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DESIGN OF AN AUTOSTEREOSCOPIC
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
For my wife, Nicole, and my parents, Dieter and Ursula,
as well as my sisters and brothers, Birgit, Heidi, Peter and
The author wishes to thank his advisor, Dr. Carl Crane,
for his guidance. He is also grateful to the members of his
committee who all showed great interest and provided
The author would also like to thank his father, Dieter
Jurczyk, for his invaluable help and encouragement.
Additional thanks go to Dr. Jarisch and Mr. Strahleck, both
from IBM Sindelfingen.
Special thanks go to his wife, Nicole, for all her love,
support and understanding that she provided through the years.
Further thanks are due to all the people at CIMAR, for their
great company and help during all phases of this project.
TABLE OF CONTENTS
ACKNOWLEDGMENTS . . iv
LIST OF TABLES . . viii
LIST OF FIGURES . . ix
ABSTRACT . . . xi
1 INTRODUCTION . . 1
1.1 Introduction . . 1
1.2 Historical Overview . 4
1.2.1 Anaglyphs . . 5
1.2.2 Polarization Projection . 8
1.2.3 Electronic Displays . 9
1.2.4 LCD Glasses . 9
1.3 Other Directly Related Work in the Field 12
2 OVERVIEW OF AUTOSTEREOSCOPIC DISPLAY UNIT (ADU) 19
2.1 Introduction . . 19
2.2 General Description . 19
2.2.1 Projection Surface . 20
220.127.116.11 Flat Inclined Display Surface 21
18.104.22.168 Corkscrew Display Surface 23
22.214.171.124 Flat Vertical Display Screen 24
2.2.2 Projection Display . 24
2.2.3 Motorized Base Unit . 26
2.2.4 Computer Equipment . 26
2.2.5 Size of Projection Surface / Resolution 27
2.3 Applications . . 27
2.4 Safety Considerations . 28
2.5 Scale Model of ADU . 29
3 THE HUMAN EYE . . 35
3.1 Introduction . . 35
3.2 The human eye . . 36
3.3 Binocular Vision . . 41
3.4 Flow of visual information . 41
3.5 Physiological Properties of the Human Eye
3.6 Physiological and Psychological Cues 43
3.6.1 Physiological Cues . 44
126.96.36.199 Accommodation . 44
188.8.131.52 Convergence . 44
184.108.40.206 Binocular Disparity 45
220.127.116.11 Monocular Movement Parallax 45
3.6.2 Psychological Cues . 45
18.104.22.168 Retinal Image Size . 46
22.214.171.124 Linear Perspective . 46
126.96.36.199 Aerial Perspective . 46
188.8.131.52 Overlapping . 47
184.108.40.206 Shades and Shadows . 47
220.127.116.11 Texture Gradient . 47
4 MATERIALS AND METHODS . 49
4.1 Introduction . . 49
4.2 Computer Hardware . 51
4.2.1 Silicon Graphics System . 52
4.2.2 PC based Pentium System . 60
4.2.3 Diamond Viper PCI Graphics Card 62
4.3 Software . . 64
4.4 Image Slicing Software Development 66
4.5 Counteracting the Keystone Effect 71
4.6 Display Software . . 76
5 SYSTEM CONFIGURATION, RESULTS AND CONCLUSIONS 78
5.1 Projection Surface . 79
5.2 Projection Display . 83
5.2.1 Technical data . 84
5.2.2 Diagram / schematic . 85
5.2.3 Internal design . 86
5.2.4 Keystoning . 86
5.2.5 Update rates/ resolution . 87
5.3 Motorized Base Unit . 87
5.4 Plexiglass Safety Cage . 90
5.5 Results . . 92
5.5 Conclusions . . 100
6 FUTURE WORK . . 102
I LISTING OF IMAGE PREPARATION PROGRAM 111
II LISTING OF IMAGE DISPLAY PROGRAM . 126
LIST OF REFERENCES . . 128
BIOGRAPHICAL SKETCH . . 136
LIST OF TABLES
5.1: Distance from screen vs. Image size . 85
LIST OF FIGURES
The Hammond motion picture syst
3-D viewing with LCD lenses .
Varifocal Mirror stereoscopic
Varifocal Mirror .
Three-dimensional viewing volum
Three-dimensional LED Display
Three-dimensional viewer by Miz
Overview of proposed flat incli
Elliptic Cone .
Projection surface: top and sid
2.4: Corkscrew display surface
ned ADU system
e views .
2.5: Flat vertical display screen . .
2.6: Two spherical mirrors . .
2.7: Top and side view of proposed ADU .
2.8: Scale model top view . .
2.9: Scale model side view . .
2.10: Image as seen from behind . .
2.11: Image with paper acting as screen .
2.12: Rotation of displayed screen image. .
3.1: Lens eye. . . .
3.2: Diagram of the human eye. . .
3.3: Rods and cones . .
3.4: Flow of Information to the brain .
3.5: Linear and aerial Perspective .
3.6: Overlapping . . .
3.7: Shades and Shadows . .
3.8: Texture Gradient . .
4.1: Translation of an object. .
4.2: Rotating an object. . .
4.3: Scaled Objects. . .
4.4: Viper WEITEK Power 9000 System Block Diagram.
4.5: Flow Chart for image slicing program .
4.6: Slice of an image . .
4.7: Snapshot of screen image slicing software
4.8: Images with a keystone distortion of angle a.
4.9: Uncorrected and corrected images. .
4.10: Image Slices in increments of 30 degrees. .
5.1: Overview of ADU . . 81
5.2: Desktop Projector . . 85
5.3: Normal vs. Keystone Images . 86
5.4: Top view of base unit . 91
5.5: Overall view of ADU system setup. ... 91
5.6: Torus located at center . ... 95
5.7: Four consecutive positions of the displayed torus. 95
5.8: Display of a sphere . 97
5.9: Image of torus low speed. . ... 97
5.10: Image of torus high speed. . ... 98
5.11: Image of torus fused image. . ... 98
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DESIGN OF AN AUTOSTEREOSCOPIC
Chairperson: Dr. Carl D. Crane III
Major Department: Mechanical Engineering
A low-cost autostereoscopic system which permits the
observation of a high resolution image by several people
simultaneously from different viewing angles is described.
The device should be suited to mass production. The display
uses a plate-like screen, which is mounted vertically, and is
attached to a motor via a shaft which runs through its center
The image is formed on the screen by projecting an image
through a modulator and an optical system onto the display
screen described above. The screen is made of aluminum, and
is coated with a semi-reflective material. The modulation of
the projected image is synchronized with the rotating disk, so
that a three-dimensional image appears on the screen.
As the screen rotates about the z-axis, it sweeps out a
cylindrical display volume.
Applications include such activities as medical imaging,
graphics (e.g. computer aided engineering, computer aided
design, etc), molecular modeling, entertainment, and
monitoring of air traffic above crowded airports. Instead of
displaying airplanes on a two-dimensional surface with
altitude displayed as a number beside the plane, the air-
traffic controller could get a much more accurate picture of
the actual situation. Military uses could include monitoring
satellites (and missiles) in earth's orbit, as well as
providing an overall view of a battlefield scene.
The search for the ideal 3-dimensional (3-D) projection
system is one that has been on-going for decades. Man's
desire to have the power to project an image that mirrors
exactly that which is seen in the real world has been the
driving force behind research into 3-D technologies. With a
better understanding of the human visual system and
utilization of advanced computer technologies, it appears as
though the goal of having projected images actually possess 3-
D attributes is now more attainable than ever before.
The primary attribute that physical objects possess is
depth. There is a front, back, side, top and bottom to
objects we encounter in our world. The physical attribute of
depth is interpreted by the human visual system using a
priority scheme designed to interpret different data
associated with that object. In the past, research into
displaying 3-D objects with projection systems has
concentrated on tricking the visual system with depth cues so
that the observer would believe that he or she was actually
seeing a physical object with depth instead of just a 2-
dimensional projection. This technique of "tricking" the
visual system into interpreting signals in a particular
fashion was necessary because until recently the technology
has not been available to actually give a projected image the
physical attribute of "depth."
The depth cues that have typically been emulated by
researchers are both physiological and psychological in
nature. Physiological depth cues include accommodation
(change in focal length of the eye lens), convergence (inward
rotation of the eyes), binocular disparity (difference between
left and right eye images), and motion parallax (image changes
due to motion of observer). Psychological depth cues include
linear perspective (distant objects appear smaller), shading
and shadowing (these indicate positions relative to light
sources), aerial perspective (distant objects appear less
distinct or cloudy), occlusion (nearer objects hide more
distant objects), texture gradient (distant objects have less
detail), and color (distant objects look darker)[McAllister,
1992]. A two-dimensional display device must provide some or
all of these depth cues in order to present a semblance of
Practitioners in the field of computer graphics (and,
more recently, volume visualization) have created illusory 3-D
images and scenes on 2-D display screens by computing and
displaying psychological depth cues. These images lack the
physiological depth cues supplied by an actual 3-D object,
provide only a single angle view, and require significant
computation to render the depth cues (calculate perspective;
remove hidden lines and surfaces; add shading, lighting, and
Stereoscopic Cathode Ray Tube (CRT) approaches (in which
the left-eye image is presented to the left eye only, while
the right eye image is presented to the right eye only) add
limited stereopsis, but still lack motion, parallax and large
angles of view, and require displaying two slightly different
images, one for each eye.
