1. CSCE 441 Computer Graphics: Clipping Polygons Jinxiang Chai

2. Reminder Required readings: HB 6-5 to 6-7
Homework#1 deadline is passed
Homework #2 will be posted tonight, due by 9/29

3. Review: Clipping Points
Given a point (x, y) and clipping window (xmin, ymin), (xmax, ymax), determine if the point should be drawn
(xmax,ymax)
(x,y)
xmin=<x<=xmax?
(xmin,ymin)
ymin=<y<=ymax?

4. Review: Clipping Lines

5. Review: Clipping Lines

6. Review Clipping Simple line clipping algorithm
- compute intersection points
- clip the line segment between the outside point and intersection point
Cohen-Sutherland
- region coding (9 regions, 4bits)
- best used when trivial acceptance and rejection is possible for most lines
Liang-Barsky
- computation of t-intersections is cheap (only one division)
- computation of (x,y) clip points is only done once
- algorithm doesn’t consider trivial accepts/rejects
- best when many lines must be clipped

7. Clipping Polygons
Clipping polygons is more complex than clipping the individual lines
- Input: polygon

8. Clipping Polygons
Clipping polygons is more complex than clipping the individual lines
- Input: polygon
- Output: original polygon, new polygon, or nothing

9. Why Is Polygon Clipping Hard?
What happens to a triangle during clipping?
- possible outcomes:
triangle->triangle
triangle->quad
triangle->5-gon

10. Why Is Polygon Clipping Hard?
What happens to a triangle during clipping?
- possible outcomes: triangle, quad, or else?

11. Why Is Polygon Clipping Hard?
What happens to a triangle during clipping?
- possible outcomes:
triangle->triangle
triangle->quad
triangle->5-gon
How many sides a clipped triangle might have?

12. How Many Sides?
Seven

13. Why Is Clipping Hard? A really tough case
Concave polygon -> Multiple polygons

14. Why Is Clipping Hard?
A really tough case

15. Outline Sutherland-Hodgman Clipping - convex polygons
Weiler-Atherton Algorithm
- general polygons
Required readings
- HB 6-8

16. Any idea?
Clipping polygon edges?

17. Any idea?
Clipping polygon edges?
Unconnected set of lines!

18. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation

19. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation

20. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation

21. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation

22. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation

23. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation

24. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation

25. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation

26. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation

27. Sutherland-Hodgman Clipping
Basic idea:
- consider each edge of the view window individually
- clip the polygon against the view window edge’s equation
- after doing all edges, the polygon is fully clipped

28. Sutherland-Hodgman Clipping
Java applet: click here.

29. Sutherland-Hodgman Clipping
Input/output for algorithm:
- input: list of polygon vertices in order
{abcdef} a f b e d c

30. Sutherland-Hodgman Clipping
Input/output for algorithm:
- input: list of polygon vertices in order
- output: list of clipped polygon vertices consisting of old vertices (maybe) and new vertices (maybe)

31. Sutherland-Hodgman Clipping
Input/output for algorithm:
- input: list of polygon vertices in order
- output: list of clipped polygon vertices consisting of old vertices (maybe) and new vertices (maybe)
- exactly what expect from the clipping operation against each edge!

32. Sutherland-Hodgman Clipping
Basic routine:
- Go around polygon one vertex at a time
- Current vertex has position E
- Previous vertex had position S, and it has been added to the output if appropriate a f b e d
{abcdef} c

33. Sutherland-Hodgman Clipping
Basic routine:
- Go around polygon one vertex at a time
- Current vertex has position E
- Previous vertex had position S, and it has been added to the output if appropriate a f b e d
{abcdef} c

34. Sutherland-Hodgman Clipping
Edge from S to E takes one of four cases:
inside
outside
inside
outside
inside
outside
inside
outside E S E S E S E S
I output E output
E output
I output
no output

35. Sutherland-Hodgman Clipping
Four cases:
S inside plane and E inside plane
Add E to output
Note: S has already been added
S inside plane and E outside plane
Find intersection point I
Add I to output
S outside plane and E outside plane
Add nothing
S outside plane and E inside plane
Add I to output, followed by E

36. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

37. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

38. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

39. Sutherland-Hodgman Algorithm
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Output E
Output I
Output I,E

40. Sutherland-Hodgman Algorithm
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Output E
Output I
Output I,E

41. Sutherland-Hodgman Algorithm
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Output E
Output I
Output I,E

42. Sutherland-Hodgman Algorithm
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Output I
Output I,E b

43. Sutherland-Hodgman Algorithm
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Output E
Output I
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44. Sutherland-Hodgman Algorithm
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Output E
Output I
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45. Sutherland-Hodgman Algorithm
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Output E
Output I
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46. Sutherland-Hodgman Algorithm
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Output E
Output I
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47. Sutherland-Hodgman Algorithm
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Output I
Output I,E

48. Sutherland-Hodgman Algorithm
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Output I
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49. Sutherland-Hodgman Algorithm
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Output E
Output I
Output I,E

50. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

51. Sutherland-Hodgman Algorithm
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Output E
Output I
Output I,E

52. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

53. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

54. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

55. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

56. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

57. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

58. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
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59. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

60. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

61. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

62. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

63. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

64. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

65. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

66. Sutherland-Hodgman Algorithm
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Output E
Output I
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67. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

68. Sutherland-Hodgman Algorithm
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Output E
Output I
Output I,E

69. Sutherland-Hodgman Algorithm
Out In
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Output E
Output I
Output I,E

70. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

71. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

72. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

73. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

74. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

75. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

76. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

77. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

78. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E

79. Sutherland-Hodgman Algorithm
Out In
No output
Output E
Output I
Output I,E
Possible error for non-convex polygons

80. Sutherland-Hodgman Algorithm
Easy to pipeline for parallel processing
Polygon from one boundary does not have to be complete before next boundary starts
Leads to substantial performance gains

81. Weiler-Atherton Algorithm
General polygon vs. polygon clipping
Handles non-convex shapes
Not as efficient as Sutherland-Hodgman
Not easy to parallelize

82. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

83. Weiler-Atherton Algorithm

84. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

85. Weiler-Atherton Algorithm

86. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

87. Weiler-Atherton Algorithm

88. Weiler-Atherton Algorithm

89. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

90. Weiler-Atherton Algorithm

91. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

92. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

93. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

94. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

95. Weiler-Atherton Algorithm

96. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

97. Weiler-Atherton Algorithm

98. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

99. Weiler-Atherton Algorithm

100. Weiler-Atherton Algorithm

101. Weiler-Atherton Algorithm

102. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

103. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

104. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

105. Weiler-Atherton Algorithm

106. Weiler-Atherton Algorithm

107. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

108. Weiler-Atherton Algorithm

109. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

110. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

111. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

112. Weiler-Atherton Algorithm

113. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

114. Weiler-Atherton Algorithm

115. Weiler-Atherton Algorithm
Process the edges of the polygon fill area in a counterclockwise order until an inside-outside pair of vertices is encountered
Follow the window boundaries in a counterclockwise direction from the exit-intersection point to another intersection point with the polygon
- previously processed?
- yes, go to the next step
- no, continue processing polygon until a previously processed vertex is encountered
Form the vertex list for this section of the clipped fill area
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

116. Weiler-Atherton Algorithm

117. Weiler-Atherton Algorithm

118. Next Lecture
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