Sutherland–Cohen Line Clipping Algorithm

1. Line Clipping

Line clipping determines which portion of a line segment lies inside the clipping window and removes the rest.

• Reduces unnecessary drawing
• Improves graphics performance
• Used in window systems

2. Idea of Cohen–Sutherland Algorithm

The algorithm divides the 2D space into nine regions around the clipping window and assigns a unique 4-bit region code to each endpoint of a line.

• Uses outcodes (region codes)
• Quickly accepts or rejects lines

3. Region Codes (Outcodes)

Bit 1: Top
Bit 2: Bottom
Bit 3: Right
Bit 4: Left

• 0000 → Inside window
• Non-zero → Outside window

4. Trivial Acceptance

If both endpoints of a line have region code 0000, the line lies completely inside the window and is accepted.

5. Trivial Rejection

If the logical AND of region codes of both endpoints is non-zero, the line lies completely outside and is rejected.

6. Partial Clipping

If neither trivial acceptance nor rejection applies, the line partially intersects the window and clipping is required.

• Calculate intersection point
• Replace outside endpoint

7. Steps of Cohen–Sutherland Algorithm

• Assign region codes to endpoints
• Check for trivial acceptance
• Check for trivial rejection
• Clip partially visible lines
• Repeat until line is accepted or rejected

8. Example

For a line intersecting the right boundary of the window:

• Calculate intersection with right edge
• Update endpoint and region code
• Apply algorithm again

9. Advantages

• Simple and efficient
• Fast rejection of invisible lines
• Widely used

10. Disadvantages

• Works only for rectangular windows
• Multiple iterations for partial lines

11. Applications

• Window-based graphics systems
• CAD applications
• 2D rendering engines

Practice Questions

1. What is Cohen–Sutherland algorithm?
2. What are region codes?
3. Explain trivial acceptance and rejection.
4. How is partial clipping performed?
5. List advantages of the algorithm.

Practice Task