Head tracking technologies (where a series of sensors
measure the position and movement of the observers head),
coupled with stereoscopic approaches (such as head mounted
displays), provide motion parallax and greater angles of view,
with the additional benefit of making the viewing volume
nearly limitless. However, they still suffer from the need to
computer-render separate images for each eye. An additional
drawback is the current physical intrusiveness of the
technology (i.e., bulky headgear).
Another system that has been investigated is computer
generated holography. This technology provides the benefit of
being able to view an object from several different angles,
but there is a huge computational burden involved with the
system. The computer programming must anticipate what the
object will look like and what the holographic interference
pattern will be for each individual angle of view [Benton,
1990]. The effort needed to calculate the necessary algorithms
limits the flexibility and applicability of this technology.
According to Kaufman , a leading scientist in the
field of computer visualization, "the ultimate highly
inspirational goal of equipment development [for volume
visualization] is a novel 3-D display technology or media for
fast presentation of 3-D volumes, as well as surfaces, from
any arbitrary direction" (1991, p. 6). Direct volume display
devices approach this goal by displaying 3-D volumes and
surfaces in a volume, providing depth rather than depth cues
[Clifton and Wefer, 1993]
1.2 Historical Overview
Stereoscopic vision is the ability to perceive depth
through the use of both eyes. Mechanical devices to view
three-dimensional (3-D) images first appeared in the 19th
century. Since then, they have remained largely a curiosity,
although technology has advanced significantly. Today,
stereoscopic vision is once again making a come-back, but this
time it is focused more on the scientific community. With the
advent of better computer monitors and better imaging
software, and a better understanding of the advantages of 3-D
information over its 2-D counterparts, various 3-D viewing
apparatuses are being developed.
Binocular stereopsis ("two-eyed solid seeing") was
discovered in 1833, when Sir Charles Wheatstone invented the
mirror stereoscope [Lipton, 1990]. The device enabled the
viewer to look at a pair of drawings, one with each eye, that
were of the same scene, but from different viewing positions.
The viewer would then see the image in "3-D", as an image
having depth. The public reacted very favorably, and within
a few years, every middle-class household in the US and Europe
had a mirror-stereoscope, which they used to see far-off
places, as well as great events of their time.
In 1858, J.C. d'Almeida developed another method for
displaying stereoscopic images. This method was called
anaglyph (ana is Greek for up, glyphein means to carve out).
The basic concept here was to display two images at the same
time, using "magic lanterns", or slide projectors, as they are
now called. The left eye image was displayed through a red
filter, while the right eye image was displayed through a
green filter. The viewers would then wear glasses with red
and green glass over the left and right eyes, respectively,
to select the appropriate view for each eye. This method
allowed the 3-D picture to be viewed by more than one person
at a time.
In 1891 Louis du Hauron suggested that one could
superimpose the red and green images onto a single piece of
film. In the 1920s and '30s several film studios made use of
this idea and made several films using this technique. The
period of these 3-D movies was only very brief: the
disadvantages of this technique were that people complained
about eye-strain and that it precluded the use of color in the
Due to improvements of the printing process by the turn
of the century, especially when it came to printing pictures,
the preferred medium of the masses became the magazine. This
pretty well ended the period of the anaglyph.
In December 1922, in a theater in New York, Laurens
Hammond [Hammond, 1922] introduced the first commercial
sequential stereoscopic motion picture, using the Teleview
process [Lipton 1991]. Figure 1.1 shows a schematic diagram
of the apparatus used for the Hammond motion-picture system.
The Hammond system used two 35 mm projectors that were
electrically synchronized using AC motors. Synchronized, but
Figure 1.1: The Hammond motion picture system. Projectors a
and b are alternately occluded by shutter 4, driven by motor
5, which is in sync with motor 7, driving shutter 8 of
selection device, used by patron to watch screen 3.
out of phase, shutters would open and close alternately in
front of the left and right projectors, thus displaying the
left, then right, then left, then right, etc., eye image. The
projectors were loaded with the appropriate left and right-eye
Every seat in the theater was equipped with a spinning
mechanical shutter. The shutter was a spinning disk, with its
motor in synchronization with the projector. Viewers were
thus able to see the left eye image with their left eye, and
the right-eye image with their right eye, thereby giving them
a 3-D image. Since each eye sees the appropriate perspective
view in sequence, this system is known as the frame-sequential
1.2.2 Polarization Projection
The polarized light projection technique made its debut
in 1939 at the Chrysler exhibit of the World's Fair in New
York. Chrysler showed a 15-minute movie produced by John A.
Norling that showed how a car was built on Chrysler's assembly
line, using time-lapse photography. Five to ten million
people saw this exhibition.
The projection technique involved two polarizers, one
that was vertically polarized, and one that was horizontally
polarized. These polarizers were mounted in front of the left
and right projector lenses, respectively. The viewers then
wore special viewing glasses that also had polarizers in them.
The polarizers thus allowed each eye to see only the intended
image. The stereoscopic images were created by a dual-camera
system. The polarizing material used was invented by Edwin L.
Hand, founder of the Polaroid Corp., and was patented in 1928.
This system was employed commercially for many years.
1.2.3 Electronic Displays
Electronic displays offer a potential for stereoscopic
displays that far surpass that of film. Electronic display
systems have the advantage of not having to wait for film
development, or having to synchronize two projectors, etc.
Since there is no wait and the pictures are immediately
available, a whole new list of possible applications arises:
medical imaging, flight simulation, molecular modeling,
industrial design, etc. Many researchers are currently
working on this, and are trying to determine ways and means to
make the most of this technology. Oftentimes this is as
simple as taking an old idea, such as the polarization
projection, and using these new displays in conjunction with
polarizers, to achieve a three-dimensional image.
1.2.4 LCD Glasses
A newer version of the polarization projection is the
idea to have a person wearing glasses with liquid crystal
lenses, that alternately turn off and turn on, while viewing
an image on a monitor. The left and right lenses are
synchronized with the screen to darken as either the left or
right image is displayed. The lenses and the screen switch at
a rate of 120 frames/sec; this translates into 60 frames/sec
for each eye. Since this is faster than what the human brain
I transmitter Stereo monitor has
/ fast scan rate and
to prevent ghosting.
Figure 1.2: 3-D viewing with LCD lenses.
can detect, no flickering is perceived.
Figure 1.2 shows an image of such a 3-D viewing system.
It can be seen that an Infrared (IR) transmitter sends pulses
that are received by a receiver in the LCD glasses. This
synchronizes the image on the screen with the image seen by
Figure 1.3: Varifocal Mirror two stereoscopic pairs (left-
and right-eye images).
1.4: Varifocal Mirror.
The advantages over the previously mentioned polarizers
are that the LCD lenses are almost completely clear when they
are not darkened, so that the image appears brighter, the
glasses are more effective at separating the images that go to
each eye, and the viewer has a wider range of motion than with
the polarizing screen, where he has to stay centered in order
to see the image.
1.3 Other Directly Related Work in the Field
Research in this field is ongoing. Typically, the
complexity of this task is so great, that only bigger
companies, or governmentally funded research institutions
participate. The amount of effort that goes into the
development of a successful three-dimensional viewing
apparatus is so great, that the time necessary can only be
counted in tens of man-years.
As early as July of 1960, J.C. Muirhead proposed the idea
of creating a variable focal length mirror. His idea was
simply to take a metalized plastic film, and stretch it over
a rigid backing to form a smooth even surface. If this is
done with sufficient care, a high quality mirror will have
Figure 1.5: Three dimensional Viewing Volume [Maguire]
\"" > '"-"i "3 f
been produced. Applying suction to the backing of the mirror,
the mirror will become concave, while applying pressure to the
backing will result in the mirror becoming convex. [J.C.
In 1967, Alan Traub proposed to create a stereoscopic
display by using a rapidly moving varifocal mirror. The
mirror could either be driven electrostatically or by a
loudspeaker. This would cause the surface of the mirror to
sweep out a volume of the image space. If one then displays
a time-varying image onto the varifocal mirror, it would
appear to be three-dimensional. He showed that this was
indeed a feasible concept by displaying sinusoidal patterns.
(see Figures 1.3 and 1.4)
This method was further enhanced by Eric Rawson who, in
1969, studied the peculiarities of this system, and determined
that for best results, the mirrors should be driven in a quasi
sawtooth manner, as this would allow for maximum depth
projection [Rawson, 1968].
In 1969, Edward T. Maguire came up with yet another
approach to the three-dimensional display. He proposed
building an apparatus having located therein, at regular
coordinate intervals, display elements which could be
Figure 1.6: Three Dimensional LED Display
Figure 1.7: Three dimensional viewer by G. Mizuno.
controlled through a computer. In his patent [Maguire, 1972]
he proposed suspending small lights by thin strings in a cube
shaped viewing area (see Figure 1.5). Although the idea was
quite good, it was none the less quite impractical to
construct, and even more difficult to view, because of the
massive amounts of bulbs and strings, that were suspended in
the viewing volume.
