The document discusses various aspects of computer graphics and color modeling. It begins by covering the basics of color, including the electromagnetic spectrum and human visual perception. It then describes different color models such as RGB, CMYK, HSV, and YIQ. The document also discusses topics like color spaces, halftoning, dithering, filling polygons using scanline algorithms, and rasterization techniques.

1. Computer Graphics
Filling & Color

2. Basics Of Color
• elements of color:

3. Basics of Color
• Physics:
– Illumination
• Electromagnetic spectra
– Reflection
• Material properties
• Surface geometry and microgeometry
• Perception
– Physiology and neurophysiology
– Perceptual psychology

4. Electromagnetic Spectrum

5. How well do we see color?
• What color do we see the best?
–Yellow-green at 550 nm
• What color do we see the worst?
–Blue at 440 nm
• Flashback: Color tables (color maps) for
color storage

6. Humans and Light
• when we view a source of light, our eyes
respond to
– hue: the color we see (red, green, purple)
• dominant frequency
– saturation: how far is color from grey
• how far is the color from gray (pink is less
saturated than red, sky blue is less saturated than
royal blue)
– brightness: how bright is the color
• how bright are the lights illuminating the object?

7. Hue
• hue (or simply, "color") is dominant wavelength
– integration of energy for all visible wavelengths is
proportional to intensity of color

8. Saturation or Purity of Light
• how washed out or how pure the color of
the light appears
– contribution of dominant light vs. other
frequencies producing white light

9. Intensity, Brightness
• intensity : radiant energy emitted per unit
of time, per unit solid angle, and per unit
projected area of the source (related to the
luminance of the source)
• brightness : perceived intensity of light

10. Combining Colors
Additive (RGB)
Shining colored lights
on a white ball
Subtractive (CMYK)
Mixing paint colors and
illuminating with white light

11. Colour Matching Experiment
Target colour
Mixing of 3 primaries
Adjust intensities to match the colour
overlap

12. RGB Color Space (Color Cube)
• Define colors with (r, g, b) amounts of red,
green, and blue

13. CMY Color Model
CMY (short for Cyan, Magenta, Yellow,
and key) is a subtractive color model.

14. The CMY Color Model
• Cyan, magenta, and yellow are the
complements of red, green, and blue
– We can use them as filters to subtract from white
– The space is the same as RGB except the origin
is white instead of black
• This is useful for hardcopy
devices like laser printers
– If you put cyan ink on the page, no red light is
reflected
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B
G
R
Y
M
C
1
1
1

15. YIQ Color Space
•YIQ is the color model used for color TV
in America. Y is brightness, I & Q are
color
– Note: Y is the same as Color space XYZ
– Result: Use the Y alone and backwards
compatibility with B/W TV!
– I and Q are hue and purity
– These days when you convert RGB image to
B/W image, the green and blue components are
thrown away and red is used to control shades
of grey (usually)

16. Converting Color Spaces
• Y = 0.299 R + 0.587 G + 0.114 B
• I = R – Y
• Q = B – Y
• Converting between color models can
also be expressed as such a matrix
transform:
• Note the relative unimportance of blue
in computing the Y
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B
G
R
Q
I
Y
31
.
0
52
.
0
21
.
0
32
.
0
28
.
0
60
.
0
11
.
0
59
.
0
30
.
0

17. Converting Color Spaces
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

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






Q
I
Y
B
G
R
1
0
1
194
.
0
509
.
0
1
0
1
1

18. HSV Color Space
• A more intuitive color space
– H = Hue
– S = Saturation
– V = Value (or brightness)
Value
Saturation
Hue

19. HSV Color Model
Figure 15.16&15.17 from H&B
H S V Color
0 1.0 1.0 Red
120 1.0 1.0 Green
240 1.0 1.0 Blue
* 0.0 1.0 White
* 0.0 0.5 Gray
* * 0.0 Black
60 1.0 1.0 ?
270 0.5 1.0 ?
270 0.0 0.7 ?

