P3D The Third Deformation of 3D, Thought experiments (4 of 6)

[abram klooswyk <abram.klooswyk@xxxxxx>]

The three Realist masks (normal/distant, medium, close-up)
only differ in aperture width, the closer masks have a little
less width, because usable width becomes smaller in close-ups
using a stereocamera with fixed lens separation (as most
stereocameras have...).

The mask aperture separation of all three Realist masks
is 62.2 mm, so viewing convergence to near points at the
window also is equal for pictures in these masks, when the
other circumstances are not changed (same viewer or same
place in projection room, no alterations on projector).
When you sit in the "orthostereo seat" for normal *distant*
shots, your viewing convergence Cv in looking at the near
points of those shots is about 2 degrees, which is equal
to the photographic convergence of those points.

The photographic convergence to a near point in a Realist
*close-up* shot with nearest point at 2.5 feet (76 cm) is
about 70/760 radian (B/I, base divided by distance),
slightly over 5 degrees. But viewing convergence is only
2 degrees, in using the Realist close-up masks.
So there is 3 degrees less viewing convergence than
photographic convergence (Cv << C).

What do we see?
As always, we have to distinguish between the theory of
geometrical stereo deformations and what we actually can
see, perception is often different from mathematics.

Let's imagine two mathematical test shots first.
Take a wire frame in the shape of a rectangular box, with
wires at the edges only, measuring 1 x 1 x 1.5 feet
(30 x 30 x 45 cm).
With your Stereo Realist, make a stereopicture of the frame
with one of the square (1 x 1) sides towards the camera
at 7 feet, and a second picture with the same front side
at 2.5 feet.
Viewing the first shot from the orthostereo seat in the
projection room, theory says that you see a frame of the same
size at the same distance as you would see in reality, so the
front side of the frame is at 7 feet and rear side is at
8.5 feet.

The second shot is mounted in a close-up mask, so the near
point separation of its front side is 62.2 mm and this front
again appears at 7 feet. Its width and height is much larger,
about 7/2,5 times, because it was closer to the camera.
The rear face of the frame was at 2.5 + 1.5 = 4 feet in
picture taking, so the separation of its image points was
72.0 mm on the uncut film (see previous post), but it is 63.4
mm on the mounted slide. So it gets the same separation as
infinity points on the normal (distant) slides.

*Geometrically* the frame now extends from seven feet to
infinity, and the rear end also gets incredibly large.
The box frame should have a large square base in infinity and
a small square face at 7 feet. It is stretched out from 7
feet to infinity. This is the shape of a four sided
truncated pyramid, therefore this deformation is also called
the frustum deformation.

Now what do we actually see of this deformation in the
projection room?
Note that there is no hyper or hypo stereo (the Base
deformation or First deformation), because B = Bv (ignoring
the difference between 70 mm and your own eye separation).
The Distance deformation or Second deformation, sometimes
called angle of view deformation, where F differs from Fv,
is *also* absent, because you are carefully seated on the
right spot in the projection room.
But here we deal with the Third Deformation, the convergence
or frustum deformation!

The answer to what we see seems to differ for different
persons and different subject matter. However, in shots
similar to the case of the imagined frame I definitely see
stretch, in fact I do in many slides taken so close with a
normal based stereocamera.

(To be continued)

Abram Klooswyk