Edwin Berlin, in 1979, suggested creating a three-
dimensional array, by using a two dimensional visual display,
in which a three-dimensional image is achieved by providing
movement around a central axis. According to his patent, the
array would be comprised of a plurality of light sources, all
of which could individually be controlled. An example of this
would be a rectangular array of LEDs (Light Emitting Diodes)
mounted in a regular fashion. This array would then have to
be rotated to achieve a three-dimensional effect (see Figure
Yet another idea, by G. Mizuno, was to use a spherical
mirror and a standard CRT display (see Figure 1.7). In his
patent, Mizuno describes displaying a picture on a CRT display
that faces towards the mirror. The diameter of the mirror
itself is approximately double the size of the CRT display,
and the mirror is made of a dark, highly reflective surface.
The CRT is located at the bottom half of the mirror, while the
viewer looks at the image by looking at the top half of the
mirror. Combining this with the appropriate images, as well
as other depth cues, this will seem to give the viewer a
three-dimensional image. This method has successfully been
used in an arcade video game, named "The Time Traveler."
Listed above are just a few of the many ideas that have
been proposed in order to make 3-D viewing a reality. As this
is such an important topic, many more will be added over the
OVERVIEW OF AUTOSTEREOSCOPIC DISPLAY UNIT (ADU)
The three-dimensional viewing device proposed here will
not require the viewer to wear any headgear, as many of the
other three-dimensional viewing methods do. The viewer will
have the ability to move about the image during viewing, as
though he were viewing a real object. As the viewer moves
around the display unit, he will be able to see the object
being displayed from various angles.
The intent of this display device is to offer a TRUE
three-dimensional display unit, where no special viewing
constraints are imposed. This device may be described as an
"Autostereoscopic Display Unit" (ADU). This is a display
device that is stereoscopic in nature, i.e., that offers depth
to the viewer, and does this automatically, i.e., without any
further aids, such as glasses or the like.
2.2 General Description
The viewing device proposed in this work is designed to
utilize computer stored or generated images and information,
and produce a three-dimensional image. The premise upon which
this theory is based is the human eye's ability to "fuse"
images that are displayed at speeds greater than 17 Hz. The
computer generated images are projected onto a flat display
surface that is being rotated at a high speed (i.e., 1200
rpm). The images that are projected onto the viewing surface
are slices of whole images. These slices of the image are
then "fused" together by the human brain into one continuous
Additionally, front and rear views of the same image may
be simultaneously projected onto the viewing device from
different angles by using a second display device. This would
allow the device to not only display the front view of an
object, but the rear view could be seen if the viewer were to
walk to the back of the display, as well as increasing the
update speed, thereby making the image more flicker-free.
While the screen is rotating, a full-color projection display
projects 'slices' of an image sequentially onto the projection
2.2.1 Projection Surface
The projection surface should ideally be a non-
transparent material, similar to that found on many movie
screens. At the same time, it should also be relatively
light-weight, to minimize inertia, as well as possible
Display Surface 1
Stationary Mirror Projection Display ro PC)
Saonay M r RBfr PC)
I Ext Synch.
Figure 2.1: Overview of proposed flat inclined display
screen ADU system, enclosed by safety viewer.
Several different options have been investigated, and
although they all share similarities, they each have their own
advantages and disadvantages.
18.104.22.168 Flat Inclined Display Surface
The projection surface is centrally mounted and is
circular when viewed from the top (see Figure 2.2). The
projection surface should be inclined at a certain angle
(i.e., 30 degrees). During operation, the projection surface
sweeps out a volume of space as it spins around its central
axis. In the case at hand, the space swept out by the device
would be in the form of an elliptic cone (see Figure 2.3).
The cylinder with V-shaped openings at the top and bottom acts
as the projection screen upon
which the image may be
A slight adjustment must
be made to the rotating
screen because, although
rotation of the projection
surface is continuous with
time, the flow of images
Figure 2.2: Elliptic Cone
displayed by the projector is
non-continuous, in terms of being able to display
continuously changing image, according to the rotational
position of the display device. A rotating shutter will have
to be added to the system to correct for the non-continuous
projection of image slices, so that the appropriate image
would only be displayed when
the display is at precisely
the right location. The
shutter would need to be
placed between the projector
and the display surface, and
would keep the displayed
image from "washing out" or
"bleeding". Figure 2.3: Projection
bleeding surface: (a) top and (b) side
Figure 2.4: Corkscrew Display Surface
22.214.171.124 Corkscrew Display Surface
Once again, the projection surface is centrally mounted,
and circular when viewed from the top. In this case, though,
the display surface is similar to a corkscrew: as you move
around the central axis, a horizontal line extends radially
from the center (see Figure 2.4).
The main advantage over the previously discussed display
surface is that during the course of one complete revolution,
each point within a cylindrical work space will be reached
exactly once. This means that we now have a complete
cylindrical work space.
Two main questions need to be discussed: 1.) how do we
manufacture such a corkscrew display, and 2.) what happens to
the focus of the projector over the entire spectrum of the
126.96.36.199 Flat Vertical Display Screen
For this case, the display screen is mounted vertically
around a central axis. As the display screen is rotated,
slices of the image are displayed onto the display screen by
a projector mounted underneath the central axis, via a set of
mirrors. The mirrors are arranged in such a way, as to
minimize distortion of the image (see Figure 2.5).
Because various slices of the image are being displayed
constantly, and the rotation of the screen is continuous, this
might well lead to a blurring effect of the image. To
counteract this blurring effect, it would be useful to either
use a stroboscopic light source inside the display unit, or a
simple shutter that opens and closes for a certain amount of
time, as previously discussed in section 188.8.131.52.
2.2.2 Projection Display
The display needed for projection may be any display that
is capable of projecting multiple images per second. The
Figure 2.5: Flat Vertical Display Screen
image projector must also be able to display images that are
stored in electronic format.
For this demonstration, a color LCD desktop projection
display will be used. This display will be controlled through
a computer, and is capable of displaying VGA images at a rate
of 53 frames/sec (Hz) at a resolution of 640 x 480 pixels.
2.2.3 Motorized Base Unit
In order for the images to be fused in the observers eye,
the projection screen needs to be rotated at a speed greater
than 17 Hz. For this reason a speed of 20 revolutions per
second was selected, resulting in an overall rotational speed
of the projection display of 1200 revolutions per minute
(rpm). In order to control and maintain this speed, a direct-
drive electric motor, synchronized with the rest of the system
through a computer is used.
2.2.4 Computer Equipment
The ADU is computer controlled. As a test platform a PC
with an Intel P5 (Pentium) processor, operating at 66 MHZ and
running OS/2 version 2.11 was chosen. OS/2 is a multi-
tasking, multi-threaded, graphical operating system, allowing
multiple programs to be run on the computer simultaneously.
The images to be displayed are generated by or downloaded
to the PC. If necessary, they are then further processed, and
a set of consecutive frames of slices of the object in 10
degree increments are generated. These frames are stored and
are then displayed by the projection display in the
appropriate order, corresponding to the rotational angle of
the ADU base unit.
If the image changes (i.e., if the image is a live
picture, such as in the case of air traffic control), the
above steps (preprocessing, generation of slices in 10 degree
increments, storage, display) are simply repeated constantly,
and new frames are continuously generated and displayed.
2.2.5 Size of Projection Surface / Resolution
The size of the projection surface may be customized for
any use, and is dependant only on the desired resolution, the
type and quality of the projection display used, and the
computing power available. Another important factor to
consider is the weight and inertia of the equipment that is
being rotated. For this reason, a pixel size of approximately
1 mm2 was selected as offering sufficient resolution. Since
the projection display has a resolution of 640 x 480 pixels,
this resulted in a maximum display size of 640 mm x 480 mm
(25.2 in x 18.9 in).
The need to display three-dimensional objects occur in a
variety of applications such as in medical imaging, monitoring
of air-traffic over busy airports, the display of a new
prototype that has not been built yet, computer graphics
applications or controlling a robot remotely with accurate
visual feedback. Other uses could include such things as
battlefield simulation or overview, monitoring of satellites,
2.4 Safety Considerations
Due to the high rate of speed at which the projection
display is moving, and especially since it is extremely hard
to see such a fast moving object, injuries might occur if
safety precautions are not taken. The first and easiest
solution might be to simply place the ADU behind a safety-
glass. The more desirable solution would be to place the ADU
in the base-opening of two spherical mirrors of equal focal
length, that face each other (see Figure 2.6). If there is an
opening in the top mirror, the viewer will see the displayed
image suspended right above the opening. A key advantage
would be that all the equipment would be well concealed from
Figure 2.6: By using two spherical mirrors, an object in the
base will appear suspended over the top opening.
the viewer, thus not distracting him or her, while at the same
time offering safety to the viewer.
