Aliasing & Antialiasing
David Luebke
1
7/27/2016
Admin
● Final project OPTIONAL
■ No project: assignments and tests count more
○ Exact weighting TBD
○ I will use the project for grade or not based on what grade you get
(i.e. doing a project can only help your grade).
● Ray tracing assignment same as last year:
http://www.cs.virginia.edu/~gfx/Courses/2004/Intro.Fall.04/assignments/raytracer.html
■ Now due Tue May 3, instead of Thu Apr 28
■ For your own sake start early and develop it incrementally
David Luebke
2
7/27/2016
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
David Luebke
3
7/27/2016
Signal Processing
● Raster display: regular sampling of a continuous
function (Really?)
● Think about sampling a 1-D function:
David Luebke
4
7/27/2016
Signal Processing
● Sampling a 1-D function:
David Luebke
5
7/27/2016
Signal Processing
● Sampling a 1-D function:
David Luebke
6
7/27/2016
Signal Processing
● Sampling a 1-D function:
■ What do you notice?
David Luebke
7
7/27/2016
Signal Processing
● Sampling a 1-D function: what do you notice?
■ Jagged, not smooth
David Luebke
8
7/27/2016
Signal Processing
● Sampling a 1-D function: what do you notice?
■ Jagged, not smooth
■ Loses information!
David Luebke
9
7/27/2016
Signal Processing
● Sampling a 1-D function: what do you notice?
■ Jagged, not smooth
■ Loses information!
● What can we do about these?
■ Use higher-order reconstruction
■ Use more samples
■ How many more samples?
David Luebke
10
7/27/2016
The Sampling Theorem
● Obviously, the more samples we take the better those
samples approximate the original function
● The sampling theorem:
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
David Luebke
11
7/27/2016
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.
David Luebke
12
7/27/2016
The Sampling Theorem
● An example: sinusoids
David Luebke
13
7/27/2016
The Sampling Theorem
● An example: sinusoids
David Luebke
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7/27/2016
The Sampling Theorem
● Show Figure 4.2 in Watt & Watt (p. 113)
David Luebke
15
7/27/2016
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
● Go to transparencies…
David Luebke
16
7/27/2016