1. Computer Graphics
Filling & Color

2. Basics Of Color
elements of color:

3. Basics of Color Physics: Perception Illumination Reflection
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) Subtractive (CMYK)
Shining colored lights on a white ball
Subtractive (CMYK)
Mixing paint colors and illuminating with white light

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

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

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 = R G 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

17. Converting Color Spaces

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

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

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

37. Flood Fill Algorithm Seed Position Edge “Color” Fill “Color”
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); }
Fill “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:
The minimum y value of the two vertices
The maximum y value of the two vertices
The x value associated with the minimum y value
The slope of the edge

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

43. Scan-Line Polygon Fill Algorithm2 4 6 8 10
Scan Line 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. 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
Parity
0 = even
1 = odd
Parity 1 D A E F

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

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

54. Edge Tables edge table (ET) active edge table (AET)
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
even
odd
odd
even
odd
even
odd

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: A A B B B B B B ' ' C C
xA,yB’,1/mAB
xC,yB’,1/mCB

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

64. Polygon Rasterization
Ignore horizontal lines
Sort edges by smaller y coordinate 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

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

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

67. Polygon Rasterization
Edge x
dx/dy
ymax G 1
2/7 8 A
4/2 3
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 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

68. Polygon Rasterization
Edge x
dx/dy
ymax G
1 2/7
2/7 8 A 3
4/2 B
-3/1 C
0/3 5
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 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

69. Polygon Rasterization
Edge x
dx/dy
ymax G
1 4/7
2/7 8 C
0/3 5
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 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

70. Polygon Rasterization
Edge x
dx/dy
ymax G
1 6/7
2/7 8 C
0/3 5
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 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

71. Polygon Rasterization
Edge x
dx/dy
ymax G
2 1/7
2/7 8 D
1/4 9
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 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

72. Polygon Rasterization
Edge x
dx/dy
ymax G
2 3/7
2/7 8 F 4
-1/2 E 6
1/1 9 D
8 1/4
1/4
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 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

73. Polygon Rasterization
Edge x
dx/dy
ymax G
2 5/7
2/7 8 F
3 1/2
-1/2 E 7
1/1 9 D
8 2/4
1/4
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 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

74. Polygon Rasterization
Edge x
dx/dy
ymax E 8
1/1 9 D
8 3/4
1/4
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 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

75. Polygon Rasterization
Edge x
dx/dy
ymax
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 9 8 D E 7 F 6 G
Edge
ymin A 1 G B 2 C D 5 E 6 F 5 4 C 3 B 2 A 1 1 2 3 4 5 6 7 8 9

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

77. Penetrating Polygons 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
even a b c d A B C D E F

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

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.