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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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