1. 1 CSCE 441: Computer Graphics Scan Conversion of Polygons Jinxiang Chai

2. 2/108 OpenGL Geometric Primitives All geometric primitives are specified by vertices GL_QUAD_STRIP GL_POLYGON GL_TRIANGLE_STRIP GL_TRIANGLE_FAN GL_POINTS GL_LINES GL_LINE_LOOP GL_LINE_STRIP GL_TRIANGLES GL_QUADS

3. 3/108 OpenGL Geometric Primitives All geometric primitives are specified by vertices GL_QUAD_STRIP GL_POLYGON GL_TRIANGLE_STRIP GL_TRIANGLE_FAN GL_POINTS GL_LINES GL_LINE_LOOP GL_LINE_STRIP GL_TRIANGLES GL_QUADS

4. 4/108 OpenGL Geometric Primitives All geometric primitives are specified by vertices GL_QUAD_STRIP GL_POLYGON GL_TRIANGLE_STRIP GL_TRIANGLE_FAN GL_POINTS GL_LINES GL_LINE_LOOP GL_LINE_STRIP GL_TRIANGLES GL_QUADS

5. 5/108 Drawing General Polygons How to draw every interior pixel? ?

6. 6/108 Drawing General Polygons How to draw every interior pixel?

7. 7/108 Drawing Curved Objects How to draw every interior pixels?

8. 8/108 Outline Methods for drawing polygons or curved objects - Scanline conversion of polygons - Boundary-fill - Flood-fill Required readings: - HB 6-10 to 6-14

9. 9/108 Drawing Rectangles Which pixels should be filled?

10. 10/108 Drawing Rectangles Is this correct?

11. 11/108 Drawing Rectangles What if two rectangles overlap?

12. 12/108 Drawing Rectangles Is this correct?

13. 13/108 Drawing Rectangles Is this correct? Overlap!!!

14. 14/108 Drawing Rectangles Solution: Exclude pixels on top and right

15. 15/108 Drawing Rectangles Artifacts are possible

16. 16/108 General Polygons – Basic Idea How to draw every interior pixel? - process the screen scan line from the bottom of the boundaries to the top - draw every interior pixel for each scan line.

17. 17/108 General Polygons – Basic Idea How to draw every interior pixel for a scan line?

18. 18/108 General Polygons – Basic Idea Intersect scan lines with edges Find ranges along x Fill interior of those ranges

19. 19/108 General Polygons – Basic Idea Intersect scan lines with edges Find ranges along x Fill interior of those ranges

20. 20/108 General Polygons – Basic Idea Intersect scan lines with edges Find ranges along x Fill interior of those ranges What about this line?

21. 21/108 General Polygons – Basic Idea Intersect scan lines with edges Find ranges along x Fill interior of those ranges Draw odd intervals only

22. 22/108 General Polygons – Basic Idea Intersect scan lines with edges Find ranges along x Fill interior of those ranges Draw odd intervals only Don’t fill top/right Edges may NOT match with line drawing algorithm

23. 23/108 General Polygons – Basic Idea Intersect scan lines with edges Find ranges along x Fill interior of those ranges Draw odd intervals only Use coherence to speed up

24. 24/108 General Polygons – Basic Idea Intersect scan lines with edges Find ranges along x Fill interior of those ranges Draw odd intervals only Use coherence to speed up Edges intersecting one scan line are mostly same as those intersecting previous scan line

25. 25/108 General Polygons – Basic Idea Intersect scan lines with edges Find ranges along x Fill interior of those ranges Draw odd intervals only Use coherence to speed up The x-value of an intersection with one scan line is close to the intersection with the previous one

26. 26/108 How to store polygon edges?

27. 27/108 How to store polygon edges? Scan Lines Associate polygon edges with scan lines

28. 28/108 How to store polygon edges? Scan Lines Associate polygon edges with scan lines: use the lowest end point of a edge to find the corresponding scan line

29. 29/108 How to store polygon edges? Scan Lines Associate polygon edges with scan lines: use the lowest end point of a edge to find the corresponding scan line

30. 30/108 How to store polygon edges? Scan Lines Associate polygon edges with scan lines: use the lowest end point of a edge to find the corresponding scan line

31. 31/108 General Polygons – Data Structures Sorted Edge Table: Scan Lines Edges Store a linked-list per scan- line. Insert edges into table at scan-line associated with lowest end-point.

32. 32/108 General Polygons – Example A B C D EF G Sorted Edge Table Insert edges into table at scan-line associated with lowest end-point!

