Transcript lecture04.ppt

CS 551/651:
Advanced Computer Graphics
Accelerating Ray Tracing Continued
Antialiasing
David Luebke
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Recap: Accelerating Ray Tracing
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Problem:
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Lots of pixels = lots of rays
Computing shadows generates even more rays
Supersampling generates even more rays
Solutions:
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Trace rays more quickly
Shoot fewer rays
Reorder ray computation
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Antialiasing
Aliasing: signal processing term with very
specific meaning
 Aliasing: computer graphics term for any
unwanted visual artifact
 Antialiasing: computer graphics term for
avoiding unwanted artifacts
 We’ll tackle these in order
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Signal Processing
Raster display: regular sampling of a
continuous function (Really?)
 Think about sampling a 1-D function:
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Signal Processing
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Sampling a 1-D function:
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Signal Processing
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Sampling a 1-D function:
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Signal Processing
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Sampling a 1-D function:
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What do you notice?
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Signal Processing
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Sampling a 1-D function: what do you notice?
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Jagged, not smooth
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Signal Processing
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Sampling a 1-D function: what do you notice?
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Jagged, not smooth
Loses information!
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Signal Processing
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Sampling a 1-D function: what do you notice?
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Jagged, not smooth
Loses information!
What can we do about these?
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Use higher-order reconstruction
Use more samples
How many more samples?
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The Sampling Theorem
Obviously, the more samples we take the better
those samples approximate the original
function
 The sampling theorem:
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A continuous bandlimited function can be completely
represented by a set of equally spaced samples, if the
samples occur at more than twice the frequency of the
highest frequency component of the function
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The Sampling Theorem
In other words, to adequately capture a
function with maximum frequency F, we need
to sample it at frequency N = 2F.
 N is called the Nyquist limit.
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The Sampling Theorem
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An example: sinusoids
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The Sampling Theorem
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An example: sinusoids
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The Sampling Theorem
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Show Figure 4.2 in the book (p. 113)
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Fourier Theory
All our examples have been sinusoids
 Does this help with real world signals? Why?
 Fourier theory lets us decompose any signal
into the sum of (a possibly infinite number of)
sine waves
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Fourier Theory:
The Ugly Stuff
Next comes the math…
 If you are not comfortable with signal theory,
you might want to read Chapter 4 in W&W or
find a good tutorial on the web
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The End
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