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1. 168 471 Computer Graphics, KKU. Lecture 8 1
Clipping on a Raster Display

2. 168 471 Computer Graphics, KKU. Lecture 8 2
Approaches to Clipping

3. 168 471 Computer Graphics, KKU. Lecture 8 3
Analytical Clipping

4. 168 471 Computer Graphics, KKU. Lecture 8 4
Clipping Lines Against Rectangles

5. 168 471 Computer Graphics, KKU. Lecture 8 5
Clipping Rules

6. 168 471 Computer Graphics, KKU. Lecture 8 6
Computing Intersections

7. 168 471 Computer Graphics, KKU. Lecture 8 7
Cohen-Sutherland Algorithm

8. 168 471 Computer Graphics, KKU. Lecture 8 8
Outcodes

9. 168 471 Computer Graphics, KKU. Lecture 8 9
Outcode Computation
typedef unsigned int outcode;
enum {TOP = 0x1, BOTTOM = 0x2, RIGHT = 0x4, LEFT = 0x8}
outcode CompOutCode(
double x, double y, double xmin, double xmax, double ymin, double ymax)
{
outcode code = 0;
if ( y > ymax )
code |= TOP;
else if ( y < ymin )
code |= BOTTOM;
if ( x > xmax )
code |= RIGHT;
else if ( x < xmin )
code |= LEFT;
return code;
}

10. 168 471 Computer Graphics, KKU. Lecture 8 10
Cohen-Sutherland Procedures

11. 168 471 Computer Graphics, KKU. Lecture 8 11
Cohen-Sutherland Procedures

12. 168 471 Computer Graphics, KKU. Lecture 8 12
Cohen-Sutherland Algorithm

13. 168 471 Computer Graphics, KKU. Lecture 8 13
Cohen-Sutherland Algorithm (cont.)

14. 168 471 Computer Graphics, KKU. Lecture 8 14
Cohen-Sutherland Procedures

15. 168 471 Computer Graphics, KKU. Lecture 8 15
Parametric Line-Clipping Algorithm
0 1 0
0 1 0
0
1 0
[ ( ) ] 0
[ ( ) ] 0
[ ] [ ] 0
[ ]
( )
i Ei
i Ei
i Ei i
i Ei
i
N P t P
N P P P t P
N P P N P P t
N P P
t
N D
where D P P
 
   
   

 
 
• Introduced by Cyrud and Beck in 1978
• Efficiently improved by Liang and Barsky
• Essentially find the parameter t from P(t) = P0 + (P1-P0)t

16. 168 471 Computer Graphics, KKU. Lecture 8 16
Parametric Line-Clipping Algorithm
(cont.)
• Formally, intersections can be classified as PE (potentially entering)
and PL (potentially leaving) on the basis of the angle between P0P1
and Ni
•Determine tE or tL for each intersection
• Select the line segment that has maximum tE and minimum tL
•If tE > tL, then trivially rejected
0 ( 90)
0 ( 90)
i
i
N D PE angle
N D PL angle
  
  

17. 168 471 Computer Graphics, KKU. Lecture 8 17
Parametric Line-Clipping Algorithm
(cont.)

18. 168 471 Computer Graphics, KKU. Lecture 8 18
Cyrus-Beck Algorithm (Pseudocode)

19. 168 471 Computer Graphics, KKU. Lecture 8 19
Clipping Circles and Ellipses
• Firstly, do a trivial accept/reject test by intersecting
the circle’s/elleipse’s extent with the clip rectengle.
• If intersection occurs, divide it into and do the trivial
accept/reject test for each.
• If scan conversion is fast or if the circle is not too
large, scissoring on a pixel-by-pixel basis would be
more efficient.

20. 168 471 Computer Graphics, KKU. Lecture 8 20
Clipping Polygons
Example of polygon clipping, (a) Multiple components.
(b) Simple convex case. (c) Concave case.

21. 168 471 Computer Graphics, KKU. Lecture 8 21
Clipping Polygons (cont.)
Polygon clipping, edge by edge. (a) Before clipping. (b) Clip on right.
(c) Clip on bottom. (d) Clip on left. (e) Clip on top; polygon is fully
clipped