Clipping and Hidden Surfaces Clipping Basic Line Clipping Cohen ...

Cohen-Sutherland Line Clip
• Out codes
1 2
0010
3
4
0101
Liang-Barsky Clipping
• Parametric clipping - view line in parametric
form and reason about the parameter values
• More efficient, as not computing the coordinate
values at irrelevant vertices
• Works for rectilinear clip regions in 2D or 3D
• Clipping conditions on parameter: Line is inside
clip region for values of t such that (for 2D):
x
y
min
min
≤x1
+ t∆x
≤x
≤ y + t∆y
≤ y
1
max
max
∆x
= x2
−x1
∆y
= y −y
2
1
7
8
Liang-Barsky Clipping
Liang-Barsky Clipping
• Infinite line intersects clip region edges at:
qk
t
k
=
p
k
where
p 1
= −∆x
q 1
= x 1
− x min
p 2 = ∆x q 2 = x max − x 1
p 3
= −∆y q 3
= y 1
− y min
p 4 = ∆y q 4 = y max − y 1
• When p k 0, line goes from inside to outside – leaving
• When p k =0, line is parallel to an edge (clipping is easy)
• If there is a segment of the line inside the clip region,
sequence of infinite line intersections must go: enter,
enter, leave, leave
Note: Left edge is 1, right edge is 2, top edge is 3, bottom is 4
9
10
Liang-Barsky Clipping
Liang-Barsky Clipping
• Compute entering t values, which are q k /p k for each p k 0
• Parameter value for small t end of line is:t small = max(0, entering
t’s)
• parameter value for large t end of line is: t large =min(1, leaving t’s)
Enter
• if t small