Design of an autostereoscopic display unit

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Design of an autostereoscopic display unit
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xii, 138 leaves : ill., col. photos ; 29 cm.
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Jurczyk, Ralf, 1964-
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Mechanical Engineering thesis Ph. D
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Thesis:
Thesis (Ph. D.)--University of Florida, 1995.
Bibliography:
Includes bibliographical references (leaves 128-135)
Statement of Responsibility:
by Ralf Jurczyk.
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Typescript.
General Note:
Vita.

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University of Florida
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DESIGN OF AN AUTOSTEREOSCOPIC
DISPLAY UNIT



















By

RALF JURCZYK


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


1995
































Copyright 1995

by

Ralf Jurczyk































For my wife, Nicole, and my parents, Dieter and Ursula,

as well as my sisters and brothers, Birgit, Heidi, Peter and

Michael.














ACKNOWLEDGMENTS


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
considerable insight.

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

CHAPTERS

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
2.2.1.1 Flat Inclined Display Surface 21
2.2.1.2 Corkscrew Display Surface 23
2.2.1.3 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
3.6.1.1 Accommodation . 44
3.6.1.2 Convergence . 44
3.6.1.3 Binocular Disparity 45
3.6.1.4 Monocular Movement Parallax 45
3.6.2 Psychological Cues . 45
3.6.2.1 Retinal Image Size . 46
3.6.2.2 Linear Perspective . 46
3.6.2.3 Aerial Perspective . 46
3.6.2.4 Overlapping . 47
3.6.2.5 Shades and Shadows . 47
3.6.2.6 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

APPENDICES

I LISTING OF IMAGE PREPARATION PROGRAM 111

II LISTING OF IMAGE DISPLAY PROGRAM . 126

LIST OF REFERENCES . . 128


. 43









BIOGRAPHICAL SKETCH . . 136














LIST OF TABLES


TABLE

5.1: Distance from screen vs. Image size . 85


viii














LIST OF FIGURES


FIGURES


1.1:
1.2:
1.3:
1.4:
1.5:
1.6:
1.7:
2.1:
2.2:
2.3:


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


em .

pair .

e .

uno .
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. .


7
10
11
11
13
15
16
21
22
22
23
25
28
30
31
31
32
32
33
37
37
39
42
46
47
47
47
53
54
54
63
67
69
69
72
75
77









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
DISPLAY UNIT

By

Ralf Jurczyk

May 1995

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

axis.

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.


xii














CHAPTER 1
INTRODUCTION


1.1 Introduction


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

three dimensions.

Practitioners in the field of computer graphics (and,

more recently, volume visualization) have created illusory 3-D








3
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

shadows; etc.).

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 [1991], 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








5

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.


1.2.1 Anaglyphs


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








6

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

movies themselves.

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

film-reel.

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








8
a 3-D image. Since each eye sees the appropriate perspective

view in sequence, this system is known as the frame-sequential

stereoscopic system.


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
fast phosphors
to prevent ghosting.
m[


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

the viewer.




































Figure 1.3: Varifocal Mirror two stereoscopic pairs (left-
and right-eye images).


1.4: Varifocal Mirror.








12

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


















* *

Th~u~


Figure 1.5: Three dimensional Viewing Volume [Maguire]


13


IG




16








\"" > '"-"i "3 f








14

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.

Muirhead]



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





































1004A


1014A


1006A


Figure 1.6: Three Dimensional LED Display
























































Figure 1.7: Three dimensional viewer by G. Mizuno.








17

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

1.6).



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,








18

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

coming years.














CHAPTER 2
OVERVIEW OF AUTOSTEREOSCOPIC DISPLAY UNIT (ADU)


2.1 Introduction


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,








20

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

three-dimensional image.

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

display.


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












Viewing Volume


Display Surface 1
Stationary Mirror Projection Display ro PC)
Saonay M r RBfr PC)


I Ext Synch.



DCMotor
Power (DC>

Figure 2.1: Overview of proposed flat inclined display
screen ADU system, enclosed by safety viewer.

injuries.

Several different options have been investigated, and

although they all share similarities, they each have their own

advantages and disadvantages.


2.2.1.1 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

displayed.

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
(a) (b)
image from "washing out" or

"bleeding". Figure 2.3: Projection
bleeding surface: (a) top and (b) side
view.


































Figure 2.4: Corkscrew Display Surface


2.2.1.2 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.








24

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

corkscrew display?



2.2.1.3 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 2.2.1.1.




2.2.2 Projection Display


The display needed for projection may be any display that

is capable of projecting multiple images per second. The
















Display Screen


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.








27
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).


2.3 Applications


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








28
visual feedback. Other uses could include such things as

battlefield simulation or overview, monitoring of satellites,

etc.


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


I
Figure 2.6: By using two spherical mirrors, an object in the
base will appear suspended over the top opening.








29

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























































Outside Mirror




Motor


Diplay Smamc









Counterweight


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
the image.

































