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CRTs – A Review
• CRT technology hasn’t changed much in 50 years
• Early television technology
– high resolution
– requires synchronization between video signal and
electron beam vertical sync pulse
• Early computer displays
– avoided synchronization using ‘vector’ algorithm
– flicker and refresh were problematic
CRTs – A Review
• Raster Displays (early 70s)
– like television, scan all pixels in regular pattern
– use frame buffer (video RAM) to eliminate sync problems
• RAM
– ¼ MB (256 KB) cost $2 million in 1971
– Do some math…
- 1280 x 1024 screen resolution = 1,310,720 pixels
- Monochrome color (binary) requires 160 KB
- High resolution color requires 5.2 MB
Display Technology: LCDs
Liquid Crystal Displays (LCDs)
• LCDs: organic molecules, naturally in crystalline
state, that liquefy when excited by heat or E field
• Crystalline state twists polarized light 90º.
Display Technology: LCDs
Liquid Crystal Displays (LCDs)
• LCDs: organic molecules, naturally in crystalline
state, that liquefy when excited by heat or E field
• Crystalline state twists polarized light 90º
Display Technology: LCDs
Transmissive & reflective LCDs:
• LCDs act as light valves, not light emitters, and thus rely on an
external light source.
• Laptop screen
– backlit
– transmissive display
• Palm Pilot/Game Boy
– reflective display
Display Technology: Plasma
Plasma display panels
• Similar in principle to
fluorescent light tubes
• Small gas-filled capsules
are excited by electric field,
emits UV light
• UV excites phosphor
• Phosphor relaxes, emits
some other color
Display Technology
Plasma Display Panel Pros
• Large viewing angle
• Good for large-format displays
• Fairly bright
Cons
• Expensive
• Large pixels (~1 mm versus ~0.2 mm)
• Phosphors gradually deplete
• Less bright than CRTs, using more power
Display Technology: DMD / DLP
Digital Micromirror Devices (projectors) or
Digital Light Processing
• Microelectromechanical (MEM) devices, fabricated
with VLSI techniques
Display Technology: DMD / DLP
• DMDs are truly digital pixels
• Vary grey levels by modulating pulse length
• Color: multiple chips, or color-wheel
• Great resolution
• Very bright
• Flicker problems
Display Technologies:
Organic LED Arrays
Organic Light-Emitting Diode (OLED) Arrays
• The display of the future? Many think so.
• OLEDs function like regular semiconductor LEDs
• But they emit light
– Thin-film deposition of organic, lightemitting molecules through vapor
sublimation in a vacuum.
– Dope emissive layers with fluorescent
molecules to create color.
http://www.kodak.com/global/en/professional/products/specialProducts/OEL/creating.jhtml
Display Technologies:
Organic LED Arrays
OLED pros:
• Transparent
• Flexible
• Light-emitting, and quite bright (daylight visible)
• Large viewing angle
• Fast (< 1 microsecond off-on-off)
• Can be made large or small
• Available for cell phones and car stereos
Display Technologies:
Organic LED Arrays
OLED cons:
• Not very robust, display lifetime a key issue
• Currently only passive matrix displays
– Passive matrix: Pixels are illuminated in scanline
order (like a raster display), but the lack of
phospherescence causes flicker
– Active matrix: A polysilicate layer provides thin
film transistors at each pixel, allowing direct pixel
access and constant illumination
See http://www.howstuffworks.com/lcd4.htm for more info
Movie Theaters
U.S. film projectors play film at 24 fps
• Projectors have a shutter to block light during frame advance
• To reduce flicker, shutter opens twice for each frame – resulting in 48
fps flashing
• 48 fps is perceptually acceptable
European film projectors play film at 25 fps
