Antialiasing & Sampling

Question 1

Rendering Equation

Answer 1

Radiance = Emitted + Reflected

Question 2

Stratified Sampling

Answer 2

Break up the domain into disjoint regions (strata) and place the sample into each region.
Uniform if Δxi = Δxj for all i ≠ j

Question 3

Importance Sampling

Answer 3

Take more samples where “signal” is more important.

Importance could be due to magnitude of values or variance.

Question 4

Regular Sampling

Answer 4

Regular error leads to aliasing. Fast to generate.

Question 5

Random Sampling

Answer 5

Less regular error, but can lead to clumping.

Question 6

Jittering

Answer 6

Error is irregular, and less clumping. More expensive selection.

Question 7

Distributed Ray Tracing

Answer 7

Take multiple samples for each pixel and average them. 16 strata for each pixel. Does not deal with diffuse interactions.

Paper: Cook et. al. 1984

Question 8

Signal Processing for Images

Answer 8

Raster image is just a sampling of a continuous function so if samples are too far apart they don’t give a true representation of the scene.

Question 9

Jaggies

Answer 9

Artifacts in renders due to sampling issues. Can cause a staircase effect on lines that are not perfectly vertical or horizontal.

Question 10

Moiré

Answer 10

A rendering artifact due to overlapping high frequency patterns that appear to show more movement than actually exists. Like a camera trying to record a brick wall.

Question 11

Temporal

Answer 11

Motion blur?

Question 12

Nyquist Limit

Answer 12

The sampling rate which is 2x the highest frequency in an image. By sampling at the nyquist limit we can void aliasing.

Problem: Man-made objects have distinct edges which have infinite frequency

Question 13

How to alleviate sampling issues due to infinite frequencies

Answer 13

After getting an image, run it through a low pass filter which passes on only lower frequencies.

Question 14

Area Sampling

Answer 14

Rather than sampling, integrate by treating lines as boxes and colouring pixels based on fraction of pixel covered.
Looks great at sufficient distance but not up close.

Question 15

Weighted sampling

Answer 15

Give different weights depending on position of sample inside the pixel.
Avoids certain temporal aliasing problems. But the correct filter is infinite.

Question 16

Anti-aliasing in ray tracing

Answer 16

1. Super Sampling: by taking more samples and weight with a filter
2. Stochastic sampling: jittered supersamples.
3. Adaptive antialiasing: Stochastic sampling but only in areas with high frequency patterns