[Blindmath] A 3d to 2d description resource?

[Richard Baldwin]

For whatever its worth, in the real world, much of what sighted people
perceive as the depth portion of 3D isn't 3D at all. Theoretically, a
sighted person can truly only see 3D due to binocular vision and the loss
of sight in one eye should make it impossible for a sighted person to
perceive depth.

However, that person without binocular vision can often see an automobile
approaching an intersection and have a pretty good idea how far away it is.

In reality, after a certain young age sighted people learn to use other
clues in addition to binocular vision to perceive the depth portion of 3D.

Presumably, it would be possible to create an experiment in which a person
with vision in only one eye is deprived of all such clues and that person
would be unable to determine the distance to an object.

Expanding on Michael's comment about sonification, if sonification works
for you, you can get a pretty good idea of the projection of a 3D object
onto a 2D plane using a normal dinner plate. (A very shallow white paper
plate might work even better and a circular disk cut from very thin
cardboard would work even better.)

Grasp the plate with both hands and hold it in front of your camera with
the surface of the plate being perpendicular to the camera. Grasp it in
such a way that both hands are the same distance from the floor.Slowly
rotate the plate with your fingers without moving your arms and hands until
the surface of the plate forms an angle of 90 degrees with the camera.

At that point, the shape of the place hasn't changed. It is still round
just like it was at the beginning. However, the projection of that 3D plate
onto the 2D camera lens has changed.

As soon as you started rotating the plate, the projection of the plate onto
the lens of the camera became an ellipse, or something close to an ellipse,
depending on the actual shape of the plate. As you rotate the plate, the
width of the projection should remain constant, but the height of the
projection should decrease.

Finally, when the surface of the plate is perpendicular to the the camera
lens, you should no longer see a circle or an ellipse. Instead you should
see a horizontal line segment. If you used a disk cut from very thin
cardboard, that line segment should be very thin and the projected shapes
from round to line segment should be near-perfect ellipses. If you used a
dinner plate, the intermediate shapes will only approximate an ellipse and
the final line segment will have some up and down thickness.

Do the same thing again, but this time hold the plate so that your hands
are on a vertical line. Now as you rotate the plate, the ellipses should
appear but this time they will have constant height and variable width.
When you reach the 90-degree point, you should see a vertical line segment.

Dick Baldwin

On Tue, Jan 31, 2012 at 2:58 AM, Michael Whapples <mwhapples at aim.com> wrote:

> Are you sure you have never encountered a picture of a tree in a 2D
> representation? The VOICE uses a 2D representation from what I know (stereo
> headphones, left and right, vertical position pitch in sound). So you tell
> us what a tree is like in 2D compared to the act of feeling it.
>
> I guess though one difficulty is the difference in a drawing and a photo,
> the latter may differ depending on lighting conditions and so you may find
> dark patches in different places depending on where the light is coming
> from and so how the shadows form on it. Depending on the purpose of the
> drawing and the detail given some things like the shadow may be ignored or
> there may just be representations of a feature rather than an accurate
> reproduction (eg. lines representing the texture of the bark, the bark may
> have much greater detail in its texture).
>
> Michael Whapples
>
> -----Original Message----- From: Pranav Lal
> Sent: Tuesday, January 31, 2012 1:35 AM
>
> To: blindmath at nfbnet.org
> Subject: [Blindmath] A 3d to 2d description resource?
>
> Hi all,
>
> Would it be worth creating a database that listed descriptions of 3d
> objects
> in 2d space? Take my example of a tree. I have felt trees before and can
> even see their pictures with the vOICe but how do I map that to the 2d
> space? I suspect View Plus already has such a collection but there is no
> reference to 3d since SVG is 2d.
>
> Of course, if there is a general approach in mathematics of converting 3d
> to
> 2d then all we would need to do is to write about it with some examples and
> see if that helps anyone.
> Pranav
>
>
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-- 
Richard G. Baldwin (Dick Baldwin)
Home of Baldwin's on-line Java Tutorials
http://www.DickBaldwin.com

Professor of Computer Information Technology
Austin Community College
(512) 223-4758
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