• American films are played ‘as is’ in Europe, resulting in everything
moving 4% faster
• Faster movements and increased audio pitch are considered
perceptually acceptable
Viewing Movies at Home
Film to DVD transfer
• Problem: 24 film fps must be converted to
– NTSC U.S. television interlaced 29.97 fps 768x494
– PAL Europe television 25 fps 752x582
Use 3:2 Pulldown
• First frame of movie is broken into first three fields (odd, even, odd)
• Next frame of movie is broken into next two fields (even, odd)
• Next frame of movie is broken into next three fields (even, odd, even)…
Additional Displays
Display Walls
•
Princeton
•
Stanford
•
UVa – Greg Humphreys
Display Wall Alignment
Additional Displays
Stereo
Visual System
We’ll discuss more fully later in semester but…
• Our eyes don’t mind smoothing across time
– Still pictures appear to animate
• Our eyes don’t mind smoothing across space
– Discrete pixels blend into continuous color sheets
Mathematical Foundations
Angel appendix B and C
I’ll give a brief, informal review of some of the
mathematical tools we’ll employ
• Geometry (2D, 3D)
• Trigonometry
• Vector spaces
– Points, vectors, and coordinates
• Dot and cross products
Scalar Spaces
• Scalars: a, b, …
• Addition and multiplication (+ and h) operations defined
• Scalar operations are
– Associative: a + (b + g) = (a + b) + g
– Commutative: a + b = b + a
ahb=bha
– Distributive: a h(b h g) = (a h b) h g
a h(b + g) = (a h b) + (a h g)
Scalar Spaces
• Additive Identity = 0
a+0=0+a=a
• Multiplicative Identity = 1
ah1=1ha=a
• Additive Inverse = -a
 a + (-a) = 0
• Multiplicative Inverse= a-1
 a h a-1 = 1
Vector Spaces
Two types of elements:
• Scalars (real numbers): a, b, g, d, …
• Vectors (n-tuples): u, v, w, …
Operations:
• Addition
• Subtraction
Vector Addition/Subtraction
• operation u + v, with:
– Identity 0 v + 0 = v
– Inverse - v + (-v) = 0
• Addition uses the “parallelogram rule”:
v
u+v
u
v
u
-v
u-v
-v
Affine Spaces
• Vector spaces lack position and distance
– They have magnitude and direction but no location
• Add a new primitive, the point
– Permits describing vectors relative to a common location
• Point-point subtraction yields a vector
• A point and three vectors define a 3-D coordinate system
Points
Points support these operations
• Point-point subtraction:
Q
Q-P=v
– Result is a vector pointing from P to Q
• Vector-point addition:
– Result is a new point
v
P+v=Q
P
• Note that the addition of two points is not defined
Coordinate Systems
Grasp
z-axis with hand
Thumb points in direction of z-axis
Roll fingers from positive x-axis towards positive y-axis
Y
Y
Right-handed
coordinate
system
Z
Left-handed
coordinate
system
X
X
Z
Euclidean Spaces
• Euclidean spaces permit the definition of distance
• Dot product - distance between two vectors
• Projection of one vector onto another
Euclidean Spaces
• We commonly use vectors to represent:
– Points in space (i.e., location)
– Displacements from point to point
– Direction (i.e., orientation)
• We frequently use these operations
– Dot Product
– Cross Product
– Norm
Scalar Multiplication
• Scalar multiplication:
– Distributive rule: a(u + v) = a(u) + a(v)
(a + b)u = au + bu
• Scalar multiplication “streches” a vector, changing its length
(magnitude) but not its direction
Dot Product
• The dot product or, more generally, inner product of two vectors
is a scalar:
v1 • v2 = x1x2 + y1y2 + z1z2
(in 3D)
• Useful for many purposes
• Computing the length (Euclidean Norm) of a vector: length(v) = ||v|| = sqrt(v •
v)
• Normalizing a vector, making it unit-length: v = v / ||v||
v
• Computing the angle between two vectors:
u • v = |u| |v| cos(θ)
• Checking two vectors for orthogonality
– u • v = 0.0
u
θ
Dot Product
Projecting one vector onto another
