T3D From Euclid to Wheatstone and further on

[abram klooswyk <abram.klooswyk@xxxxxx>]

>From Euclid to Wheatstone and further on

1. Perspective.
The Dome of the Duomo in Florence is not built in concrete or steel.
Neither of them were available. The Romans *had* concrete, but the 
technique was lost in the Middle Ages and re-invented well after the 
Florence Duomo was built. 
The dome is built of *brick*. It is composed of two shells. 
Between the inner and outer shell are staircases on which you can climb
to the top. When you arrive there your admiration for its architect, 
Filipo Brunelleschi (1377-1446) will be at the same high level. 
This admiration gets even higher when you know that he probably was the 
first to use central linear perspective in paintings, after the theo- 
retical work by his fellow townsman Leon Battista Alberti (1404-1472), 
who published the method in 1435.
Of course perspective was used in earlier times, you can see it in wall 
paintings in Pompei, and in the 14th century Giotto used already several
rules for it. But the mathematical method of Alberti for central linear
perspective brought about an explosion of paintings using this new 
technique in the 15th through 17th century. Leonardo da Vinci, Piero
della Francesca and Albrecht DUerer are among the great artists who used
the technique. People were excited about the visual space it created. 
Many works of that area still look impressive.  

Why was central linear perspective not invented earlier? The geometry
for it was available since Euclid. 
It had to wait for the great change of mind which brought about the 
Renaissance. This was not just a Rebirth of ancient art and science, 
but added important new ideas.
 
In the Middle Ages gothic architecture was maybe the highest expression 
of the world image of those times: man looked at heaven, heaven was the
centre of his world.  
But in the humanistic Renaissance man found *himself* to be in the 
centre of the world, indeed the centre of perspective. So he looked 
around and explored other continents with great discovery travels 
(Vasco da Gama, Columbus). Before central perspective was invented 
America could not have been discovered.
    (Please don't write me that anonymous tribes crossing the non-
    existing Bering street, or Bjarni HerjÛlfsson, or Leif Ericson, did 
    so before, I'm talking about mainstream cultural developments...:-))
Interestingly, the discovery travels also included the *dead* human
body,
studying its anatomy. Galen (130-200 AD) only dissected animals, but
now,
after a slow start in the 14th century, dead humans were dissected, 
leading to the great work by Andreas Vesalius in the 16th century.
Central linear perspective perfectly fits in the world image of the 
Renaissance

2. Stereoscopy.
In the 18th century a new change of mind in Western culture turned 
attention to *individual* man himself. Rousseau wrote "Emile" (1762),
which generally is seen as a turning point. Then the American Congress 
(1776) and the French Assemble National (1789) made the declarations 
of Human Rights, which eventually led to the abolishment of slavery.
In medical science now also the *living* body comes at the centre, the
basics of modern physiology begin with Lavoisier, Galvani and Johannes
Mueller. Auenbrugger discovers lung percussion (1761). Laennec makes 
a stethoscope (1812) and describes heart sounds in some detail. 
(The latter two inventions technically could have been made in any 
age, but had to wait till the human mind was prepared for them.)
The accommodation of the eye was studied by Thomas Young (1773-1829).

Since Euclid's time also many *binocular* phenomena were studied. 
Many of the ancient scientific works were preserved by Arabs, but Arab
scientists made considerable progress themselves, the outstanding 
example is Alhazen (Ibn al-Haytham), who studied vision in the 11th 
century, and who described several binocular phenomena for the first 
time. Except for his geometrical optics, his work has been neglected 
until recently.

Since ancient times visual *distance* and *depth* perception also were 
studied, but except for Leonardo da Vinci nobody wrote anything on 
*binocular* depth perception. A few hints to it are recorded in the 
18th century, but the great step forward came only with Wheatstone.

[Leonardo (1452-1519) was in several ways a genius ahead of his time, 
which means not understood by his contemporaries. And his anatomy 
drawings, some better than those by Vesalius, but made more than a 
century earlier, were not published until 1797. Of his mechanical 
inventions, like the helicopter, has been said that several of them 
could not work. Still his ideas were brilliant, but many were 
inaccessible on handwritten sheets in mirror writing. 
So his influence on mainstream science and engineering in the 15th 
through 18th century was limited. 
There is an interesting Leonardo museum in his birth village Vinci,
near Florence - Leonardo had no surname, he came "from Vinci"]

Wheatstone's 1838 reading was published with engraved stereodrawings,
the
printing plate was probably made by "Js.Basire.sc." from Wheatstone's
original drawings, probably introducing small errors in some. 
One simple drawing consists of 5 dots on a row, unequally spaced in left 
and right hand view:

           . . . . .                         .  .  .  .  .  