2.5 Scale Model of ADU
The first prototype of the ADU was built from commonly
used materials. The projection source was a standard slide
projector and the screen was a semi-transparent piece of
plexiglass. The test image was projected from the projection
source, up through an opening in the base of the ADU, where it
was reflected by two small mirrors (approximately 10 x 10 cm
and 16 x 12 cm). The structure that held the stationary
projection screen was made of metal sheeting, as was the arm
that held the larger of the two mirrors. The stationary arm
extended approximately 50 cm away from center of the opening
in the base of the ADU (see Figures 2.8 2.11).
The imaging on the semi-transparent screen appeared to be
out of focus, but after numerous attempts to re-focus the
image, it was determined that the problem lay in the choice of
the screen material itself (see Figures 2.9 and 2.10). The
fact that the screen was semi-transparent made the image
appear "washed out" and "fuzzy", but when a piece of white
paper was held directly in front of the screen, the image was
in fact clear and focused (see Figure 2.11). As a direct
result of this observation, the conclusion was formed that the
Figure 2.7: Top and side views of proposed ADU.
Figure 2.8: Top view of scale model, showing display screen
on the left, and the projection mirror on the arm at right.
Figure 2.9: View from the side, showing the fuzzy quality of
Figure 2.10: Image as seen from behind, through the
Figure 2.11: Similar to Figure 2.7 but with a piece of paper
acting as the screen.
screen material must be constructed of a non-transparent
material so that the image quality would not be lost.
This of course has the disadvantage that we no longer can
display the image on both sides of the screen, as was
demonstrated in Figure 2.10. One possible solution to this
problem may be the use of a beam-splitting prism between the
light source and the screen. This would then allow two copies
of the same image to be displayed simultaneously on the front
and back of the display
screen. The drawback to
this method may be the
loss of light due to
diffraction of the light,
to areas other than the
screen, or a blurry image,
if the two images are not
Another issue that
Figure 2.12: Rotation of
became apparent after the displayed screen image.
construction of this prototype was the fact that the arm of
the ADU needs to be approximately 50 cm away from the light
source in order to achieve an image of the desired size
(approx. 25 x 20 cm). Once the arm of the ADU is brought into
a state of motion, it may present a danger to viewers, due to
its high rotational speeds.
As anticipated, the displayed image rotated around a
central point on the screen when the ADU was manually rotated.
The angle of the image rotation was directly proportional to
the movement of the ADU.
This development, although anticipated, reinforced the
need for a computer-based solution to negate this effect. The
drawback of this solution would have the consequence of
further limiting the usable display area of the image (see
THE HUMAN EYE
A basic understanding of the human visual system is very
useful when dealing with the issue of displaying information
in three dimensions. A short overview of the human eye will be
given in the following section.
Binocular vision, using the information gathered by our
two eyes, is the most important source of our depth
perception. This will also be discussed in detail in the
following sections. In addition, psychological cues, as well
as physiological properties of the eye will be discussed.
It is interesting to note that light sensitive structures
have evolved independently in a vast number of plants and
animals. Though electromagnetic radiation takes many forms,
ranging from low energy radio waves to high energy gamma rays,
only the middle wavelengths have enough energy for vision, but
not so much that they can damage tissue. It is this relatively
narrow band of wavelength that we use to gather visual
information about our environment.
The following discussion is intended to give a quick and
practical overview of the subject matter.
3.2 The human eye
The adult human eye is a globe shaped organ with a
diameter of about 2.5 cm (see Figure 3.1). It is encased in a
tough but elastic coat of connective tissue, the sclera. The
forward portion of the sclera, the cornea, is transparent and
more strongly curved; it functions as the first element in the
light focusing system of the eye. Just inside the sclera is a
layer of darkly pigmented tissue, the choroid, through which
many blood vessels run. The choroid not only provides the
blood supply to the eye, it also acts as a light absorbing
layer. This layer, like the black inner surface of a camera,
helps prevent internally reflected light (and light from
outside the eye that has not entered through the lens) from
blurring the image. In nocturnal animals, by contrast, the
choroid layer is usually highly reflective. Although the
reflectivity reduces resolution, it increases light
sensitivity by sending unabsorbed light back through the
receptor layer for another opportunity to be processed. This
mirror-like layer accounts for the way a cat's eyes seem to
glow in the dark.
Figure 3.1: Lens eye.
sclera vitreous humor
h aqueous humor
chorou -- Hr -
Figure 3.2: Diagram of the human eye.
Just behind the junction of the main part of the sclera
and the cornea, the choroid becomes thicker and has smooth
muscles embedded in it; this portion of the choroid is called
the ciliary body. Forward of the ciliary body, the choroid
leaves the surface of the eyeball and extends into the cavity
of the eye as a ring of pigmented tissue, the iris. The iris
contains smooth muscle fibers arranged both circularly and
radially. When the circular muscle fibers contract, the
opening in the center of the iris, the pupil, is reduced; when
radial muscles contract, the pupil is dilated. The iris
regulates the amount of light admitted to the eye in much the
same way that the diaphragm of a camera controls the
The lens, which functions as the second element in the
light focussing system, is suspended behind the pupil by a
suspensory ligament attached to the ciliary body. The exact
shape of the lens is controlled by an array of tiny muscles
mounted here. The lens and its suspensory ligament divide the
cavity of the eyeball into two chambers. The chamber between
the cornea and the lens is filled with a watery fluid, the
aqueous humor. The chamber behind the lens is filled with a
gelatinous material, the vitreous humor.
The retina, which contains the receptor cells, is a thin
tissue covering the inner surface of the choroid. It is
Rod synaptic body
Figure 3.3: Rods and Cones
composed of several layers of cells: the receptors, sensory
neurons, and interneurons. The receptors are of two types,
rods and cones (see Figure 3.3). The rod cells are more
abundant toward the periphery of the retina, and are extremely
sensitive to light; they allow us to see in dim light, but
produce colorless, poorly defined images. The cone cells,
which are specialized for color vision in bright light, are
especially abundant in the central portion of the retina, an
area also known as the fovea. Because of the high density of
receptors in the fovea, we are able to see the small area in
the center of the visual field in fine detail.
The rods and cones synapse in the retina with short
sensory neurons (bipolar cells), which themselves synapse with
the retinal ganglion cells, whose axons', bundled together as
the optic nerve, run to the visual centers of the brain (see
Figure 3.3). The interconnection of neurons in the retina
enables the eye to extensively modify the information
transmitted from the hundred million or so receptor cells
through the few million axons of the optic nerve to the
brain.[Keeton et al., 19861 The amount of data transferred to
the brain is thus reduced by a factor of several 1000, when
compared to the information that was taken in by the eyes.
1 Axons are that part of a nerve cell through which impulses
travel away from the cell body.
3.3 Binocular Vision
The eyes of all creatures can be classified into several
classes according to their stage in the evolutionary process.
Some eyes detect only the intensity of light, and would better
be called detectors. There are two functions characteristic of
highly advanced eyes such as those of humans: the imaging
property and movement of the eyeball.
It is accepted that binocular vision, vision in which the
fields of view of the two eyes overlap, is the most important
source of depth perception. The retina of an eye can collect
only two-dimensional image information because it is of
spherical shape. Therefore, cues of the third dimension
(depth) can never be collected by the retina of a single eye.
Instead, the visual information gathered by both eyes has to
somehow be combined in the brain, so that we may perceive
3.4 Flow of visual information
The brain has two entrances where the optic nerves from
the retinas enter the cerebrum. Axons from the ganglion cells
in the retina run in the optic nerve to the optic chiasm, a
crossing or intersection of the optic nerves on the ventral
(front) surface of the brain. There the fibers from receptors
looking out on the left half of the visual field in the left
eye join those representing the left half in the right eye,
and travel to the right lateral geniculate nucleus (LGN) of
the thalamus (a part of the
rear portion of the
rear portion of the left right left right
visual visual visual visual
forebrain, center for the field field field field
integration of sensory
impulses). Similarly, eve
information from the right 1 256 347 8
visual field of each eye optic nerve
projects to the left LGN. optic chiasm
From there each nucleus sends
axons to the primary visual halamus
cortex, where the two images
of its half of the world, one right left
from each eye, are fe fe
integrated. Though the inputs 3 8 6
4 2 7 5
from the left and right primary visual primary visual
visual fields are not Figure 3.4: Flow of
Figure 3.4: Flow of
initially integrated Information to the brain
anatomically in the brain, we see no division between them in
our conscious experience.
It is interesting to note in Figure 3.4 that the LGN
sorts the visual information; image parts depicting the same
part of the image, but observed by the two eyes separately,
are moved into adjoining locations in the brain; i.e. 3 and 1
denote an object to the right of the viewer viewed by the
right and left eye, but they are mapped right next to each
other in the left half of the LGN.
3.5 Physiological Properties of the Human Eye
The following parameters and properties of the human eye
are mentioned for reference purposes:
Average separation of the two eyes (pupil
distance): 6.5 cm
Diameter of the pupil (depending on brightness) :
Maximum angular resolution: approx 0.5 (1/120)
Maximum transmission rate of information: 4.3
Mbits/sec for both eyes, and 5 bits/s for a single
nerve. NB: The maximum transmission speed for sound
information from both ears is approx. 8 kbits/sec.
