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On Mon, 06 Dec 1999 20:06:51 +0200, Margus Ramst <mar### [at] peak eduee> wrote:
>Well. You asked for it, you are gonna get it...
>
snip
>I hope this <ahem> brief tutorial proves helpful. If not, ask and I will try to
>explain in a more intelligible manner.
>
>Margus
Very educational Margus. Thanks
------------
dav### [at] cwcomnet
http://www.hamiltonite.mcmail.com
------------
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Margus!
MANY thanks for your explanation. It's very informative. Seems, I'm getting
understood the types of projections. Really!
Good luck for you!
Pavel Rumyantsev
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Margus Ramst wrote:
>The standard perspective camera traces rays from a fixed viewpoint, mapping
>samples to a rectangle. Because the horisontal and vertical angle between
camera
>rays remains constant, they do not hit the rectangle at constant intervals.
>Instead, they are positioned more sparsely towards the edges of the
rectangle.
>This is what causes the distortion of distances (stretching) I mentioned
>earlier.
I think it's the other way around.
The rays *does* hit the rectangle at constant intervals, the horisontal and
vertical angle between camera rays *doesn't* remains constant. *That* is
what causes the distortion of distances.
An example: When the camera is perpendicular to a plane with a checker
pattern, the checker pattern is NOT distorted.
But if you imagined a *sphere* around the camera, *then* the rays would be
positioned more sparsely towards the sides.
Well, at least I think so :-)
Greetings,
Rune
---
Updated December 10: http://rsj.mobilixnet.dk
Containing 3D images, stereograms, tutorials,
The POV Desktop Theme, 350+ raytracing jokes,
miscellaneous other things, and a lot of fun!
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On Sun, 12 Dec 1999 04:48:09 +0100, "Rune" <run### [at] inamecom>
wrote:
>I think it's the other way around.
>The rays *does* hit the rectangle at constant intervals, the horisontal and
>vertical angle between camera rays *doesn't* remains constant. *That* is
>what causes the distortion of distances.
Any projection leading to decreasing the number of dimensions leads to
some kind of distortion. Our eyes distort the image, too, but the
projection is not on a planar surface rather a part of a sphere. Our
brain corrects this and we do not notice it, but other kinds of
distortion are quite obvious to the eye.
>An example: When the camera is perpendicular to a plane with a checker
>pattern, the checker pattern is NOT distorted.
*Only* in the central pixel of the image <grin>. Try rendering the
same but bring the camera very close to the checkered plane and
increase the angle to something very big, say 160. See for yourself :)
>But if you imagined a *sphere* around the camera, *then* the rays would be
>positioned more sparsely towards the sides.
With the spherical projection no distortion would occur provided the
screen was spherical. Some old monitors which are quite bulgy can give
great results at 3D provided that you can guess the curvature and then
convert it to POV units.
Peter Popov
pet### [at] usanet
ICQ: 15002700
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The only way the checker pattern isn't distorted is with the orthographic
camera. The distortion of the perspective camera becomes obvious at high camera
angles (this is why the panoramic camera was added). At angles -> zero the
distortion of the perspective camera is indeed negligible, since it starts to
look like orthographic projection (rays are nearly parallel). But try an angle
of, say, 150 and you know what I mean.
Believe me, at least in the principles of planar and spherical projection I was
not mistaken.
Margus
Rune wrote:
>
> I think it's the other way around.
> The rays *does* hit the rectangle at constant intervals, the horisontal and
> vertical angle between camera rays *doesn't* remains constant. *That* is
> what causes the distortion of distances.
> An example: When the camera is perpendicular to a plane with a checker
> pattern, the checker pattern is NOT distorted.
>
> But if you imagined a *sphere* around the camera, *then* the rays would be
> positioned more sparsely towards the sides.
>
> Well, at least I think so :-)
>
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Margus Ramst wrote:
>The only way the checker pattern isn't distorted is with the orthographic
>camera. The distortion of the perspective camera becomes obvious at high
>camera angles (this is why the panoramic camera was added). At angles ->
>zero the distortion of the perspective camera is indeed negligible, since
>it starts to look like orthographic projection (rays are nearly parallel).
>But try an angle of, say, 150 and you know what I mean.
I know what you mean, but what you say / do is wrong /something different.
the second thing you do is pull back the camera to keep the object at the
same scale. The object camera distance is what determines the perspective.
Not the camera angle.
Try the following:
put a box at origin, rotate 45*y.
