1. Scan Conversion of Polygons
Dr. Scott Schaefer

2. Which pixels should be filled?
Drawing Rectangles
Which pixels should be filled?

3. Drawing Rectangles
Is this correct?

4. What if two rectangles overlap?
Drawing Rectangles
What if two rectangles overlap?

5. Drawing Rectangles
Is this correct?

6. Drawing Rectangles
Overlap!!!
Is this correct?

7. Solution: Exclude pixels on top and right
Drawing Rectangles
Solution: Exclude pixels on top and right

8. Artifacts are possible
Drawing Rectangles
Artifacts are possible

9. General Polygons – Basic Idea
Intersect scan lines with edges
Find ranges along x
Fill interior of those
ranges
Don’t fill top/right
Edges may NOT match
with line drawing algo

10. General Polygons – Basic Idea
Use coherence to speed up
Intersect scan lines with edges
Find ranges along x
Fill interior of those
ranges
Don’t fill top/right
Edges may NOT match
with line drawing algo

11. General Polygons – Basic Idea
Use coherence to speed up
Intersect scan lines with edges
Find ranges along x
Fill interior of those
ranges
Edges intersection one scan line are mostly same as those intersecting previous scan line

12. General Polygons – Basic Idea
Use coherence to speed up
Intersect scan lines with edges
Find ranges along x
Fill interior of those
ranges
The x-value of an intersection with one scan line is close to the intersection with the previous one

13. General Polygons – Data Structures
Edge:
maxY:
currentX:
xIncr:
Edge
maxY
currentX
xIncr

14. General Polygons – Data Structures
Edge:
maxY:
currentX:
xIncr:
Edge
maxY
currentX
xIncr
Horizontal edges will not be used!!!

15. General Polygons – Data Structures
Active Edge Table:
Store a linked-list per scan-line.
Insert edges into table at scan-line associated with lowest end-point.
Scan Lines
Edges

16. General Polygons – Data Structures
Active Edge List:
List of all edges intersecting current scan-line sorted by their x-values
Edges

17. General Polygons – Algorithm
line = 0
While (line < height )
Add edges to Active Edge List from Active Edge Table starting at line
Remove edges that end at line
Fill pixels
Increment x-values on edges in Active Edge List
Increment line

18. General Polygons – ExampleC
Active Edge Table B D G
Active Edge List F E A

19. General Polygons – ExampleC
Active Edge Table B D G AB
Active Edge List F E A

20. General Polygons – ExampleC
Active Edge Table B BC D G AB
Active Edge List F E A

21. General Polygons – ExampleC
Active Edge Table B BC D CD G AB
Active Edge List F E A

22. General Polygons – ExampleC
Active Edge Table B BC D CD G ED AB
Active Edge List F E A

23. General Polygons – ExampleC
Active Edge Table B BC D CD G ED AB
Active Edge List F E A

24. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB
Active Edge List F E A

25. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E A

26. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB AG A
maxY
currentX
xIncr

27. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB AG FG ED A
maxY
currentX
xIncr

28. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB AG FG ED A
maxY
currentX
xIncr

29. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB AG FG ED A
maxY
currentX
xIncr

30. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB AG FG ED A
maxY
currentX
xIncr

31. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB AG FG ED A
maxY
currentX
xIncr

32. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB ED A
maxY
currentX
xIncr

33. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB ED A
maxY
currentX
xIncr

34. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB ED A
maxY
currentX
xIncr

35. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB ED A
maxY
currentX
xIncr

36. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB ED CD A
maxY
currentX
xIncr

37. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB ED CD A
maxY
currentX
xIncr

38. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB CD A
maxY
currentX
xIncr

39. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB CD A
maxY
currentX
xIncr

40. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB BC CD A
maxY
currentX
xIncr

41. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E AB BC CD A
maxY
currentX
xIncr

42. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E BC CD A
maxY
currentX
xIncr

43. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E BC CD A
maxY
currentX
xIncr

44. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E BC CD A
maxY
currentX
xIncr

45. General Polygons – ExampleC
Active Edge Table B BC D CD G FG ED AB AG
Active Edge List F E BC CD A
maxY
currentX
xIncr

46. General Polygons – Problems
Sliver polygons may not be drawn correctly
No simple solution
Long, thin triangles
cause problems
Want triangles with
good aspect ratio
(close to equilateral)

47. Boundary Fill
Start with drawn outline of a polygon and an interior point
Recursively recolor outward from that point
If neighbor different, then recolor and recur
Everything within the boundary is changed to that color

48. Boundary Fill
How to define a neighbor?
8-connected
4-connected

49. Boundary Fill – Example

50. Boundary Fill – Example

51. Boundary Fill – Example

52. Boundary Fill – Example

53. Boundary Fill – Example

54. Boundary Fill – Example

55. Flood Fill Start with a point
Define color under that point as the interior color
Recursively recolor outward from that point
If neighbor is interior color, then recolor and recur
Contiguous regions of the same color are recolored

56. Flood Fill – Example

57. Flood Fill – Example

58. Flood Fill – Example

59. Flood Fill – Example

60. Flood Fill – Example

61. Flood Fill – Example

62. Flood Fill – Example

63. Flood Fill – Example

64. Flood Fill – Example

65. Flood Fill – Example

66. Flood Fill – Example

67. Flood Fill – Example

68. Flood Fill – Example

69. OpenGL: Drawing Polygons
Lots of different primitives supported
GPU only draws triangles
OpenGL triangulates all polygons
Problems with concave polygons!
How data is passed to GPU makes a significant difference in speed
GL_QUADS
GL_POLYGON
GL_TRIANGLES
GL_TRIANGLE_FAN
GL_TRIANGLE_STRIP
GL_QUAD_STRIP

70. Performance Nvidia 7300 GT1 Nvidia 8800 GTX1 ATI Radeon HD 48502
New Drivers
Immediate Mode
15.5
21.0
33.0
Display Lists
28.3
22.0
463.5
497.5
Vertex Arrays
33.5
35.5
75.0
335.0
Vertex Buffer Objects
50.0
200.0
476.3
506.0
Frames per second displaying a 413,236 triangle model. CPU was an Intel Core or Core i

71. Tile-Based Rasterization
Screen

72. Tile-Based Rasterization

73. Tile-Based Rasterization

74. Tile-Based Rasterization

75. Tile-Based Rasterization
Each thread draws polygon into local frame buffer
Copies local frame buffer into global frame buffer when complete

76. Even More Parallelization

77. Even More Parallelization

78. Even More Parallelization

79. Point in Triangle

80. Even More Parallelization

81. Even More Parallelization
Only need to check until first polygon hit