Advanced Computer Graphics
Last Ray Tracing; Antialiasing
David Luebke
cs551dl@cs.virginia.edu
http://www.cs.virginia.edu/~cs551dl
David Luebke 7/27/2016
Administrivia
Read Chapter 4
 Hand back Exercise 1
 Go over it (Dale)
 Hand out Assignment 1

David Luebke 7/27/2016
Recap

Speedup Techniques
– Intersect rays faster
Bounding volumes
 Spatial partitions
 Reordering ray intersection tests
 Optimizing intersection tests

– Shoot fewer rays
– Shoot “smarter” rays
David Luebke 7/27/2016
Optimizing Ray
Intersection Tests

Fine-tune the math!
– Share subexpressions
– Precompute everything possible

Code with care
– Even use assembly, if necessary
– Will get its own lecture
David Luebke 7/27/2016
Speedup Techniques

Speedup Techniques
– Intersect rays faster
– Shoot fewer rays
– Shoot “smarter” rays
David Luebke 7/27/2016
Shoot Fewer Rays

Adaptive depth control
– Naïve ray tracer: spawn 2 rays per
intersection until max recursion limit
– In practice, few surfaces are
transparent or reflective
Contribution of most rays to image: 0%
 Don’t shoot rays w/ contribution near 0%

David Luebke 7/27/2016
Shoot Fewer Rays

Adaptive sampling
– Shoot rays coarsely, interpolating their
values across pixels
– Where adjacent rays differ greatly in
value, sample more finely
– Stop when some maximum resolution
is reached

Show example
David Luebke 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 7/27/2016
Signal Processing
Raster display: regular sampling of a
continuous function (Really?)
 Think about sampling a 1-D function:

David Luebke 7/27/2016
Signal Processing

Sampling a 1-D function:
David Luebke 7/27/2016
Signal Processing

Sampling a 1-D function:
David Luebke 7/27/2016
Signal Processing

Sampling a 1-D function:
– What do you notice?
David Luebke 7/27/2016
Signal Processing

Sampling a 1-D function: what do
you notice?
– Jagged, not smooth
David Luebke 7/27/2016
Signal Processing

Sampling a 1-D function: what do
you notice?
– Jagged, not smooth
– Loses information!
David Luebke 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 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 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 7/27/2016
The Sampling Theorem

An example: sinusoids
David Luebke 7/27/2016
The Sampling Theorem

An example: sinusoids
David Luebke 7/27/2016
The Sampling Theorem

Show Figure 4.2 in the book (p. 113)
David Luebke 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

David Luebke 7/27/2016
Fourier Theory:
The Ugly Stuff
Next comes the math…
 Read Chapter 4

David Luebke 7/27/2016