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1. The false perspective in which even supposedly receding parallel lines remain
parallel. There's no size change with distance.
2. Ambiguous or impossible connection between picture elements. Picture elements are
connected, even though perspective cues tell us they should not be near each other.
The example below left is shown in isometric style. The conventional wisdom has been that
perspective rendering of such pictures is not possible, or would destroy the illusion.
The same illusion is shown at the right in perspective, using two vanishing points. The illusory nature of the object is
certainly not diminished by this presentation, though I don't claim that it is greatly enhanced.
Some persons experience an interesting effect while
comparing these two pictures. Look at the perspective
view for a while, then shift your attention to the
isometric view at the right. The isometric view may
now appear "wrong" or "warped", and you may feel
that the top and bottom of the frame are not parallel,
and diverge at the rear of the frame!
STEREO DRAWING
Stereo drawings require two pictures, one for each eye. To view such drawings requires some practice. Generally two
methods are used: (1) parallel viewing and (2) cross-eyed viewing. Both methods require one to learn a new visual
skill.
Normally when we look at the "real" world, our eyes converge on an object and they also focus on the same object.
We habitually do this, and our brains have become accustomed to a one-to-one correspondence between focus and
convergence.
We can learn to "unlock" focus and convergence, enabling us to view stereo pairs without optical aid. In this document
we use a display method which can be adapted to either parallel-eye viewing or crossed-eye viewing. Three drawings
will be shown side by side. The middle drawing is to be viewed with the right eye. The other two are identical and one
is to be viewed with the left eye. Here's how to view them.
(1) Parallel viewing. This is sometimes called wall-eyed viewing. Use the left and middle pictures only.
Look at a distant object then bring your eyes down to the paper trying not to converge or focus on the
paper. You'll see a blurred double image. Consciously try to bring the double image into one. Now try to
focus your eyes on it without allowing the two images to drift apart.
Parallel viewing is limited to pictures about 2.5 inches wide, the spacing of the typical human eye.
(2) Cross eyed viewing. Use the right and middle pictures only. Hold your finger exactly halfway between
your eyes and the page. Focus on your finger. Your eyes will be converged on the finger also, and you
should be conscious of the two pictures out of focus behind your finger, but probably nearly coincident.
Move your finger a bit until the two pictures are fully coincident. Now hold the convergence while
refocusing from your finger to the page. Finally, you can remove your finger from the field of view.
Crossed eyed viewing can be used with large pictures. Paintings have been presented this way. Salvadore
Dali painted some of this kind. For those who can learn the skill of viewing, this is one of the most effective
ways for viewing stereo without special glasses.
(2) Mirror method. For completeness, we illustrate a method rarely used in printed books. Popular
Photography magazine experimented with it for a while. One picture of the pair is printed normally, ad the
other is printed beside it, but reversed left/right. That picture is viewed through a mirror which re-inverts it.
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other is printed beside it, but reversed left/right. That picture is viewed through a mirror which re-inverts it.
We will not use that method here.
For practice, try this illustration from Sir Charles Wheatstone's book The Stereoscope.[2]
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Don't expect to succeed the first time. This skill takes conscious effort and concentration. When you do succeed, you'll
see the pictures snap into full three-dimensional depth. The picture will look like a wire-frame box. You'll actually see
two 3-D images, one with normal depth, one with inverted (pseudoscopic depth). On either side of these you'll see
fainter, phantom images with no depth. Ignore them.
Here's some more practice examples:
If you use cross eyed viewing on the pair intended for parallel, or vice versa, you will see a "pseudoscopic" depth, in
which near and far are reversed. In the first picture, the pseudoscopic view appears as if you are looking down onto a
truncated pyramid. In the second picture, the cone seems upright in the normal view, but tilted back and viewed from
its base in the pseudoscopic view. Wire-frame stereo drawings often look interesting either way.
Here's another example for practice.
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This coiled spring is more difficult to view:
Now, can illusion pictures be drawn this way? Some can. The three-tined fork illusion, sometimes called "Schuster's
conundrum," succeeds remarkably well. This is strictly an illusion of ambiguous connectivity; there's no depth
ambiguity at all.
Here's my color 3d rendition of the classic "Crazy Crate".
