1. Clipping Polygons
Dr. Scott Schaefer

2. Clipping Polygons

3. Clipping Polygons

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

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

6. How Many Sides? 7

7. Why Is Polygon Clipping Hard?
Concave polygon Multiple polygons

8. Why Is Polygon Clipping Hard?
A really tough case

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

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

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

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

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

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

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

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

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

18. 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

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

20. 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)

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

22. Sutherland-Hodgman Algorithm
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23. Sutherland-Hodgman Algorithm
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28. Sutherland-Hodgman Algorithm
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30. Sutherland-Hodgman Algorithm
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Possible error for non-convex polygons

66. 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

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

68. Weiler-Atherton Algorithm
Process the edges of the polygon 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
Repeat until at a previously processed vertex
Return to the exit-intersection point and continue processing the polygon edges in a counterclockwise order

69. Weiler-Atherton Algorithm

70. Weiler-Atherton Algorithm

71. Weiler-Atherton Algorithm

72. Weiler-Atherton Algorithm

73. Weiler-Atherton Algorithm

74. Weiler-Atherton Algorithm

75. Weiler-Atherton Algorithm

76. Weiler-Atherton Algorithm

77. Weiler-Atherton Algorithm

78. Weiler-Atherton Algorithm

79. Weiler-Atherton Algorithm

80. Weiler-Atherton Algorithm

81. Weiler-Atherton Algorithm

82. Weiler-Atherton Algorithm

83. Weiler-Atherton Algorithm

84. Weiler-Atherton Algorithm

85. Weiler-Atherton Algorithm

86. Weiler-Atherton Algorithm

88. Sutherland-Hodgman Algorithm
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