33. 33/108 General Polygons – Example A B C D EF G Sorted Edge Table Insert edges into table at scan-line associated with lowest end-point!

34. 34/108 General Polygons – Example A B C D EF G ABAG Sorted Edge Table Insert edges into table at scan-line associated with lowest end-point!

35. 35/108 General Polygons – Example A B C D EF G ABAG Sorted Edge Table Exclude horizontal edges! Insert edges into table at scan-line associated with lowest end-point!

36. 36/108 General Polygons – Example A B C D EF G ABAG FGED Sorted Edge Table Insert edges into table at scan-line associated with lowest end-point!

37. 37/108 General Polygons – Example A B C D EF G ABAG FGED CD Sorted Edge Table Insert edges into table at scan-line associated with lowest end-point!

38. 38/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Insert edges into table at scan-line associated with lowest end-point!

39. 39/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Which edges are intersecting with the current scan line? Insert edges into table at scan-line associated with lowest end-point!

40. 40/108 General Polygons – Data Structures Active Edge List: Edges List of all edges intersecting current scan-line sorted by their x-values

41. 41/108 Linked List A data structure consisting of a group of nodes which together form a sequence Each node includes - a datum - a reference (link) to the next node

42. 42/108 General Polygons – Data Structures Active Edge List: Edges List of all edges intersecting current scan-line sorted by their x-values Implement active edge list with linked list

43. 43/108 General Polygons – Data Structures Active Edge List: Edges List of all edges intersecting current scan-line sorted by their x-values Implement active edge list with linked list So what kind of information should be stored in the linked list for our polygon drawing algorithm?

44. 44/108 General Polygons – Data Structures Edge: maxY: highest y-value currentX: x-value of end- point with lowest y-value xIncr: 1 / slope mazY currentX xIncr Edge

45. 45/108 Scan line intersection Scan line y k +1 Scan line y k mazY currentX xIncr Edge

46. 46/108 Scan line intersection Scan line y k +1 Scan line y k mazY currentX xIncr Edge with x k and 1/m, we can efficiently compute the next endpoint! - increment y k by 1 - increment x k by 1/m with y end, we know when to end the edge.

47. 47/108 General Polygons – Data Structures Edge: maxY: highest y-value currentX: x-value of end- point with lowest y-value xIncr: 1 / slope mazY currentX xIncr Edge Horizontal edges will not be used!!!

48. 48/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill interior pixels on the current scan line Increment x-values on edges in Active Edge List Increment line

49. 49/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill interior pixels on the current scan line Increment x-values on edges in Active Edge List Increment line Incrementally update the coordinates of intersection points!

50. 50/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List

51. 51/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill pixels Increment x-values on edges in Active Edge List Increment line

52. 52/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List maxY currentX xIncr AGAB

53. 53/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List maxY currentX xIncr AGAB

54. 54/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill interior pixels on the current line Increment x-values on edges in Active Edge List Increment line

55. 55/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List maxY currentX xIncr AGAB

56. 56/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill pixels Increment x-values on edges in Active Edge List Increment line

57. 57/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List maxY currentX xIncr AGAB

58. 58/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List AGAB maxY currentX xIncr

59. 59/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List?

60. 60/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List maxY currentX xIncr EDFG

61. 61/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List maxY currentX xIncr EDFG Is it correct?

62. 62/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill pixels Increment x-values on edges in Active Edge List Increment line

63. 63/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Sorted Edge Table Active Edge List AGAB maxY currentX xIncr EDFG

64. 64/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill pixels Increment x-values on edges in Active Edge List Increment line

65. 65/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AGAB maxY currentX xIncr EDFG

66. 66/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill pixels Increment x-values on edges in Active Edge List Increment line

67. 67/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AGAB maxY currentX xIncr EDFG ??? ?

68. 68/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AGAB maxY currentX xIncr EDFG

69. 69/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AGAB maxY currentX xIncr EDFG

70. 70/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AGAB maxY currentX xIncr EDFG

71. 71/108 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 scan line

72. 72/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AGAB maxY currentX xIncr EDFG

73. 73/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AB maxY currentX xIncr ED

74. 74/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AB maxY currentX xIncr ED

75. 75/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AB maxY currentX xIncr ED

76. 76/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AB maxY currentX xIncr ED

77. 77/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AB maxY currentX xIncr EDCD

78. 78/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AB maxY currentX xIncr EDCD

79. 79/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AB maxY currentX xIncr CD

80. 80/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List AB maxY currentX xIncr CD

81. 81/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List BC maxY currentX xIncr CDAB

82. 82/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List BC maxY currentX xIncr CDAB

83. 83/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List BC maxY currentX xIncr CD

84. 84/108 General Polygons – Example A B C D EF G ABAG FGED CD BC Active Edge Table Active Edge List BC maxY currentX xIncr CD

85. 85/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill pixels //draw pixels on the scanline Increment x-values on edges in Active Edge List Increment scan line // move to the next scanline

86. 86/108 Pixel Fill-in Which intervals should we draw? - Odd intervals. But need to pay attention to scan lines passing through vertices.