20. Intuitive Color Spaces

21. Halftoning
• A technique used in newspaper printing
• Only two intensities are possible, blob of ink and
no blob of ink
• But, the size of the blob can be varied
• Also, the dither patterns of small dots can be used

22. Halftoning

23. Halftoning – dot size

24. Spatial versus Intensity
Resolution
• Halftone Approximation: Dither
– n  n pixels encode n2 + 1 intensity levels
• The distribution of intensities is
randomized: dither noise, to avoid
repeating visual artifacts

25. Dithering
• Halftoning for color
images

26. Filling Polygons
• So we can figure out how to draw lines
and circles
• How do we go about drawing polygons?
• We use an incremental algorithm known
as the scan-line algorithm

27. 27
Polygon
• Ordered set of vertices (points)
– Usually counter-clockwise
• Two consecutive vertices define an edge
• Left side of edge is inside
• Right side is outside
• Last vertex implicitly connected to first
• In 3D vertices are co-planar

28. Filling Polygons
• Three types of polygons
1. Simple convex 2. simple concave 3. non-simple
(self-intersection)
Convex polygons have the property that intersecting lines
crossing it either one (crossing a corner), two (crossing an edge,
going through the polygon and going out the other edge), or an
infinite number of times (if the intersecting line lies on an edge).

29. Convex
Does a straight line connecting ANY two
points that are inside the polygon intersect
any edges of the polygon?

30. Concave
The polygon edges may also touch each
other, but they may not cross one another.

31. Complex
Complex polygons are basically concave
polygons that may have self-intersecting
edges. The complexity arises while
distinguishing which side is inside the
polygon when filling it.

32. Some Problems
1. Which pixels should be filled in? 2. Which happened to the top
pixels? To the rightmost pixels?

33. Flood Fill
• 4-fill
– Neighbor pixels are only up, down, left, or
right from the current pixel
• 8-fill
– Neighbor pixels are up, down, left, right,
or diagonal

34. 4 vs 8 connected
Define: 4-connected versus 8-connected,
its about the neighbors

35. 4 vs 8 connected
 Fill Result: 4-connected versus 8-connected
“seed pixel”

36. Flood Fill
• Algorithm:
1.Draw all edges into some buffer
2.Choose some “seed” position inside the area
to be filled
3.As long as you can
1.“Flood out” from seed or colored pixels
» 4-Fill, 8-Fill

37. Flood Fill Algorithm
void boundaryFill4(int x, int y, int fill, int boundary)
{
int curr;
curr = getPixel(x, y);
if ((current != boundary) && (current != fill))
{
setColor(fill);
setPixel(x, y);
boundaryFill4(x+1, y, fill, boundary);
boundaryFill4(x-1, y, fill, boundary);
boundaryFill4(x, y+1, fill, boundary);
boundaryFill4(x, y-1, fill, boundary);
}
}
Seed Position
Fill “Color”
Edge “Color”

38. Scan-Line Polygon Example
Polygon
Vertices
Maxima /
Minima
Edge
Pixels
Scan
Line Fill

39. Scan Line Algorithms
Create a list of vertex events (bucket sorted by y)

40. Initialize all of the edges

41. • For each edge, the following information needs to be
kept in a table:
1. The minimum y value of the two vertices
2. The maximum y value of the two vertices
3. The x value associated with the minimum y value
4. The slope of the edge

42. An Example
0 (10, 10)
1 (10, 16)
2 (16, 20)
3 (28, 10)
4 (28, 16)
5 (22, 10)

43. Scan-Line Polygon Fill
Algorithm
2
4
6
8
10 Scan Line
0
2 4 6 8 10 12 14 16

44. Scan-Line Polygon Fill
Algorithm
• The basic scan-line algorithm is as
follows:
– Find the intersections of the scan line with
all edges of the polygon
– Sort the intersections by increasing x
coordinate
– Fill in all pixels between pairs of
intersections that lie interior to the polygon

45. 45
Scanline Algorithms
• given vertices, fill in the pixels
arbitrary polygons
(non-simple, non-convex)
• build edge table
• for each scanline
• obtain list of intersections, i.e., AEL
• use parity test to determine in/out
and fill in the pixels
triangles
• split into two regions
• fill in between edges