3.6 Physiological and Psychological Cues for Depth
According to current psychology, there are ten cues
available for depth perception. These may be further
subdivided into two subgroups: physiological cues and
psychological cues. It is believed that the four physiological
cues are more important than the six psychological ones.
3.6.1 Physiological Cues
Accommodation is the muscular tension of the ciliary body
needed in order to adjust the focal length of the crystalline
lens. This cue is available even when we see an object with a
single eye; therefore it is said to be a monocular depth cue.
However, this cue is only effective when combined with other
binocular cues, and for short viewing distances (less than 2
When we look at a certain point on an object with both
eyes, the angle between the two viewing axes is called the
convergence angle. The muscular tension needed to rotate both
eyes to the appropriate positions can thus be used as a
binocular cue: convergence.
Experiments have shown an interaction between
accommodation and convergence: the information of convergence
corresponding to a certain distance automatically brings about
a certain degree of accommodation. At the same time,
information about accommodation influences convergence,
although this effect is weaker.
184.108.40.206 Binocular Disparity
When an observer looks at a point on an object, the rays
of light originating at that point focus upon the center of
the retinas in both eyes. The rays originating from points
other than the one watched, however, do not focus on
corresponding points on both retinas. This effect is called
binocular disparity or binocular parallax.
220.127.116.11 Monocular Movement Parallax
If only one eye is used, but the object (or the observer)
moves rapidly, one can make use of an effect similar to that
of binocular disparity. This effect is called monocular
3.6.2 Psychological Cues
Cues obtained from the image itself, rather than from the
positions of muscles, are called psychological cues. Here the
sense of depth is often assisted by our own experience, as
well as our imagination. In all, these cues may be sorted into
18.104.22.168 Retinal Image Size
To a certain degree, we know the actual size of many
objects. We can use this information, along with the image on
our retina, to tell us the distance to the object.
22.214.171.124 Linear Perspective
When viewing an image we sometimes
note that all lines seem to converge to -
one point in the distance: the -
vanishing point. When viewing a scene, Figure 3.5: Linear
such as buildings on a street, they Perspective
seem to get smaller the further away
they are. This effect is called linear perspective (see Figure
126.96.36.199 Aerial Perspective
While looking into the distance, we often notice that
distant landscapes often look hazy, due to the scattering
effect of small particles in the air (dust, fog, smog, etc.).
Subconsciously we take this fact into account; this effect is
called areal perspective.
Two objects that overlap each 1 H
other often offer a cue for depth i
perception. In general, an object whose Figure3.6: Overlapping
outline pattern is continuous is
perceived to be in front of the one whose pattern is non-
continuous (see Figure 3.6).
188.8.131.52 Shades and Shadows
Shades and shadows are
also important psychological
cues for depth perception. / ;
Figures 3.7 a and 3.7 b both
show pictures of a square Figure 3.7: Shades and Shadows
protrusion on a wall. It is interesting to note that Figure
3.7 a really looks like a convexity (a square coming out of
the wall), while Figure 3.7 b looks like a concavity on the
wall (i.e. a window in a wall). The origin of this illusion is
that most illumination comes from above.
184.108.40.206 Texture Gradient
Texture gradient is very
similar to the linear
perspective described above.
Figure 3.8: Texture Gradient
When looking at a uniform texture, such as a brick pavement or
a gravel road, the gradient in its roughness offers a cue for
depth perception. [Okoshi 1976]
MATERIALS AND METHODS
The first step in the development of the ADU system was
the definition of hardware and software needs. There are many
different computer systems available on the market today, so
that specifications for the ADU systems needed to be carefully
defined so as to optimize the compatibility between the ADU
hardware, and the computer hardware and software.
The hardware and software needs were determined through
the testing of a computer program, written by the author,
which slices computer generated images into segments, stores
theses sliced images into a data file for later use, and
displays them rapidly onto a computer monitor. The process of
slicing the images, and subsequently redisplaying these image
files through the system in rapid succession requires an
extremely coordinated effort between the computer, the video
card, and the software. Many trial runs were performed before
an optimal combination of software and hardware products was
found. The details concerning the computer trials and the
individual components of the system that were finally chosen
are discussed later in this chapter in the materials section.
The next step in the development of the ADU system was
the building of prototype systems using easily obtainable
components to build the ADU. The light source used for the
prototype unit was a common slide projector and the unit was
stationary. The prototype was tested for displayability of
the image onto the screen and to determine the logistics of
actually building the unit to scale. The materials needed to
build the actual full-size screen were modified through trials
of projecting the images onto different metal- and polymer-
based screens. The shape of the screen needed for the ADU and
the focal length of the projection device were also
investigated at this stage (see figures 2.8 and 2.9).
Research as to which multi-media projection device would
enable the system to display many images in a very short
amount of time resulted in the conclusion that the Proxima
desktop projector was the unit best suited for the task. A
demonstration unit was used to experiment with the
capabilities of the projector until the final unit was
purchased. This allowed for preplanning as to how to best
utilize the unit before it was actually received.
The final version of the ADU system was built and tested
using all of the necessary components (e.g., aluminum screen,
Proxima desktop projector, Pentium computer system, motor with
belt drive, and computer imaging program). The final unit
was tested extensively so that the quality of the image would
have the optimal three-dimensional effect and resolution. The
details of these trials are described in the results section
of this dissertation.
4.2 Computer Hardware
One of the most important components of this project is
the computer hardware. The computer is not only used to
display the images, but it is also used to generate these
images and to control other ADU components (speed of rotation,
when to display which image, etc.).
In order to optimally match utilization of the
capabilities of the hardware with what was needed to complete
the task at hand, two separate computer platforms were chosen.
For the initial part of modeling the item to be displayed, as
well as for the actual slicing process, a Silicon Graphics
Crimson R4100 was selected. This system has many of the
features necessary for ultra-fast graphics built directly into
the hardware, making it extremely fast for all graphics
operations, such as the previously mentioned simulations, or
For the remainder of the tasks, (e.g., displaying images,
controlling display components) a Pentium based PC system was
selected as the most versatile system for the task.
4.2.1 Silicon Graphics System
The Silicon Graphics Iris Crimson is a UNIX based
workstation. Silicon Graphics is widely accepted as the
industry leader in producing high-end graphical workstations.
Much of their great speed in graphical processing stems from
the fact, that their systems off-load many of the tasks to
specialized hardware. These tasks include such things as
simple matrix operations, as well as shading and z-buffering,
In computer graphics programming, data are constantly
being manipulated or transformed by mathematical operations.
The manipulation protocols are known as transformations and
the converted data are then referred to as transforms.
Literally, a transformation is a function (or an equation)
that defines how one set of data is to be changed or
transformed into another. There are three fundamental
operations that transform data in different ways and they are:
translation, rotation and scaling. Each of these mathematical
operations is considered a transformation. As an example, a
rotation transformation would describe how a wheel is supposed
to be affected as it is moved.
One of the simplest transformations produces a
translation of data. A translation defines how a point is
supposed to be moved from one location in space to another.
Mathematically this means taking every point in the object,
and adding an appropriate value to each of its x and y values:
x = x + x
Xnew X translate
Ynew + translate
The values of xtranslate
or y_translate can be
either positive or
negative and define how
much the point (x,y)
should be translated in
the x and y directions,
respectively. (see Figure
Figure 4.1: Translation of an
The next transformation is a rotation around a point.
The simplest point to choose is the origin. The equations for
rotations around the origin in the two-dimensional case are
very straight forward:
rotate = X COSa y sina
Yrotate = x sina + y costa .
For any given point (x,y),
as well as an angle a, the Obj trotated45 degrees
above equation allows the 'Pinal Object
user to compute the new, |
rotated values of x and y,
respectively. (see Figure Figure 4.2: Rotating an object.
The last of the basic transformations is scaling.
Scaling a two-dimensional polygon can be achieved by
multiplying each of the coordinates of the original polygon by
a scale factor. This can be done by applying the following
equations to each of the coordinates of the object:
scaled = x scalex
Yscaled = Y scaley
For any given point (x,y),
this equation allows the
user to compute the new Scaled Object
coordinates, given a
scaling factor in the x
and y-directions. Figure 4.3: Scaled Objects.
These three basic graphical operations are the heart of
computer graphics. In order to perform these operations in a
better, faster fashion, these operations have been rewritten
in terms of matrix operations. The key advantage here is that
it is then possible to perform a certain combination of these
transformations with only one operation for each point, by
simply multiplying all the transformation matrices together.
Once this master transformation matrix is determined, it may
be applied to all points in question by multiplying this
[Pnew] = [ [Po ] ,
where [T] is a 4x4 matrix in homogeneous coordinates, and Pold
and Pnew are the homogeneous coordinates of a point in the
One of the main reasons for choosing homogeneous
coordinates is that now translation, rotation and scaling can
all be treated the same, by using multiplication, rather than
having to use addition for the translation, and multiplication
for the rest of the operations.
