1. Sang Il Park Sejong University
Scan Conversion
Sang Il Park
Sejong University

2. Line Attributes Butt cap Round cap Projecting square cap Miter join
Round Join
Bevel join

3. Area Filling
How can we generate a solid color/patterned polygon area?

4. How to decide interior -Parity Fill Approach
For each pixel determine if it is inside or outside of a given polygon.
Approach
from the point being tested cast a ray in an arbitrary direction
if the number of crossings is odd then the point is inside
if the number of crossings is even then the point is outside

5. How to decide interior -Parity Fill Approach
Very fragile algorithm
Ray crosses a vertex
Ray is coincident with an edge
Commonly used in CAD
Suitable for H/W

6. How to decide interior -Winding Number
A winding number is an attribute of a point with respect to a polygon that tells us how many times the polygon encloses (or wraps around) the point. It is an integer, greater than or equal to 0. Regions of winding number 0 (unenclosed) are obviously outside the polygon, and regions of winding number 1 (simply enclosed) are obviously inside the polygon.
Initially 0
+1: edge crossing the line from
right to left
-1: left to right
use cross product of line and
edge vectors
No cross vertices

7. Area Filling (Scan line Approach)
Take advantage of
Span coherence: all pixels on a span are set to the same value
Scan-line coherence: consecutive scan lines are identical
Edge coherence: edges intersected by scan line i are also intersected by scan line i+1

8. Area Filling (Scan line Approach)
For each scan line
(1) Find intersections (the extrema of spans)
Use Bresenham's line-scan algorithm
(2) Sort intersections (increasing x order)
(3) Fill in between pair of intersections

9. Area Filling (Scan line method)

10. Area Filling (Seed Fill Algorithm)
basic idea
Start at a pixel interior to a polygon
Fill the others using connectivity
seed

11. Seed Fill Algorithm (Cont’)
4-connected
8-connected
Need a stack.
Why?

12. Seed Fill Algorithm (Cont’)
start position

13. Seed Fill Algorithm (Cont’)8 6 4 2 8 6 4 2
interior-defined
boundary-defined
flood fill algorithm
boundary fill algorithm

14. Seed Fill Algorithm (Cont’) 1 2 3 4 5 6 7 1 2 3 4 5 6 7
hole
boundary pixel
interior pixel
seed pixel
The stack may contain duplicated or unnecessary information !!!

15. Boundary Filling

16. Scan Line Seed Fill scan line conversion seed filling +
Shani, U., “Filling Regions in Binary Raster Images:
A Graph-Theoretic Approach”, Computer Graphics,
14, (1981),

17. Boundary Filling Efficiency in space!
finish the scan line containing the starting position
process all lines below the start line
process all lines above the start line

18. Flood Filling
: Start a point inside the figure, replace a specified interior color only.

19. Problems of Filling Algorithm
What happens if a vertex is shared by more than one polygon, e.g. three triangles?
What happens if the polygon intersects itself?
What happens for a “sliver”?
Solutions?
Redefine what it means to be inside of a triangle
Different routines for nasty little triangles

20. Aliasing in CG
Which is the better?

21. Aliasing in CG
Digital technology can only approximate analog signals through a process known as sampling
The distortion of information due to low-frequency sampling (undersampling)
Choosing an appropriate sampling rate depends on data size restraints, need for accuracy, the cost per sample…
Errors caused by aliasing are called artefacts. Common aliasing artefacts in computer graphics include jagged profiles, disappearing or improperly rendered fine detail, and disintegrating textures.

22. The Nyquist Theorem
the sampling rate must be at least twice the frequency of the signal or aliasing occurs

23. Aliasing Effects

24. Artifacts - Jagged profiles
Jagged silhouettes are probably the most familiar effect caused by aliasing.
Jaggies are especially noticeable where there is a high contrast between the interior and the exterior of the silhouette

25. Artefacts - Improperly rendered detail

26. Artefacts - Disintegrating textures
The checkers should become smaller as the distance from the viewer increases.

27. Antialiasing
Antialiasing methods were developed to combat the effects of aliasing. The two major categories of antialiasing techniques are prefiltering and postfiltering.

28. Prefiltering
Eliminate high frequencies before sampling (Foley & van Dam p. 630)
Convert I(x) to F(u)
Apply a low-pass filter
A low-pass filter allows low frequencies through, but attenuates (or reduces) high frequencies
Then sample. Result: no aliasing!

29. High Frequency

30. Prefiltering

31. Prefiltering

32. Basis for Prefiltering Algorithms

33. Catmull’s Algorithm A2 A1 AB A3 Find fragment areas
Multiply by fragment colors
Sum for final pixel color

34. Prefiltering Example

35. Prefiltering So what’s the problem?
Problem: most rendering algorithms generate sampled function directly
e.g., Z-buffer, ray tracing

36. Supersampling
The simplest way to reduce aliasing artifacts is supersampling
Increase the resolution of the samples
Average the results down
Or sometimes, it is called “Postfiltering”.

37. Supersampling The process:
Create virtual image at higher resolution than the final image
Apply a low-pass filter
Resample filtered image

38. Supersampling: Limitations
Q: What practical consideration hampers super-sampling?
A: Storage goes up quadratically
Q: What theoretical problem does supersampling suffer?
A: Doesn’t eliminate aliasing! Supersampling simply shifts the Nyquist limit higher

39. Supersampling: Worst Case
Q: Give a simple scene containing infinite frequencies
A: A checkered ground plane receding into infinity
See next slide…

41. Supersampling
Despite these limitations, people still use super-sampling (why?)
So how can we best perform it?

42. Sampling in the Postfiltering method
Supersampling from a 4*3 image.
Sampling can be done randomly or regularly. The method of perturbing the sample positions is known as "jittering."

43. Stochastic Sampling
Stochastic: involving or containing a random variable
Sampling theory tells us that with a regular sampling grid, frequencies higher than the Nyquist limit will alias
Q: What about irregular sampling?
A: High frequencies appear as noise, not aliases
This turns out to bother our visual system less!

44. Stochastic Sampling An intuitive argument:
In stochastic sampling, every region of the image has a finite probability of being sampled
Thus small features that fall between uniform sample points tend to be detected by non-uniform samples

45. Stochastic Sampling Integrating with different renderers: Ray tracing:
It is just as easy to fire a ray one direction as another
Z-buffer: hard, but possible
Notable example: REYES system (?)
Using image jittering is easier (more later)
A-buffer: nope
Totally built around square pixel filter and primitive-to-sample coherence

46. Stochastic Sampling
Idea: randomizing distribution of samples scatters aliases into noise
Problem: what type of random distribution to adopt?
Reason: type of randomness used affects spectral characteristics of noise into which high frequencies are converted

47. Stochastic Sampling
Problem: given a pixel, how to distribute points (samples) within it?
Grid Random Poisson Disc Jitter

48. Stochastic Sampling Poisson distribution: Completely random
Add points at random until area is full.
Uniform distribution: some neighboring samples close together, some distant

49. Stochastic Sampling Poisson disc distribution:
Poisson distribution, with minimum- distance constraint between samples
Add points at random, removing again if they are too close to any previous points
Very even-looking distribution

50. Stochastic Sampling Jittered distribution
Start with regular grid of samples
Perturb each sample slightly in a random direction
More “clumpy” or granular in appearance

51. Nonuniform Supersampling
Adaptive Sampling

52. Adaptive Sampling Problem: Final Samples
Many more blue samples than white samples
But final pixel actually more white than purple!
Simple filtering will not handle this correctly
Final Samples

53. Filters

54. Antialiasing