Liang Barsky algorithm - Computer Graphics - The Logic Tutorial

Liang-Barsky Algorithm

The Liang-Barsky algorithm is a line-clipping algorithm used in computer graphics to determine whether a line segment intersects a given rectangular window. It efficiently eliminates the portion of a line that lies outside the window.

Algorithm Steps:

1. Calculate the parameter values of the intersection points with the window boundaries using the parametric form of the line equation.
2. Initialize the parameter values for the intersection points (P1 and P2) to 0 and 1 respectively.
3. Check if the line is parallel to any of the window boundaries. If so, determine if it lies outside the window.
4. If the line is not parallel to any of the window boundaries, compute the new parameter values of intersection points based on the window boundaries.
5. Check if there is a valid range for the intersection points. If not, the line lies entirely outside the window.
6. If a valid range exists, clip the line accordingly using the calculated parameter values.

Example:

Consider a line segment defined by points P1(x1, y1) and P2(x2, y2), and a rectangular window defined by points (xmin, ymin) and (xmax, ymax).

Let's assume:

• P1(2, 3), P2(10, 8)
• Window: xmin=4, ymin=4, xmax=8, ymax=7

Using the Liang-Barsky algorithm, we find:

1. Calculate the line parameters: dx = x2 - x1, dy = y2 - y1.
2. Initialize P1 = 0, P2 = 1.
3. Compute the intersection parameters using the window boundaries.
4. Determine the valid parameter range for intersection.
5. If the range is valid, clip the line segment.

Conclusion:

The Liang-Barsky algorithm efficiently determines whether a line segment intersects a given rectangular window and clips the portion of the line outside the window. It is widely used in computer graphics for rendering and display purposes.