87. 87/108 General Polygons – Algorithm line = 0 While (line < height ) Add edges to Active Edge List from Sorted Edge Table starting at line Remove edges that end at line Fill pixels //draw pixels on the scanline Increment x-values on edges in Active Edge List Increment scan line // move to the next scanline

88. 88/108 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)

89. 89/108 Drawing Curved Objects How to draw every interior pixels? - process the scan line from the bottom to top - find the intersection positions between the current scan line and the boundaries of fill region - use coherence properties to reduce the process - fill interior pixel in the odd intervals. ?

90. 90/108 Drawing Curved Objects Scan-line fill for regions with curved boundaries Extend Scan-line fill for polygons to drawing curved objects - need to calculate intersection points based on curved equation - cannot use the straightforward incremental calculations - For simple curves such as circles or ellipses, use midpoint method for incremental calculations of intersection points. ?

91. 91/108 A More General Fill Approach How to deal with curved or irregular boundaries?

92. 92/108 A More General Fill Approach Basic idea of Boundary fill algorithm - pick an interior pixel - continue re-coloring pixels until it reaches boundary pixels or previously visited pixels. Particularly useful for interactive painting packages - interior points are easily selected or annotated - the figure interior is then painted in the fill color Paint demo

93. 93/108 Boundary Fill Start with drawn boundaries 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

94. 94/108 Boundary Fill Start with drawn boundaries 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

95. 95/108 Boundary Fill Work for inner and outer boundaries

96. 96/108 Boundary Fill Start with drawn outline of a polygon and an interior point Recursively recolor outward from that point  If neighbor pixels are not boundary pixels or previously visited pixels, then recolor and recur Everything within the boundary is changed to that color

97. 97/108 Boundary Fill How to define a neighbor? 4-connected 8-connected

98. 98/108 Boundary Fill – Example Black pixels indicate boundary pixels.

99. 99/108 Boundary Fill – Example Black pixels indicate boundary pixels. Red pixels indicate the filled color (previously visited pixels).

100. 100/108 Boundary Fill – Example Continue checking neighboring pixels until reaching boundary pixels (boundary color) or previously visited pixels (fill color)!

101. 101/108 Boundary Fill – Example Continue checking neighboring pixels until reaching boundary pixels or previously visited pixels!

102. 102/108 Boundary Fill – Example Continue checking neighboring pixels until reaching boundary pixels or previously visited pixels!

103. 103/108 Boundary Fill – Example Continue checking neighboring pixels until reaching boundary pixels or previously visited pixels!

104. 104/108 Boundary Fill – Example Continue checking neighboring pixels until reaching boundary pixels or previously visited pixels!

105. 105/108 Boundary Fill

106. 106/108 Boundary Fill -Might not fill regions correctly if some interior pixels are already displayed in the fill color. - Need to change the color of those pixels before boundary fill

107. 107/108 Boundary Fill – Example Black pixels indicate boundary pixels.

108. 108/108 Boundary Fill – Example Black pixels indicate boundary pixels.

109. 109/108 How to Deal with This? Multiple color boundaries? How to paint this region to yellow?

110. 110/108 How to Deal with This? Multiple color boundaries? How to paint this region to yellow? Three keys: - a start pixel - annotated interior pixels - a paint color

111. 111/108 Flood Fill/ Seed 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 are re-colored

112. 112/108 Flood Fill – Example

113. 113/108 Flood Fill – Example

114. 114/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

115. 115/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

116. 116/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

117. 117/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

118. 118/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

119. 119/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

120. 120/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

121. 121/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

122. 122/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

123. 123/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

124. 124/108 Flood Fill – Example Continue setting the colors for neighboring pixels if it is interior pixels!

125. 125/108 Boundary-Fill vs. Flood-Fill Both need to start with an interior pixel. Boundary-Fill requires annotating boundary pixels while flood-fill requires annotating interior pixels. Both are appealing to fill in the irregular boundaries.