But interestingly the *most* simple, and the *first*, stereo drawing to
which Wheatstone refers is *not* illustrated by a stereodrawing, only
by an "aerial view" diagram. It is about only *two* lines in stereo: 
"If two vertical lines near each other, but at different distances from
the spectator be regarded first with one eye and then with the other ...
(...)."
"Now if the two lines be drawn on two pieces of card, at the respective
distances at which they appear to the eye, and these cards be afterwards
viewed by either means above directed [free viewing with or without free 
viewing aids, the stereoscope was only presented after this paragraph
AK], the observer will no longer see two lines on a plane surface, as
each card separately shows; but two lines will appear, one nearer to him 
than the other, precisely as the original vertical lines themselves." 
So the not drawn first stereo drawing looks like:

                | |                               |   |

This drawing is sometimes referred to as "the Wheatstone Stereogram".

Some people still maintain that stereodrawings were made before
Wheatstone, they have a hard time in explaining why no stereodrawings 
with four scratches or a couple of dots survive from those times. 
I have tried to fuse dots and scratches in prehistoric caves in 
France, on the pyramids, the Parthenon, the Roman colosseum, in the 
prehistoric rock drawings of Sweden (were actually dots play a great 
role), in the Alhambra, in medieval churches, but all in vain. 
[:-), have to visit some places yet]. 

Some say there were no stereodrawings before Wheatstone because the
Stereoscope was not invented, so a merely technical cause. This is
unlikely because: 
1. Wheatstone made stereodrawings before he made a stereoscope, and 
   he describes freeviewing, crossed and uncrossed, and aids for it.
2. If *we* can freeview, why man in other ages couldn't learn to do it? 
   And indeed several 18th century writers *have* done crossed eyed 
   fusion experiments with objects, two candles is the typical set up. 
   Even a "free viewing aid" for it was described in early 18th century
   (a rectangular hole in a board).
But stereodrawing still was *unthinkable* in the times before "Emile"
was written. And the Stereoscope could not have been invented before 
the stethoscope.

3. "3D" at the millennium passing.
In recent years "computer graphics" has been developed, often referred
to as "3D" graphics. Professionally I sometimes use a "3D" rendering 
computer program. The program makes images on a monitor which look like
objects seen with one eye. The screen is flat, so the images are 2D. 
For me, 3D means stereoscopy. Stereoscopy has the oldest rights on the 
term "3D" (and, for that matter, on the term "stereo"), but it was
captured by computer programmers. 
When I print the rendered images I always print them as stereo pairs, 
by rotating the virtual "object" some 4 degrees about a vertical axis 
(this introduces some keystoning, which I must accept). 
When I view the images in stereo, I look at the 3D image with my 
cyclopean retina (Julesz), my brain brings a 3D image to my mind. 
I always refer to the flat 2D pictures, on screen and printed, as 
"so-called 3D". The programmers however, and most people from the 
"ray tracing community", call these mono-pictures: 3D.

In a talk on similar pictures a few years ago, I have argued that, 
when this computer output is called "3D", the perspective drawings 
and paintings from the Renaissance on *also* should be called "3D". 
But there is a difference, *in the computer* many of these programs 
use a true 3-dimensional representation of objects. The x, y and z 
coordinates of points are indeed in the computer's memory.

People from the cyber-graphics community like to see themselves as the
pioneers of this age. The fact that they call the flat 2D on-screen 
output "3D" says a lot about them. They obviously think that the 2D
image, brought to their *own* mind when they look at the monitor, is 
less important than the 3D "object" which is in the "mind" of the 
*computer*. But when they really *are* the pioneers, it means that 
man in this age is going to identify himself with a computer.

4. Conclusion.
In this tentative analysis I have tried to make clear that there are 
strong connections between the general world image of a certain period, 
the way there is or was looked at images, and the imaging techniques 
used in that age. 
Except for a few geniuses, nobody can look beyond the horizon of his
time.
Finding back stereo drawings dating from the 18th century maybe cannot 
*completely* by excluded, but looking farther back for them really is a
waste of time.

So I arrive at three propositions:
America could not have been discovered before central linear
perspective.
The stereoscope could not have been invented before the stethoscope.
Man at this millennium end tends to identify himself with the computer.

I suppose these are enough provocations for now.

Abram Klooswyk

----------
(I have written earlier on some of the basic ideas expressed here, 
 in 1985 in the German "Stereo-journal")


------------------------------