In homogeneous coordinates, we add a third coordinate to
a point. Instead of being represented by a pair of numbers
(x,y), each point is represented by a triple (x,y,W). At the
same time, we say that two sets of homogeneous coordinates
(x,y,W) and (x',y',W') represent the same point if, and only
if one is a multiple of the other. Thus, (2,3,6) and (4,6,12)
are the same point represented by different coordinate
triples. In other words, each point has many different
homogeneous coordinate representations. Another important
rule of homogeneous coordinates is that at least one of them
must be non-zero. This means that (0,0,0) is not allowed. If
the W coordinate is non-zero, we may divide through by it:
(x,y,W) represents the same point as (x/W, y/W, 1). in
general, when W is non-zero, the latter representation is
preferred, and the numbers x/W and y/W are then called the
Cartesian coordinates of the homogeneous point. Points with
a value of W=0 are points at infinity, and seldom occur in
Because points are now three-element row vectors,
transformation matrices must now be 3 x 3. The 3 x 3 matrix
form for the translation matrix in homogeneous coordinates is
[i 1 0 tx
y' = 0 1 t .y
0 0 1
Similarly, the equations for rotation may be represented
in matrix form as:
[x cose -sine 0 x
y1 = sine cose 0 y ,
1 0 0 1 1
and the matrix form of the scaling transformations are:
x s 0 0
y[ = Sy 0 y .
Since the main part of this project will be dealing with
three-dimensional data points, rather that 2-D data, the above
methods should ideally be used for 3-D data. Just as 2-D
transformations can be represented by 3 x 3 matrices using
homogeneous coordinates, so can 3-D transformations be
represented by 4 x 4 matrices, as long as the homogeneous
representations of points in 3-space are used. Thus, a 3-D
data point (x,y,z) would now be represented as (x,y,z,W),
where two quadruples represent the same point if one is a non-
zero multiple of the other. Also, the quadruple (0,0,0,0) is
not allowed. As in the 2-D case, standard representation of
a point (x,y,z,W) with W 0 is given by (w/W, y/W, z/W, 1).
All of the other rules mentioned for the 2-D case also apply.
Translation in 3-D is a simple extension from the 2-D
1 0 0 tX
0 1 0 ty
0 0 1 tz
Rotation around the z-axis is thus extended to
cose -sine 0 0
sine cose 0 0
0 0 1 Otz
0 0 0 1
* z '
while rotation around the x-axis is given by
1 0 0 0
/ 0 cose -sine 0 0 y
z' 0 sine cos 0 z '
1 0 0 0 1 1
and rotation around the y-axis is
cose 0 -sine 0
0 1 0 0
-sine 0 cose 0
0 0 1 0
0 0 0 1
Similarly, scaling is given by
s 0 0 0
x/ x x
y/ 0 s 0 Ot y
/ 0 0 s 0t z
1 z z 1
0 0 0 1
As before, any number of transformations, scalings and
rotations may be applied at the same time, simply by
premultiplying all the appropriate matrices, and applying this
global transformation matrix to all points of the object.
Since these matrix operations are so important to
computer graphics, but are computationally very intensive,
Silicon Graphics has developed a specialized processor to
pipeline the computations. It is so pipelined, that the
matrix is broken up into its various elements, and each of the
multiplication and addition functions are done separately (in
a separate pipeline), but simultaneously, leading to an
overall improvement by a factor of about 25.
Similarly, many other functions are incorporated into the
hardware of the Silicon Graphics Reality Enginde. All of
these make the Silicon Graphics the clear choice for
performing graphical operations.
4.2.2 PC based Pentium System
Unfortunately, the Silicon Graphics system mentioned
above is a multi-user, multi-tasking system. While this is
clearly a significant advantage for many applications, it is
also a disadvantage when there is a need for a single task,
where timing is critical. Displaying the pregenerated
graphics is just such a task. As the ADU hardware is rotating
with a certain speed, it is important to be able to display
the correct image synchronized with the position of the ADU.
After careful consideration, it was determined that a
Pentium based PC system would meet all the requirements. The
system chosen was a Gateway 2000m system, with a Pentium
processor, operating at 66 MHz. The system was ordered with
a 256 kB cache, 16 Megabytes (Mb) of RAM, a 540 Mb harddrive,
and a Diamond Viper PCI video card.
The PCI bus plays an important part in speeding up the
display of graphics. It replaces the slower AT-style ISA
system bus, and is even faster than the VESA local bus, that
has become the de-facto standard for many 486 based systems.
The Peripheral Component Interchange (PCI) bus was developed
by Intel to make full use of the Pentium's computing power.
The old ISA bus limited communication between the
processor and the expansion cards (such as the video card) to
a slow 8 MHz on a 16 bit wide bus, leading to a theoretical
maximum throughput of only 16 Mb/sec. Especially for graphics
and hard drive access, this caused quite a bottleneck. With
the advent of the VESA local bus (VLB), the processor is now
able to communicate with the expansion cards at up to 33 MHz
(40 MHz with the new standard), over a bus that was a full 32
bits wide. This was a major improvement, especially since
most 486's only ran at 33 MHz (at least externally some run
as high as 99 MHz internally, such as the 486 DX4-100).
Since the Pentium is a 64-bit processor, using a VLB
would once again cause a bottleneck for data transfer to the
expansion cards. Tests have shown this to cause the Pentium's
performance to drop by 9 to 17 percent.
Another problem with the VL-Bus is that the bus operates
synchronously with the processor. Since some of the
peripherals run considerably slower than the processor, wait
states often have to be inserted by the CPU to allow the cards
in the expansion slots time to catch up, further deteriorating
the performance. Another disadvantage of this synchronous
operation is that as a result, the VL-Bus runs slower with a
25 MHz CPU than it does with a 33 MHz CPU.
The PCI Bus is entirely separate from the CPU's bus.
According to the PCI specifications, this separate 64 bit bus
is run at a speed of 33 MHz, and operates synchronously: The
CPU sends out instructions and accesses system memory without
waiting for peripherals to respond. This means that, even if
PCI add-in cards will not run any faster than their VL-Bus
counterparts, they at least will not tie up the CPU as long as
the CPU is not waiting for data, leaving the CPU free to
handle other processing tasks.
4.2.3 Diamond Viper PCI Graphics Card
The Diamond Viper PCI card is based on the Weitek P9000
fixed function accelerator chip. This chip is known as one of
the fastest Windows accelerators at the 8-bit color depth.
Since the P9000 chip does not include VGA circuitry, the card
includes a separate VGA chip: the Oak Technology frame buffer
is used to handle these tasks.
The board comes with drivers for Windows, OS/2, AutoCAD,
and a few other applications. It also supports some of the
VESA SVGA modes, which provides support for many other
applications, as well as power-saver modes. The card comes
equipped with 2 Mb of VRAM, as well as 256 kB of DRAM.
Vertical scan-rates lie between 56 to 80 Hz, and the maximum
resolution for this video card is 1280 x 1024 at 256 colors (8
The Power P9000 Interface Controller is an accelerated 2-
D graphics device used with Windows, AutoCAD, etc. It
supports draw, fill, and bit block transfer (BitBlt)
operations at the full speed of interleaved page-mode VRAMs
(132 million pixels per second) at screen sizes of up to 2
million pixels. It also performs full bit block-transfer
(BitBit) from screen to screen (up to 40 million pixels per
second), and from the PC to the screen at PCI bus bandwidth
(132 Mbit / sec).
Optional Ext Sync
*- VIdeo/Sync Sync
Host (Address Bus) Bus Parameter S B CRT
v d Inte rfce Engine e-. RAMDAC Green
." ,' rawing
0 pea to. Engine n '
Sf m (Frame
';; ^ VRAM Cnt,. Buaer)
.aet Aces Refresh
Figure 4.4: Viper WEITEK Power 9000 System Block Diagram.
This video card is extremely easy to use, since the Power
9000 appears to the PC as an array of memory. In combination
with the PCI bus, and a flat memory model operating system
such as OS/2, this feature makes it possible to transfer
graphics images directly from the system RAM to the video card
at extremely high speeds.
Once the hardware platforms were selected, it was
necessary to choose the software. For the Silicon Graphics
system, there is a limited choice of software. The operating
system is a version of UNIX, and the preferred compiler used
for programming is a C++ compiler. Other utilities used in
the creation of programs were the GLm routines, as well as
Inventor v. 2.0.
For the PC, though, the selection of software was more
complicated. After initially trying to use DOS 6.2 and
Windows 3.1, along with a Borland C++ compiler, it was soon
discovered that DOS imposed too many restrictions. The
biggest problem turned out to be DOS's 640 kB "barrier", and
the fact that DOS accesses memory in segments of only 64 kB at
a time. Since the graphics that need to be displayed are 640
x 480 pixels in size, there is a storage requirement of
roughly 300 kB.
