1. Primitive Drawing Algorithm
Graphics Laboratory
Korea University

2. Contents Output Primitives Color Models
How can we describe shapes with primitives?
Color Models
How can we describe and represent colors?

3. Output Primitives Points Lines Polygons DDA algorithm
Bresenham’s algorithm
Polygons
Scan-line polygon fill
Inside-outside tests
Boundary-fill algorithm
Anti-aliasing

4. Points Single coordinate position
Set the color of the specified screen position
Within the frame buffer x y

5. Lines Intermediate positions between two endpoints
DDA, Bresenham’s line algorithms
Jaggies
/ Aliasing

6. DDA Algorithm Digital differential analyzer (DDA) Algorithm overview
Scan-conversion line algorithm for
Based on calculating either y or x
Algorithm overview
Sample the line at unit intervals in one coordinate
If |m| is below 1, sample in x coordinate
Else, sample in y coordinate
Determine corresponding integer values in other coordinate
Until the final endpoint is reached

7. In the Case of |m| < 1 y y x x : Lost Pixel <When we sample
in x coordinate>
<When we sample
in y coordinate>

8. Bresenham’s Line Algorithm (1 / 3)
Accurate and efficient
Use only incremental integer calculations
Can be adapted to circles and other curves
Specified Line Path 12 11 A 10 B 10 11 12
Which pixel is appropriate, A or B?

9. Bresenham’s Line Algorithm (2 / 3)
Vertical pixel separation as d1, d2
From the mathematical line path
If d1-d2 < 0, yk is selected
Else, yk+1 is selected
xk+1 yk
yk+1 y d2 d1
|m| < 1

10. Bresenham’s Line Algorithm (3 / 3)
Decision parameter pk
The sign of pk is same as the sign of d1-d2
Due to x > 0
Parameter c is constant
Independent of pixel position
Incremental representation

11. Polygons Filling polygons Scan-line fill algorithm
Inside-outside test
Boundary fill algorithm 11 1 2 3 4 5 6 7 8 9 10 5 6 7 8 9 4 3 1 2

12. Scan-Line Polygon Fill
Topological difference between 2 scan lines
y: intersection edges are opposite sides
y’: intersection edges are same side y 1 2 2 y’ 1 1

13. Scan-Line Polygon Fill (cont.)
Edge Sorted Table B yC yB xC
1/mCB C C’ E yD
yC’ xD
1/mDC yE xD
1/mDE D yA yE xA
1/mAE yB xA
1/mAB A 1
Scan-Line Number

14. Inside-Outside Tests Self-Intersections Odd-Even rule
Nonzero winding number rule
exterior
interior

15. Boundary-Fill Algorithm
Proceed to Neighboring Pixels
4-Connected
8-Connected

16. Antialiasing Supersampling (postfiltering)
Pixel-weighting masks
Area Sampling (prefiltering)
Pixel phasing
Shift the display location of pixel areas
Micropositioning the electron beam in relation to object geometry

17. Supersampling Subpixels increase resolution Maximum intensity level: 922
(10, 20): Level 3 Intensity
(11, 20): Level 1 Intensity
(11, 21): Level 2 Intensity
(12, 20): Level 3 Intensity 21 20 10 11 12

18. Weighted Supersampling
Pixel-weighting masks
More weights to subpixels near the center
Maximum intensity level: 16
More variations in pixel intensity 1 2 4

19. Weighted Supersampling22
(10, 20): Level 7 Intensity
(11, 20): Level 1 Intensity
(11, 21): Level 3 Intensity
(12, 20): Level 5 Intensity 21 20 10 11 12

20. Area Sampling
Intensity is proportional to overlapped area of each pixel
2 adjacent vertical (or horizontal) screen grid lines  trapezoid 22
(10, 20): 90%
(10, 21): 10% 21 20 10 11 12

21. Filtering Techniques Filter Functions (Weighting Surface) Box Filter
Cone Filter
Gaussian Filter

22. Contents Output Primitives Color Models
How can we describe shapes with primitives?
Color Models
How can we describe and represent colors?

23. Color Frame Buffer 255 150 75 255 150 75 255 150 75 Blue channel
255
150 75
255
150 75
Blue channel
Green channel
Red channel

24. Color Models
RGB
CMY
HSV

25. RGB Color Model R G B Color Colors are additive 0.0 0.0 0.0 Black 1.0
Red
0.0
1.0
0.0
Green
0.0
0.0
1.0
Blue
1.0
1.0
0.0
Yellow
1.0
0.0
1.0
Magenta
0.0
1.0
1.0
Cyan
1.0
1.0
1.0
White

26. RGB Color Cube

27. CMY Color Model C M Y Color Colors are subtractive 0.0 0.0 0.0 White
1.0
0.0
0.0
Cyan
0.0
1.0
0.0
Magenta
0.0
0.0
1.0
Yellow
1.0
1.0
0.0
Blue
1.0
0.0
1.0
Green
0.0
1.0
1.0
Red
1.0
1.0
1.0
Black

28. CMY Color Cube

29. HSV Color Model Spectral color (Hue) Amount of white (Saturation)
Black (Value)
Hue Angle
Saturation

30. HSV Color Model H S V Color 1.0 1.0 Red 60 1.0 1.0 Yellow 120 1.0 1.0
1.0
1.0
Red 60
1.0
1.0
Yellow
120
1.0
1.0
Green
180
1.0
1.0
Cyan
240
1.0
1.0
Blue
300
1.0
1.0
Magenta *
0.0
1.0
White *
0.0
0.5
Gray * *
0.0
Black

31. HSV Color Model
Cross section of the HSV hexcone