head won't change the perspective (OK, it will slightly, since the pivot point of the head is not between the eyes), it just changes the orientation of your field of vision. You're right, though, that this stuff would rarely be needed for painting since generally you don't need to have such wide fields of vision. But anything beyond 90 degrees will see your image starting to look funny, and I at least would like to be able to bypass that nuisance.

[jfrancis]

It's all about the head (or camera) motion. This material only applies if you are willing to rotate the camera. That's why I said above, if you're going to rotate it, why stop there? Why not translate it down the street and around the corner? You could say that Picasso persective is the only true perspective because it shows you all the various sides and angles of an object.

[jfrancis]

... and just to really complicate things:

http://www.digitalartform.com/archives/2004/12/telephoto_and_w.html

particularly this:

"If film and lenses were perfect... you would need only one lens!
In a perfect world, I'd walk about with only my Canon 14 super-wide lens. I'd worry only about my camera position, secure in the knowledge that the 14mm lens was wide enough to capture my entire subject under 99% of conditions. Then if I wanted a picture for my Web site of just my friend in the middle of the frame, I'd crop down to just the center and use that. The result would be the same as if I'd used a 100mm portrait lens."

http://photo.net/learn/making-photographs/lens

[Affected]

I don't think that lens info makes it any more complicated. All it means is that camera position is what changes perspective. It would be much harder if different focal lengths gave different perspectives...

[treeshark]