• If v is a unit vector and we have another vector, w
• We can project w perpendicularly onto v
w
v
u
• And the result, u, has length w • v
u = w cos( )
 vw
= w 
 v w
=v w




Dot Product
Is commutative
• u•v=v•u
Is distributive with respect to addition
• u • (v + w) = u • v + u • w
Cross Product
The cross product or vector product of two vectors is a
vector:
 y1 z 2 - y 2 z1 
v1  v 2 = - ( x1 z 2 - x 2 z1)
 x1 y 2 - x 2 y1 
The cross product of two vectors is orthogonal to both
Right-hand rule dictates direction of cross product
Cross Product Right Hand Rule
See: http://www.phy.syr.edu/courses/video/RightHandRule/index2.html
Orient your right hand such that your palm is at the
beginning of A and your fingers point in the direction of A
Twist your hand about the A-axis such that B extends
perpendicularly from your palm
As you curl your fingers to make a fist, your thumb will
point in the direction of the cross product
Cross Product Right Hand Rule
See: http://www.phy.syr.edu/courses/video/RightHandRule/index2.html
Orient your right hand such that your palm is at the
beginning of A and your fingers point in the direction of A
Twist your hand about the A-axis such that B extends
perpendicularly from your palm
As you curl your fingers to make a fist, your thumb will
point in the direction of the cross product
Cross Product Right Hand Rule




See: http://www.phy.syr.edu/courses/video/RightHandRule/index2.html
Orient your right hand such that your palm is at the
beginning of A and your fingers point in the
direction of A
Twist your hand about the A-axis such that B
extends perpendicularly from your palm
As you curl your fingers to make a fist, your thumb
will point in the direction of the cross product
Cross Product Right Hand Rule




See: http://www.phy.syr.edu/courses/video/RightHandRule/index2.html
Orient your right hand such that your palm is at the
beginning of A and your fingers point in the
direction of A
Twist your hand about the A-axis such that B
extends perpendicularly from your palm
As you curl your fingers to make a fist, your thumb
will point in the direction of the cross product
Cross Product Right Hand Rule




See: http://www.phy.syr.edu/courses/video/RightHandRule/index2.html
Orient your right hand such that your palm is at the
beginning of A and your fingers point in the
direction of A
Twist your hand about the A-axis such that B
extends perpendicularly from your palm
As you curl your fingers to make a fist, your thumb
will point in the direction of the cross product
2D Geometry
Know your high school geometry:
• Total angle around a circle is 360° or 2π radians
• When two lines cross:
– Opposite angles are equivalent
– Angles along line sum to 180°
• Similar triangles:
– All corresponding angles are equivalent
Trigonometry
Sine: “opposite over hypotenuse”
Cosine: “adjacent over hypotenuse”
Tangent: “opposite over adjacent”
Unit circle definitions:
• sin () = x
• cos () = y
• tan () = x/y
• etc…
(x, y)
Slope-intercept Line Equation
Slope
=m
= rise / run
Slope
P = (x, y)
y
= (y - y1) / (x - x1)
= (y2 - y1) / (x2 - x1)
P2 = (x2, y2)
P1 = (x1, y1)
Solve for y:
y = [(y2 - y1)/(x2 - x1)]x + [-(y2-y1)/(x2 - x1)]x1 + y1
or: y = mx + b
x
Parametric Line Equation
Given points P1 = (x1, y1) and P2 = (x2, y2)
x = x1 + t(x2 - x1)
y = y1 + t(y2 - y1)
When:
• t=0, we get (x1, y1)
• t=1, we get (x2, y2)
• (0<t<1), we get points
on the segment between
(x1, y1) and (x2, y2)
y
P2 = (x2, y2)
P1 = (x1, y1)
x
Other helpful formulas
Length = sqrt (x2 - x1)2 + (y2 - y1)2
Midpoint, p2, between p1 and p3
• p2 = ((x1 + x3) / 2, (y1 + y3) / 2))
Two lines are perpendicular if:
• M1 = -1/M2
• cosine of the angle between them is 0
Reading
Chapters 1 and Appendix B of Angel