CS248 Midterm Review
Szymon Rusinkiewicz
CS248 Midterm
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Monday, November 1, 7-9 pm
Gates B01 and B03
Designed to be 1-hour exam
Mostly “short answer” questions
Covers through Thursday’s lecture
Raster Displays, Resolution,
Perception
• CRTs
– physical vs. addressable resolution
– 3 phosphors for “red”, “green”, and “blue”
– Traditional (triads, shadow mask) vs.
Trinitron (stripes, aperture grille)
• Human spatial frequency sensitivity
– General trend: lower sensitivity at higher
frequencies
– Sensitivity highest in fovea
– Phase sensitivity (Vernier acuity)
Raster Displays, Resolution,
Perception
• Human temporal frequency sensitivity
– Flicker sensitivity – how often must we
redraw a CRT to avoid flicker? (50-70 Hz,
depending on brightness and contrast)
– Perceived motion – update rate – how
often must we change the picture so it
looks like it is moving? (12 Hz = cartoons,
24 Hz = film, 60 Hz interlaced = video)
– Lag time – virtual reality and headmounted displays – how often must we
update to avoid motion sickness (up to 100
Hz)
Raster Displays, Resolution,
Perception
• Human intensity sensitivity
– How many bits per pixel do we need? (line
drawings = 3 bits, full-color pictures = 5-7 or
more)
– Response to intensity is nonlinear
– Power laws, gamma
– Gamma in cameras, CRTs; gamma
correction
• Dithering
– Trade off spatial resolution for intensity res.
– Moves low-frequency error to high freq.
Raster Displays, Resolution,
Perception
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Sample questions:
1. A scene is photographed with a TV
camera with gamma=0.5 and displayed
on a CRT with gamma=2.4. If we want
system gamma to be 1.0, we should do
gamma correction with what exponent?
2. You are doing clustered-dot dithering on
an image for output on a 300 dpi laser
printer. If you need at least 75 dpi
“effective” resolution, how many shades
of gray can you output?
Color
• Perception of color
– Three cones sensitive to “red”, “green”,
and “blue”
– Overlapping response curves
• Color spaces
– , ,  space vs. R, G, B space vs. X, Y, Z
space, 3x3 matrices to convert between
them
– Gamut, chromaticity diagrams
Color
• Combining colors
– Additive vs. subtractive mixing
– Primaries
• Intuitive colorspaces
– Single and double cones, hexcones
– HSL, HSV
– When are these useful? When is RGB
preferable?
Color
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Sample questions:
1. What are the ideal spectra for the
primaries used in additive mixing? Why?
2. The point (255, 127, 127) in RGB space
is nearest to what point in single-hexcone
HSV space?
3. You are scuba diving at the bottom of the
lake, and are looking at the sun through
water. Assuming the water scatters blue
light, does the sun appear more bluish?
Sampling and Antialiasing
• The sampling and reconstruction
pipeline:
– Prefiltering
– Sampling
– Resampling
– Reconstruction
• Fourier transform, aliasing in the
frequency domain
• Filtering and convolution
Sampling and Antialiasing
• Prefiltering vs. postfiltering
• Desirable filters for antialiasing
• Supersampling
– Regular vs. stochastic
• Unweighted/weighted area sampling
– Why is this an approximation?
Sampling and Antialiasing
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Sample questions:
1. Which of the following would affect your
choice of a reconstruction filter?
a. Pixel shape
b. Choice of prefilter
c. Actual size of the display
2. What is the result of convolving a 1-D box
filter with itself?
Digital Compositing
• The compositing approximation
– Conditions for validity (in theory and in
practice)
• Deriving alpha mattes
– Blue screen (or green screen)
– Chroma key
– Computing during rendering
• Compositing algebra
Digital Compositing
• Sample question:
You are doing the special effects for a movie,
and need to composite a computer
generated object over a live background.
Why should you use an 8-bit alpha matte
rather than a binary (1-bit) matte, even if
the computer-generated object is fully
opaque?
Rasterization
• Rasterization of lines
– Definition of “one-pixel-thick” line – which
points get rasterized?
– DDA algorithm – use coherency to reduce
work done at each pixel
• Rasterization of polygons
– General case – AET
– Also uses a DDA to maintain endpoints on
each scanline
– Meshing rules
Rasterization
• Sample question:
– If you rasterized this line, which pixels
would get turned on?
Transformations
• Homogeneous coordinates – let us
represent translation via a matrix
multiplication
• Matrices for rotation, translation, scale,
shear in 2D, 3D
• Composing (concatenating)
transformations – multiply matrices in
reverse order
• Classes of transformations
Transformations
• Sample question:
Which of the following are commutative?
a. Rotation and scale
b. Rotation and translation
c. Translation and scale