After much research, the OS/2m 2.1 Operating System was
chosen instead of the DOS/Windows combination. OS/2 is a full
32 bit operating system, featuring preemptive multitasking1
1 Preemptive Multitasking: An operating system's ability to
interrupt, or preempt, a thread (a unit of execution, often times
a single program) when a higher priority thread is ready to
and multiple threads2. In addition to native applications,
OS/2 runs most DOS and Windows 3.1 programs. The OS/2 2.1
interface, known as the Workplace Shell, is markedly different
from Windows 3.1, and is considered a step toward a truly
Data files and applications are represented by icons that
reside in folders or on the desktop. One benefit to this
system is that separate tools to manage programs and files,
such as the Windows programs, are no longer necessary. Icons
can also represent services and devices, such as printers or
shredders. Printing or deleting a file is as simple as
dragging the appropriate icon and dropping it on the desired
The file system for OS/2 has also been improved: it
supports both an extended version of the old-fashioned file
allocation table (FAT), as well as the newer high performance
file system (HPFS). HPFS enhances the original FAT system in
several respects, including support for 255 character
filenames, and the ability to attach extended attributes (such
as the name of an application with which it is associated) to
any file. This allows for simplified launching of
2 A unit of execution. Under DOS and Windows 3.1, each
application is limited to one thread, and so can only do one
thing at a time; under OS/2, an application can create multiple
threads that appear to execute simultaneously.
applications by double-clicking on data files. This feature
eliminates the need for specific extensions for each type of
OS/2 also offers a flat-memory-model which allows the
user to allocate as much memory as is available on the system
at one time. The flexibility in memory allocation allows the
user to perform complex graphical tasks without being limited
by either a 64 kB page size or a 640 kB barrier.
CSET++ was chosen as the C++ compiler for the ADU system.
This compiler was developed by IBM, and it combines good
performance with full integration into OS/2's workplace shell.
It is capable of compiling for the Pentium processor, thereby
taking full advantage of the processing speed that the Pentium
system offers, since speed is so important to this application
(transferring the pregenerated images from the hard drive to
the video display unit).
4.4 Image Slicing Software Development
The computer program written for the ADU by the author
was designed to generate an image, break it into many thin
slices, and store these slices in a data file for later
retrieval. The slicing software was developed on, and was
designed to be used with the Silicon Graphics system. The
Silicon Graphics system is very efficient at processing three-
Figure 4.5: Flow Chart for Image Slicing Program
dimensional data. In order to fully utilize many of the
built-in functions that help to simplify the programming, the
ADU program was written using C++, and made extensive use of
the GL graphics library, developed by, and for Silicon
A flowchart, showing an overview of the main program
functions is shown below in Figure 4.4. A complete program
listing is given in Appendix I.
As can be seen below, the program initially reads the
data representing the three-dimensional object into memory.
Once this is done, transformations may be applied to it. By
carefully defining an appropriate orthographic "window" into
this virtual world, then following it up with a rotation
around the z-axis by an angle that is equivalent to the
current rotational value, and then translating it to the focal
point of our object, an image, as it would bee seen from the
desired angle, is generated. The image would be a complete
three-dimensional image, unless the image depth is changed to
a very shallow one. The necessary step entails sorting all
the data points, discarding any points that are outside the
predetermined range, and displaying only the ones within a
predefined range (i.e. data points between -1 mm to +1 mm,
when looking into the picture plane, or even better, data
Figure 4.6: Slice of an image depicting a Kawasaki Mule.
Figure 4.7: Snapshot of screen showing front and side view of
the Kawasaki Mule, and the slicing plane (top right).
points that took up only a certain percentage of the
displayable area). Fortunately, much of this can be
accomplished by using matrices as well as various GL function
calls, which results in a "cleaner," less complicated computer
program. Such an image slice is shown in detail in Figure 4.6
Figure 4.7 displays a snapshot taken from the computer
screen. The top left corner simply displays general
information, and is not important for this discussion. The
top right corner of the figure shows the entire image that is
to be rendered; in this case it is a vehicle that is currently
being automated for a different project. The gray plane that
can be seen slicing the object in half is directly related to
the angle of rotation for the ADU display, and shows exactly
which part of the object is currently being generated. The
image at the bottom right shows what the final image for that
rotational angle of the ADU will look like, taking into
account the desired thickness of the slice.
After generating the image in the manner described above,
the pixels are read back from the screen, and the image is
stored in a graphics file, after being rotated around the
center point to compensate for the rotational effect of the
ADU. The graphics file is initially stored as a ppm file,
encoded with the appropriate rotational angle of the ADU.
One sample slice was shown in Figure 4.6. It is
important to note, that the amount of graphical information is
dependant on the desired "thickness" of the slice. A sample
collection of these slices, shown in 30 degree increments, is
shown in Figure 4.11, at the end of this chapter.
4.5 Counteracting the Keystone Effect
Even though the projector being used has built into it a
100 keystone correction, this will not provide enough
correction to see a perfect rectangular image. For this
reason it is useful to introduce a keystone distortion in the
same magnitude, but in the opposite direction. Since the
keystoning effect is cumulative, this will effectively cancel
out the distortions caused by the inclination of the various
Figure 4.8 shows two images. On the left is an
undistorted image, the way it is typically seen on a CRT
computer display. On the right, an image is displayed that
has experienced a specific keystone distortion, with an angle
of a. The coordinate systems for both cases are located in
the center of the image, and the x and y axes are as indicated
above. The original image has a height of ho, and a width of
Figure 4.8: Normal, rectangular image, and an image with a
keystone distortion of angle a.
From the figure above, the change in width may be
Aw = h0 tan(a) .
It is also clear by looking at the above figures, that the
height does not change. This has the consequence that if we
are given a point (x,y), that after the transformation the new
point will be (Xne, y). In other words, we need to find the
transformation that will take us from x to Xnew.
This is best broken down into two separate steps. The
first step involves finding the value of a as a function of x
for values of y = 0 (this is not an important consideration in
this case, since we will have an undistorted image, and are
looking to distort it the width in this case is the same for
any value of y).
Assuming that the angle a increases linearly from the
center (x = 0) to the outside (x = i wo ) from a value of a =
0 to a value of a = afinal, we can readily determine an equation
for a as a function of x:
a(x) = x (a)
The second part involves determining another equation to
describe the new value of the x-coordinate, Xn, as a function
of the y-coordinate. For this reason, we again take two
At y= 0 : x = x0, and
at y= h : x= xo + Ax
2 0 *0 (b)
= 0 + ho tan () .
The equation for a straight line is
y = m x + b (c)
Using the first equation along with the equation above, yields
b = m x0 (d)
Now using the second equation from (b), and (c), we obtain
-h0 = m (xo + ho tan(a) ) + b
= mxo + h0 tan (a) m x0 .
Collecting terms, this simplifies to
m I ho tan(a) ho= ,
which further reduces to
Solving (c) for x, and then using the results from equations
(d) and (e), we can determine the new value of the x-
Xnew = y tan(a(x) ) + x0 ,
where a(x) is given by equation (a).
Given any coordinate (x,y) in a rectangular window, one
can now determine the new, keystoned image. One of the
problems in executing this algorithm is that at the top of the
image, data points will be so close together that some will
have to be ignored, while at the bottom there will be too many
Figure 4.9: Uncorrected and corrected images superimposed on
top of each other.
data points to fit onto the screen, so that some of the outer
points will be dropped off the side of the screen.
It should be noted that although overall the image will
now seem undistorted, the pixels are still skewed, resulting
in a higher resolution at the bottom of the screen when
compared to the top of the screen.
Figure 4.9 shows two images superimposed on top of each
other. A rectangle and a triangle are displayed in both their
original, and their keystoned form. A 150 keystone angle was
used for the calculation. It is interesting to note that the
-240 -160 -80 0 80 160 240
closer a point is to the y-axis, the less distortion will
4.6 Display Software
After having generated several images on the Silicon
Graphics corresponding to the various angles of the ADU, they
then have to be displayed on the projection screen. For this
reason a program was written that runs in a loop which
constantly reads data from the hard drive into the PC's
memory, and then transfers these data to the video card by
using BitBlt routines (BLT stands for Block transfer, and
denotes the task of moving a rectangular block of data from
one location to another). Since this involves transferring
great amounts of data (each of the stored video images is
approximately 300 kB in size), an optimum code needed to be
generated. For this reason, C++ was used, in conjunction with
several C++ callable assembler subroutines, whose job it was
to transfer large amounts of memory at very high rates of
speed. This code may be found in Appendix II.
A very important factor here is to make proper use of the
hardware. Since the author used a Pentium system with a PCI
bus, as well as an accelerated Video card on the PCI bus, data
transfer was significantly enhanced over PC's with just a
regular ISA bus.
Figure 4.10: Image Slices in increments of 30 degrees.
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Figure 4.10: (continued).
SYSTEM CONFIGURATION, RESULTS AND CONCLUSIONS
This chapter discusses the development of each of the
components of the ADU and explains how and why the various
components were selected. A description of trial runs, as
well as the conclusions drawn from these runs are also
discussed in this chapter.
As discussed in previous chapters, the goal of this
dissertation was to create a three-dimensional display device.