46. Scan-Line Polygon Fill Algorithm
(cont…)

47. Examples:

48. Solutions:

49. Scan Line Algorithms
Create a list of the edges intersecting the first scanline
Sort this list by the edge’s x value on the first scanline
Call this the active edge list

50. 1. Horizontal Edges

51. Polygon Fill
B C
A
F
D
E
Parity
0 = even
1 = odd
Parity 0
1
0

52. Polygon Fill 2
B C
A
F
D
E
Parity
0 = even
1 = odd
Parity 0
1
0
1
0

53. 2. Bottom and Left Edges vs. Top
and Right Edges

54. Edge Tables
• edge table (ET)
– store edges sorted by y in linked list
• at ymin, store ymax, xmin, slope
• active edge table (AET)
– active: currently used for computation
– store active edges sorted by x
• update each scanline, store ET values + current_x
– for each scanline (from bottom to top)
• do EAT bookkeeping
• traverse EAT (from leftmost x to rightmost x)
– draw pixels if parity odd

55. Scanline Rasterization Special
Handling
• Intersection is an edge end point, say: (p0, p1, p2) ??
• (p0,p1,p1,p2), so we can still fill pairwise
• In fact, if we compute the intersection of the scanline with
edge e1 and e2 separately, we will get the intersection
point p1 twice. Keep both of the p1.

56. Scanline Rasterization Special
Handling
• But what about this case: still (p0,p1,p1,p2)

57. Edge Table

58. Active Edge Table (AET)
• A list of edges active for current scanline,
sorted in increasing x
y = 9
y = 8

59. Edge Table Bookkeeping
• setup: sorting in y
– bucket sort, one bucket per pixel
– add: simple check of ET[current_y]
– delete edges if edge.ymax > current_y
• main loop: sorting in x
– for polygons that do not self-intersect, order of
edges does not change between two scanlines
– so insertion sort while adding new edges suffices

60. Parity (Odd-Even) Rule
Begin from a point outside
the polygon, increasing the x
value, counting the number of
edges crossed so far, a pixel
is inside the polygon if the
number of edges crossed so
far (parity) is odd, and
outside if the number of
edges crossed so far (parity)
is even. This is known as the
parity, or the odd-even, rule.
It works for any kind of
polygons.
Parity starting from
even
odd
odd
odd
odd
even
even
even

61. Polygon Scan-conversion
Algorithm
Construct the Edge Table (ET);
Active Edge Table (AET) = null;
for y = Ymin to Ymax
Merge-sort ET[y] into AET by x value
Fill between pairs of x in AET
for each edge in AET
if edge.ymax = y
remove edge from AET
else
edge.x = edge.x + dx/dy
sort AET by x value
end scan_fill

62. Rasterization Special Cases
-Edge Shortening Trick:
-Recall Odd-Parity Rule Problem:
-Implement “Count Once” case with edge shortening:
Count once
Count twice
or
or
Count once
Count twice
or
or
A
B
C
A
B
C
A
B
C
B'
A
B
C
B'
C
B
A
B
C
B
A
B'
B
B'
xA,yB’,1/mAB xC,yB’,1/mCB

63. Polygon
Rasterization
• Ignore horizontal lines
0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9

64. Polygon
Rasterization
• Ignore horizontal
lines
• Sort edges by
smaller
y coordinate
0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6

65. Polygon
Rasterization
• For each
scanline…
• Add edges
where
y = ymin
• Sorted by x
• Then by dx/dy
0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax

66. Polygon
Rasterization
Plotting rules for
when segments
lie on pixels
1.Plot lefts
2.Don’t plot rights
3.Plot bottoms
4.Don’t plot tops
0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax

67. Polygon
Rasterization
• y = 1
• Delete y = ymax
edges
• Update x
• Add y = ymin
edges
• For each pair
x0,x1, plot from
ceil(x0)
to ceil(x1) – 1 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
G
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax
G 1 2/7 8
A 1 4/2 3