Let's try the Penrose Illusion (impossible triangle). Here we use the fact that a horizontal line has ambiguous depth
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Let's try the Penrose Illusion (impossible triangle). Here we use the fact that a horizontal line has ambiguous depth
even in stereo. So we've oriented the triangle with one side horizontal. The other sides have been given true
stereoscopic depth, but no perspective depth cues are used.
But now try viewing this version. Here we haven't used the cheap trick of horizontal lines. We've used a different
cheap trick. We've simply expanded the horizontal dimension of one picture by about 5%.
Why should this work at all? It seems to defy logic. Let's try the same trick with some other isometric pictures.
And another:
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Feel free to view any of these pseudoscopically. It doesn't seem to matter a lot. You get a vague sensation of
stereoscopic depth either way!
Some people have a weak perception of depth in such drawings even when both pictures are identical! This may be
due to the artificial method for viewing them, particularly the slight keystone distortion of each picture when cross-
eyed viewing is used. The absence of focus cues may play a role also.
I haven't prejudiced you by suggesting what you should see in these examples. Generally one experiences the same
ambiguity of depth, as in the "flat" isometric version, but there's an added cue of stereoscopic depth as well. The
stereoscopic depth seems to fluctuate depending on where one fixes one's attention within the picture. Clearly we are
getting a conflict of depth and solidity cues. The stereoscopic cues and the isometric perspective cues do not agree.
ILLUSIONS OF SHAPE
There's a large class of illusions called pattern-dominance or pattern-conflict illusions. They fall within a larger class
of illusions of shape.
Pattern-dominance illusions, as usually presented, seem to be strictly due to conflict of overlapping patterns in a single
plane. Our perception of the geometry of one pattern is altered by the presence of the other pattern. The illusion seems
not to rely upon any suggestion of perspective in the drawing.
Most people judge that the circles in the left drawing a bit off-round, being gently flattened at four places, near the
corners of the squares. Few would say that the circles distort the squares in this case.
We can test this by making another drawing (on the right) in which the squares dominate the background field of view,
while a lone circle competes with that. Will the circle show distortion, but the squares remain square? Yes, that's what
most people see.
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Both versions of the illusion persist in stereo rendering even though the circles and squares now lie in different planes
when seen in depth.
Some explain the following illusion by claiming the radial lines are interpreted by the brain as parallel lines receding
to a vanishing point. This supposedly makes one circle (usually the right one) seem smaller, though they are drawn the
same size and therefore subtend the same angle to the eye. Again, I find this explanation unpersuasive.
The Ehrenfels illusion presents a perfect square upon a background of
radial lines. The square seems tilted forward. (Or, it appears to be a
rhombus, with the top edge longer than the lower edge.) It still seems
tilted or distorted when the square is drawn on a transparent sheet held
some distance in front of the plane of the radial line pattern. In stereo
rendering there's a strong illusion that the square is tilted, the top edge
nearer than the lower edge, even though there are no stereoscopic cues to support this interpretation.
A related illusion, the Herring illusion, presents parallel lines against a background of radial lines. The parallel lines
appear bowed or bent. They still appear bent if they are on a transparent sheet some distance in front of the plane of the
radial line pattern. This fact comes through in stereo rendering also.
This one is repeated below in larger scale, for crossed-eye viewing only.
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[2] Wheatstone, Sir Charles. "Contributions to the Physiology of Vision. Part the First; On Some Remarkable, and
Hitherto Unobserved, Phenomena of Binocular Vision," Philosophical Transactions of the Royal Society, 1838, Part 1,
pp 371-94. Reprinted in The Scientific Papers of Sir Charles Wheatstone, London, 1879, pp. 225-259. Online copy,
complete.
[3] Seckel, Al. The Art of Optical Illusions. Carlton Books, 2000.
[4] Seckel, Al. More Optical Illusions. Carlton Books, 2002.
Al Seckel's books are, in my biased opinion, the best general illusion collections published, and are very reasonably
priced. See these descriptions, and order them from your favorite book source.
This document is an ongoing project, for which feedback is welcomed by the
author, who hopes that these drawings can stimulate an exchange of ideas.
Use the address shown here. Expect to see additions and changes in this
section of my web pages in the future.
Return to top of this page.
Return to illusions page
Return to front page and main menu.
Since 8/30/01 people who had no illusions came here to get some.
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