The **Liang-Barsky algorithm** is a line clipping algorithm. This algorithm is more efficient than Cohen–Sutherland line clipping algorithm and can be extended to 3-Dimensional clipping. This algorithm is considered to be the faster parametric line-clipping algorithm. The following concepts are used in this clipping:

- The parametric equation of the line.
- The inequalities describing the range of the clipping window which is used to determine the intersections between the line and the clip window.

This Algorithm was developed by Liang and Barsky. It is used for line clipping as it is more efficient than Cyrus Beck algorithm and Cohen Sutherland algorithm because it uses more efficient parametric equations to clip the given line.These parametric equations are given as: x = x1 + tdx , y = y1 + tdy, 0 <= t <= 1

Where dx = x2 – x1 & dy = y2 – y1

Liang Barsky line clipping algorithm uses 4 inequalities with 2 parameters p & q which are defined in the algorithm below.

**Algorithm**

1. Read 2 endpoints of line as p1 (x1, y1) & p2 (x2, y2).

2. Read 2 corners (left-top & right-bottom) of the clipping window as (xwmin, ywmin, xwmax, ywmax).

3. Calculate values of parameters pi and qi for i = 1, 2, 3, 4 such that

p1 = -dx, q1 = x1 – xwmin

p2 = dx, q2 = xwmax – x1

p3 = -dy, q3 = y1 – ywmin

p4 = dy, q4 = ywmax – y1

4. if pi = 0 then line is parallel to ith boundary

if qi < 0 then line is completely outside boundary so discard line

else, check whether line is horizontal or vertical and then check the line endpoints with the corresponding boundaries.

5. Initialize t1 & t2 as

t1 = 0 & t2 = 1

6. Calculate values for qi/pi for i = 1, 2, 3, 4.

7. Select values of qi/pi where pi < 0 and assign maximum out of them as t1.

8. Select values of qi/pi where pi > 0 and assign minimum out of them as t2.

9. if (t1 < t2)

{

xx1 = x1 + t1dx

xx2 = x1 + t2dx

yy1 = y1 + t1dy

yy2 = y1 + t2dy

line (xx1, yy1, xx2, yy2)

}

10. Stop.

**Advantages**

- More efficient than other algorithms as line intersection with boundaries calculations are reduced.
- Intersections of line are computed only once.

**Program**