Figure 2.10: Image as seen from behind, through the
transparent screen.


Figure 2.11: Similar to Figure 2.7 but with a piece of paper
acting as the screen.








33

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

aligned properly.

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








34

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

Figure 2.12).














CHAPTER 3
THE HUMAN EYE


3.1 Introduction


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.








36

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 -
ina

pupil

lens)


i cornea


fovea


optic nerve
optic nerve


ciliary body
suspensory ligament


Figure 3.2: Diagram of the human eye.








38

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

apperature.

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








39

















Outer
segment



membranous
lamellae



stalk
Sbasal body

Inner mitochondrion
segment










nucleus


Rod synaptic body

Cone








Figure 3.3: Rods and Cones








40
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

depth.


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








42

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
visual visual
from each eye, are fe fe

integrated. Though the inputs 3 8 6
4 2 7 5
left right
from the left and right primary visual primary visual
cortex cortex
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,








43

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) :

2-8 mm

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

Perception


According to current psychology, there are ten cues

available for depth perception. These may be further

subdivided into two subgroups: physiological cues and








44

psychological cues. It is believed that the four physiological

cues are more important than the six psychological ones.



3.6.1 Physiological Cues



3.6.1.1 Accommodation

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

meters).



3.6.1.2 Convergence

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,








45

information about accommodation influences convergence,

although this effect is weaker.



3.6.1.3 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.



3.6.1.4 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

movement parallax.




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

six categories.










3.6.2.1 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.



3.6.2.2 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
and aerial
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

3.5).



3.6.2.3 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.










3.6.2.4 Overlappina

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).



3.6.2.5 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.


3.6.2.6 Texture Gradient

Texture gradient is very

similar to the linear

perspective described above.


Figure 3.8: Texture Gradient








48

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]














CHAPTER 4
MATERIALS AND METHODS


4.1 Introduction


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








50

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.








51

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








52

operations, such as the previously mentioned simulations, or

the image-slicing.

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,

among others.

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








53

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

4.1)


--




x traslate



Figure 4.1: Translation of an
object.
object.


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.

4.2)

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.








55

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

matrix:

[Pnew] = [ [Po ] ,


where [T] is a 4x4 matrix in homogeneous coordinates, and Pold

and Pnew are the homogeneous coordinates of a point in the

format [x,y,z,0].



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








56
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

these applications.

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

thus:


[i 1 0 tx
y' = 0 1 t .y
0 0 1








57
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

case:


L/
y' =
z
-1


1 0 0 tX

0 1 0 ty

0 0 1 tz

000 1


x
Y
* z
1


Rotation around the z-axis is thus extended to


1
=


cose -sine 0 0
sine cose 0 0
0 0 1 Otz

0 0 0 1


x

* z '
1_


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


x'
=' -
zI
1


cose 0 -sine 0
0 1 0 0
-sine 0 cose 0
0 0 1 0
0 0 0 1


x
y
zi
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








61
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








62

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

bitplanes).

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)








63

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
Commands .
Host (Address Bus) Bus Parameter S B CRT
v d Inte rfce Engine e-. RAMDAC Green


." ,' rawing
0 pea to. Engine n '
., VRAM
Sf m (Frame
';; ^ VRAM Cnt,. Buaer)
.aet Aces Refresh
Power 9000

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.










4.3 Software


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
execute.








65
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

graphic-oriented environment.

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

task graphic.

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.








66

applications by double-clicking on data files. This feature

eliminates the need for specific extensions for each type of

document.

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








68

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

Graphics systems.

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.


molm


Figure 4.7: Snapshot of screen showing front and side view of
the Kawasaki Mule, and the slicing plane (top right).








70

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

below.

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.








71

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

mirrors.

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

Wo.













wO+AW


wO i


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

computed as

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


WO-Av


I








73

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:


2 final
a(x) = x (a)
w
0



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

points:

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
1
= mxo + h0 tan (a) m x0 .
2 0



Collecting terms, this simplifies to


m I ho tan(a) ho= ,




which further reduces to

1
m (e)
tan(a) (e)



Solving (c) for x, and then using the results from equations

(d) and (e), we can determine the new value of the x-

coordinate:

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


320

240 ...-7

160




-80

-160

-240

-320
-240 -160 -80 0 80 160 240
Y-Axis








76
closer a point is to the y-axis, the less distortion will

occurr.


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.

I Ill." ...... u.


- I -
>f-"


^^^ ,,,...--- / -i^ -.~ ^
Maur ti.)




Figure 4.10: (continued).














CHAPTER 5
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

eye.

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








80

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.









81





/
/
/

















Displayscreen, mirrors and motor.
/
/
/'
/'
/ /
S /










I'








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








82

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

plate.

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








83

electrically controlled to stay at a constant speed of 1200

rpm.


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

slide projector.








84

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.








85

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








86

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,

for display.



5.2.4 Keystoning

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
Keystone Images








87

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

been.


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








88

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

speed.

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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