68. Polygon
Rasterization
• y = 2
• Delete y = ymax
edges
• Update x
• Add y = ymin
edges
• For each pair
x0,x1, plot from
ceil(x0)
to ceil(x1) – 1 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax
G 1 2/7 2/7 8
A 3 4/2 3
B 8 -3/1 3
C 8 0/3 5
G

69. Polygon
Rasterization
• y = 3
• Delete y = ymax
edges
• Update x
• Add y = ymin
edges
• For each pair
x0,x1, plot from
ceil(x0)
to ceil(x1) – 1 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax
G 1 4/7 2/7 8
C 8 0/3 5
G

70. Polygon
Rasterization
• y = 4
• Delete y = ymax
edges
• Update x
• Add y = ymin
edges
• For each pair
x0,x1, plot from
ceil(x0)
to ceil(x1) – 1 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax
G 1 6/7 2/7 8
C 8 0/3 5
G

71. Polygon
Rasterization
• y = 5
• Delete y = ymax
edges
• Update x
• Add y = ymin
edges
• For each pair
x0,x1, plot from
ceil(x0)
to ceil(x1) – 1 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax
G 2 1/7 2/7 8
D 8 1/4 9
G

72. Polygon
Rasterization
• y = 6
• Delete y = ymax
edges
• Update x
• Add y = ymin
edges
• For each pair
x0,x1, plot from
ceil(x0)
to ceil(x1) – 1 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax
G 2 3/7 2/7 8
F 4 -1/2 8
E 6 1/1 9
D 8 1/4 1/4 9
G

73. Polygon
Rasterization
• y = 7
• Delete y = ymax
edges
• Update x
• Add y = ymin
edges
• For each pair
x0,x1, plot from
ceil(x0)
to ceil(x1) – 1 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
F
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax
G 2 5/7 2/7 8
F 3 1/2 -1/2 8
E 7 1/1 9
D 8 2/4 1/4 9
G
E

74. Polygon
Rasterization
• y = 8
• Delete y = ymax
edges
• Update x
• Add y = ymin
edges
• For each pair
x0,x1, plot from
ceil(x0)
to ceil(x1) – 1 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
F
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax
E 8 1/1 9
D 8 3/4 1/4 9
G
E

75. Polygon
Rasterization
• y = 9
• Delete y = ymax
edges
• Update x
• Add y = ymin
edges
• For each pair
x0,x1, plot from
ceil(x0)
to ceil(x1) – 1 0 1 2 3 4 5 6 7 8 9
0
1
2
3
4
5
6
7
8
9
A
B
C
D
F
Edg
e
ymi
n
A 1
G 1
B 2
C 2
D 5
E 6
F 6
Edge x dx/dy ymax
G
E

76. For each scanline:
1. Maintain active edge list (using vertex events)
2. Increment edge’s x-intercepts, sort by x-intercepts
3. Output spans between left and right edges
Scan Line Algorithms
delete insert replace

77. Penetrating Polygons
S
I
T
a
2
BG
b
c
3
d
e
1
False edges and new polygons!
Compare z value & intersection when AET is
calculated

78. Example
Let’s apply the rules to scan line 8 below. We fill in the pixels from
point a, pixel (2, 8), to the first pixel to the left of point b, pixel (4, 8),
and from the first pixel to the right of point c, pixel (9, 8), to one pixel
to the left of point d, pixel (12, 8). For scan line 3, vertex A counts
once because it is the ymin vertex of edge FA, but the ymax vertex of
edge AB; this causes odd parity, so we draw the span from there to
one pixel to the left of the intersection with edge CB.
odd
odd
even even
a b c d
A
B
C
D
E
F

79. Four Elaborations (cont.)
A B
C D
E
F
G
H
I
J
E
A B
C D
F
G
H
I
J

80. Halftoning
For 1-bit (B&W) displays, fill patterns with different fill densities can
be used to vary the range of intensities of a polygon. The result is
a tradeoff of resolution (addressability) for a greater range of
intensities and is called halftoning. The pattern in this case should
be designed to avoid being noticed.
These fill patterns are chosen to minimize banding.