Set up your camera at a position on the -z-axis you like and keep the camera
image again but with such a bigger +w and +h that the box has the same hight,
in pixels, as in your first image.
Cut out the boxes of both images and compare. You will see that there is no
difference in perspective (distorion)
Ingo
--
Photography: http://members.home.nl/ingoogni/
Pov-Ray : http://members.home.nl/seed7/
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The thing that determines distortion is proximity to the image edge. Of course,
if you increase the angle to 150 degrees, the box becomes smaller in the image,
so all samples of the box are closer to the image center. This cancels out the
distortion. If the box would be at the image edge with both camera angles, there
would be a definite difference.
What I'm saying is that the distortion towards the image edges increases as the
camera angle increases. This is not perspective distortion, it is a specific
distortion of dimensions inherent to this type of mapping.
Margus
ingo wrote:
>
> Try the following:
> put a box at origin, rotate 45*y.
> Set up your camera at a position on the -z-axis you like and keep the camera
>
> image again but with such a bigger +w and +h that the box has the same hight,
> in pixels, as in your first image.
> Cut out the boxes of both images and compare. You will see that there is no
> difference in perspective (distorion)
>
> Ingo
>
> --
> Photography: http://members.home.nl/ingoogni/
> Pov-Ray : http://members.home.nl/seed7/
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Margus Ramst wrote:
>The only way the checker pattern isn't distorted is with the orthographic
>camera. The distortion of the perspective camera becomes obvious at high
camera
>angles (this is why the panoramic camera was added). At angles -> zero the
>distortion of the perspective camera is indeed negligible, since it starts
to
>look like orthographic projection (rays are nearly parallel). But try an
angle
>of, say, 150 and you know what I mean.
>Believe me, at least in the principles of planar and spherical projection I
was
>not mistaken.
What I meant when I said the checker pattern wouldn't become distorted, was
that each square of the checker pattern would be the same size and shape in
the output image. That might have been uncorrect wording but anyway, that's
what I meant :-)
I still insists that the rays *does* hit a plane perpendicular to the camera
viewing direction at *constant* *intervals*, and thus, the horisontal and
vertical angle between the camera rays *doesn't* remains constant.
However I said that the rays would be positioned more sparsely towards the
sides. That, of course, is wrong. The rays are positioned more sparsely
towards the *middle*.
Greetings,
Rune
---
Updated December 10: http://rsj.mobilixnet.dk
Containing 3D images, stereograms, tutorials,
The POV Desktop Theme, 350+ raytracing jokes,
miscellaneous other things, and a lot of fun!
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Argh! You are right about the distribution of rays, of course. I don't know what
made me claim the opposite; the logic is quite clear.
Well, I still believe my descriptions of all the other cameras are correct; as
well as what concerns different types of distortion.
Margus
Rune wrote:
>
> What I meant when I said the checker pattern wouldn't become distorted, was
> that each square of the checker pattern would be the same size and shape in
> the output image. That might have been uncorrect wording but anyway, that's
> what I meant :-)
>
> I still insists that the rays *does* hit a plane perpendicular to the camera
> viewing direction at *constant* *intervals*, and thus, the horisontal and
> vertical angle between the camera rays *doesn't* remains constant.
> However I said that the rays would be positioned more sparsely towards the
> sides. That, of course, is wrong. The rays are positioned more sparsely
> towards the *middle*.
>
> Greetings,
>
> Rune
>
> ---
> Updated December 10: http://rsj.mobilixnet.dk
> Containing 3D images, stereograms, tutorials,
> The POV Desktop Theme, 350+ raytracing jokes,
> miscellaneous other things, and a lot of fun!
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Margus Ramst wrote:
>
> Well. You asked for it, you are gonna get it...
>
To correct a stupid mistake:
As I said, with the standard perspective, the scene is mapped to a rectangle.
However, I was wrong about the distribution of samples.
Camera rays hit the rectangle at *constant intervals*; in order for this to
happen, the angle between consecutive rays has to decrease towards the image
edges. Thus, in model space, rays are distributed more densely as they move away
from the camera axis. *This* is what causes features to be stretched towards the
edges.
Note also that since camera rays hit the mapping rectangle at constant
intervals, they also hit at constant intervals all surfaces coplanar with the
mapping rectangle. This means that, given two points parallel to the viewing
plane, the distance between these points remains constant regardless of their
position in screen space. The distance is not distorted towards the image edges.
However, for all points not parallel with the viewing plane, distortion does
occur.
Margus
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