Midpoint Subdivision Algorithm

1. Introduction

When a line extends outside the visible region, line clipping is required. The midpoint subdivision method clips lines by repeatedly dividing them into halves.

• Recursive clipping technique
• Simple and intuitive approach

2. Basic Idea

If a line segment is partially visible, the algorithm finds the midpoint of the line and checks its visibility, then recursively processes each half.

• Divide line into two segments
• Test visibility of midpoint

3. Working Principle

The algorithm continues subdividing the line until a segment is either completely inside or outside the clipping window.

• Inside → accept segment
• Outside → reject segment

4. Algorithm Steps

• Check endpoints of the line
• If both inside → accept
• If both outside → subdivide
• Find midpoint of line
• Repeat recursively

5. Midpoint Calculation

xm = (x1 + x2) / 2
ym = (y1 + y2) / 2

6. Termination Condition

Subdivision stops when the line segment becomes very small or when it is fully accepted or rejected.

• Avoids infinite recursion
• Ensures algorithm termination

7. Advantages

• Conceptually simple
• No region codes required
• Works for any clipping window

8. Disadvantages

• Recursive and slower
• Not efficient for long lines

9. Comparison with Cohen–Sutherland

Midpoint Subdivision        Cohen–Sutherland
-------------------------  -----------------------------
Recursive                  Iterative
No region codes             Uses region codes
Slower                      Faster
Simple logic                More optimized

10. Applications

• Educational graphics systems
• Simple line clipping tasks
• Recursive graphics algorithms

Practice Questions

1. What is midpoint subdivision algorithm?
2. Explain its working principle.
3. How is midpoint calculated?
4. List advantages and disadvantages.
5. Compare with Cohen–Sutherland algorithm.

Practice Task