This was to be achieved by projecting images onto a rotating
screen, so that, due to the eye's relatively slow response
time, the images would be fused in the observers' mind, and
he/she would perceive a three-dimensional image in space.
A description of the process involved in the development
of the ADU is described on a component by component basis in
the following sections. These sections are then followed by
a summary of the overall results.
5.1 Projection Surface
The following is a list of the specifications for the
projection surface that were developed by the author when he
first started working on this aspect of the project. Ideally,
the projection surface should have the following properties:
be moderately reflective,
be relatively thin,
be light-weight to reduce inertia, and
still be rigid enough to withstand the torque due
to the high velocity of the projection surface.
Several materials were tested for this application.
Initially it was thought that a semi-transparent material
would be most suitable to this application, since the
displayed image could then be seen from both sides of the
display screen. Unfortunately, it was discovered that instead
of being able to observe the image from both sides, the image
became extremely blurry, making it a strain on the viewer's
Because of this, it was decided to use a one-sided
display screen. For weight reasons, an aluminum plate was
chosen. The plate has a thickness of 4 mm, and an overall
size of 400 x 400 mm. This gives each pixel a display area of
approximately 0.7 mm2. The reason that it does not give each
pixel an exact size of 0.7 mm2 is that the pixels are not
perfect squares: at the bottom they are somewhat compressed,
leading to a higher resolution, yet at the same time also
allowing less displayable width, while at the top they are
drawn apart. This phenomenon is called keystoning and is
discussed in detail later in this chapter.
Several different methods for mounting the screen were
available at the time of construction. After reviewing
available options, the author chose to use a rectangular
screen as the projection surface. The screen was mounted in
an upright position so that as it spins around its central
axis it sweeps out a volume in space. This volume of space
contains a certain amount of addressable picture elements,
also known as voxels. By being able to individually address
each one of these single voxels over a period of time, T, it
is possible to display a picture in three-dimensional space.
This three-dimensional effect is possible due to the human
eye's ability to fuse images.
Since the display screen was being rotated at a high rate
of speed (1200 rpm), it was important not to put too much load
on the motor driving it, since this would have led to a
degradation of the picture quality if the entire display
assembly were to begin to oscillate.
Displayscreen, mirrors and motor.
Figure 5.1: Overview of ADU Side view showing display
screen, mirrors and motor.
The main design question was how to find a way to display
onto this rotating screen. The most obvious solution would
have been to mount the display projector onto the rotating
base plate in such a way, that the display projector is always
in the same relative position with the display screen. This,
however, would have involved mounting the projector at least
80 cm from the center of rotation. At the high rate of speed
at which the ADU is operating (ca. 1200 rpm), the forces
acting on the system, as well as the possibilities of injury
due to a mechanical failure, would have been extremely high.
Another possible solution was to mount the display
projector under the display table in such a manner that it
projected in an upward direction. The picture was then
projected via two mirrors, angled in a certain way, onto the
display screen. The two mirrors were fixed with respect to
the display screen; to achieve this, both the mirrors, as well
as the display screen, had to be mounted to the rotating base
The latter of the two ideas described above was selected
as the most promising. A schematic overview of the display
apparatus is shown in Figure 5.1 above. It depicts a side
view of the display device, where the display screen is
rotated by 90 degrees, with the display screen protruding
into, and out of, the plane of the paper. The two mirrors can
clearly be seen, the first inclined at roughly 45 degrees, the
second almost vertical. The paths of the top and bottom-most
rays are also displayed as dashed lines, originating from the
projection display, mounted below the rotating display screen.
The entire display apparatus is rotated by means of an
electric motor, which is connected to the apparatus through a
sprocket drive belt. The speed of rotation may be
electrically controlled to stay at a constant speed of 1200
5.2 Projection Display
A projection display was needed that would be able to
display graphical information at a high rate of speed. If this
information was to be current, an electronic display needed to
be used rather than a film-based display, such as Super-8
based film projector.
For the initial demonstration of the non-moving scale
model, a slide projector was used to verify the feasibility of
the design, and to verify the quality of the display screen.
This of course only provided a stationary picture, so updates
were not possible.
Until recently, electronic displays lacked the resolution
and speed that is necessary for projecting images for the ADU
system. Over the last two years, though, high resolution
displays have become available. These displays typically have
VGA computer interfaces, and are capable of displaying color
graphics at a resolution of 640x480. They are usually based
on a small active matrix LCD display, that is then illuminated
from behind, and projected through a set of lenses onto a
projection screen, similar to a slide that is displayed in a
After a review of all available projection displays, the
Proxima Desktop Projector 2800 was chosen for this project.
It is an LCD projector that delivers bright, high quality
images, with a fast response time. The Proxima system offered
the most features of the various projectors that were
considered, as well as being the projector with the highest
update speed, and the shortest distance required from the lens
to the display. Another very useful feature is the fact that
the Proxima projector displays in an upward direction, rather
than a forward one. All these features combined made this
projector the best choice for the project.
5.2.1 Technical data
This particular desktop projector is typically used as a
multimedia projector for business and/or technical workgroup
presentations. It incorporates active matrix technology with
an integrated digital video processor, to produce bright,
brilliant color images with clean, true video images, as well
as razor sharp graphics and animation. The resolution of this
projector is 640 x 480, displaying in 2 million colors out of
a palette of 16 million. Up to 52 separate images may be
displayed per second, at an average refresh rate of 30-50 ms.
The image size of the projected image varies according to the
distance from the desktop projector to the projection screen.
At the minimum projection distance of 0.8 meters, the
displayed image has a size of 45 x 35 cm. Other sizes are
shown (measured diagonally) in Table 5.1 below.
Distance from Screen Diagonal Image Size
1.2 m 89 cm
1.8 m 136 cm
2.4 m 183 cm
3.0 m 330 cm
3.6 m 278 cm
4.3 m 325 cm
Table 5.1: Distance from Screen vs. Image Size
Video input may be supplied in either video, SVHS or
computer formats, such as VGA, SVGA, EGA, CGA formats. The
video formats can be in either PAL, NTSC or SECAM format.
5.2.2 Diagram / schematic
The following is a diagram of the Proxima Series 2800
Desktop projector. It is an
off-the-shelf projection display,
designed to be used as a
S multimedia presentation tool.
Several minor modifications
had to be made, such as
removing the top lid (used to
protect the lens during transport). This then made it
possible to project straight up, through the opening of the
rotating base unit.
5.2.3 Internal design
Internally, the Proxima desktop projector is designed
similarly to a slide projector. Instead of the slide,
however, three separate LCD panels are used to display the
red, green and blue sub-images. As the light is emitted by
the light bulb, it travels through a beam splitter, which
splits it into three separate beams. Each of these beams then
runs through either the red, green or blue LCD panel; after
this, these beams are then recombined into one complete beam,
Normal projected images have a rectangular shape. The
effect called "keystoning" occurs when the front of the
desktop projector is no longer perpendicular to the projection
screen (in the vertical
plane), or when the projector
is not placed parallel to the
floor (the horizontal plane).
It may also occur if the
Figure 5.3: Normal vs.
projector is somehow tilted Keystone Images
sideways. Keystoning typically manifests itself when the
projected image becomes trapezoidal. (see Figure 5.3)
This particular projector accounts for the fact that
oftentimes images need to be displayed higher than the actual
height of the projector, for better viewing by an audience.
Because of this, a 10.5 correction for keystoning has been
built into the projector. Since the upwards projection onto
the screen is approximately 30, some of the keystoning effect
may still be noticed in the displayed image, although it was
only a 150 angle, instead of the full 30 that it could have
5.2.5 Update rates/ resolution
The maximum update rate is determined by the active
matrix LCD screen of the projection display. The refresh rate
of this screen is approximately 30 gsec. This is the amount
of time it takes for an image to be completely drawn on the
screen. A maximum of 52 complete frames can be displayed in
one second, leading us to an actual display rate of 52 frames
per second (fps).
5.3 Motorized Base Unit
The display has to be rotated at a constant speed,
synchronized with the image that is being projected. In order
to achieve this goal, a stepper motor should ideally be
chosen. For test purposes, a generic 1 HP router was used.
This router was then connected to a variable voltage power
supply, so that the speed of rotation could be adjusted. The
router motor was then fitted with a pulley so that it could be
connected to the base of the display unit via a drive belt.
One of the major concerns in the construction of the ADU
became apparent after reevaluating the prototype that was
built earlier (see figures 2.8-2.11). The fact that the arm,
which held the outside mirror of the ADU, needed to be
approximately 50 cm away from the projection display in order
to display an image of the desired size, caused some safety
concerns1. The main concern was that injuries might occur
from such an appendage with any part of the observers' body,
especially since it would be traveling at such a high rate of
To reduce this risk of injury, the author decided to move
the projector further away from the rotating display unit.
This made it possible to reduce the diameter of the base unit
significantly. As a result of this decision, however, it was
necessary to increase the size of the mirrors needed in the
assembly, causing three new problems:
SA weight of 500 grams revolving at 20 rev/sec and a radius
of 0.5 m will exert a force of almost 4000 N, or 400 g's!
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