liang barsky Line Clipping Algorithm

The Liang-Barsky line clipping algorithm is another line clipping algorithm used in computer graphics. It is similar to the Cohen-Sutherland algorithm, but it is more efficient because it avoids the calculation of intersection points for line segments that are completely outside the clip region.

The algorithm works as follows:

1. Calculate the values of `p1`, `p2`, `-dx`, `dx`, `-dy`, and `dy`, where `p1` and `p2` are the endpoints of the line segment, `dx` is the difference between the x-coordinates of the endpoints, and `dy` is the difference between the y-coordinates of the endpoints.

2. Calculate the values of `u1`, `u2`, and `r`, where `u1` is the distance from the start point of the line segment to the left edge of the clip region, `u2` is the distance from the start point of the line segment to the right edge of the clip region, and `r` is the distance between the endpoints of the line segment.

3. If `r` is less than zero, the line segment is degenerate and can be discarded.

4. If `dx` is zero, check whether the line segment lies completely to the left or right of the clip region. If it does, the line segment can be discarded.

5. If `dy` is zero, check whether the line segment lies completely above or below the clip region. If it does, the line segment can be discarded.

6. If `r` is greater than zero, calculate the values of `t1` and `t2`, where `t1` is the distance from the start point of the line segment to the intersection point with the left or bottom edge of the clip region, and `t2` is the distance from the start point of the line segment to the intersection point with the right or top edge of the clip region.

7. If `t2` is less than zero, the line segment lies completely to the right or above the clip region and can be discarded.

8. If `t1` is greater than `r`, the line segment lies completely to the left or below the clip region and can be discarded.

9. If `t1` is greater than zero, update `p1` to the intersection point with the left or bottom edge of the clip region.

10. If `t2` is less than `r`, update `p2` to the intersection point with the right or top edge of the clip region.

11. If the line segment is not discarded, it lies partially or completely inside the clip region and can be drawn.

The Liang-Barsky algorithm is more efficient than the Cohen-Sutherland algorithm because it avoids the calculation of intersection points for line segments that are completely outside the clip region. However, it is more complex and requires more calculations than the Cohen-Sutherland algorithm.