Clipping

📘 Clipping in Computer Graphics — Exam Notes

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🔹 1. Introduction

Clipping is the process of removing (cutting off) parts of objects that lie outside a specified region called the clipping area.

👉 In simple terms: Only the visible part inside a boundary is displayed; everything else is discarded.

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🔹 2. Clipping Window & Viewport

✔️ Clipping Window

• The selected visible region in world coordinates
• Defined by boundaries: [ x_{min},\ x_{max},\ y_{min},\ y_{max} ]

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✔️ Viewport

• The area on the screen where the clipped image is displayed

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✔️ Relationship

• First clip → then map to viewport

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🔹 3. Types of Clipping

1. Point Clipping
2. Line Clipping
3. Polygon Clipping
4. Text Clipping

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🔹 4. Point Clipping

✔️ Concept

A point is visible if it lies inside the clipping window.

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✔️ Condition

A point ((x, y)) is inside if: [ x_{min} \le x \le x_{max} ] [ y_{min} \le y \le y_{max} ]

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🔹 5. Line Clipping

✔️ Concept

• A line may be:

  • Completely inside → accept
  • Completely outside → reject
  • Partially inside → clip

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🔸 5.1 Cohen–Sutherland Line Clipping Algorithm (Important)

✔️ Idea

• Divide plane into 9 regions
• Assign a 4-bit code (Region Code) to each endpoint

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✔️ Region Code Format

Each bit represents:

• Top
• Bottom
• Right
• Left

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✔️ Steps

1. Assign region codes to endpoints

2. If both codes = 0000 → Accept line

3. If logical AND ≠ 0 → Reject line

4. Else → Clip line:

   • Find intersection with boundary
   • Replace point and repeat

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✔️ Advantages

• Fast
• Easy to implement

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🔸 5.2 Liang–Barsky Algorithm

✔️ Idea

• Uses parametric equations of line
• More efficient than Cohen-Sutherland

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✔️ Line Equation

[ x = x_1 + u(x_2 - x_1) ] [ y = y_1 + u(y_2 - y_1) ]

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✔️ Advantages

• Fewer calculations
• More precise

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🔹 6. Polygon Clipping

✔️ Concept

Used to clip complex shapes (polygons).

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🔸 6.1 Sutherland–Hodgman Algorithm

✔️ Steps

1. Take polygon edges

2. Clip against each boundary:

   • Left
   • Right
   • Top
   • Bottom

3. Generate new vertices

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✔️ Cases

• Inside → Inside
• Outside → Outside
• Inside → Outside
• Outside → Inside

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🔹 7. Text Clipping

✔️ Methods

1. All-or-None String Clipping

   • Entire text visible or invisible

2. Character Clipping

   • Individual characters clipped

3. Component Clipping

   • Each character treated as polygon

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🔹 8. Important Terms

• Clipping Window: Visible region
• Viewport: Display area
• Region Code: Binary code for position
• Intersection Point: Where line meets boundary

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🔹 9. Diagram Descriptions

✔️ Clipping Window

• Draw rectangle (window)
• Show objects partly inside/outside

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✔️ Cohen-Sutherland Regions

• Divide plane into 9 regions
• Label region codes

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✔️ Line Clipping

• Draw line crossing boundary
• Show clipped portion

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🔹 10. Advantages of Clipping

• Improves efficiency
• Displays only required part
• Saves memory and processing time

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🔹 11. Limitations

• Complex calculations for polygons
• May require multiple steps

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📝 Likely Exam Questions

1. Define clipping in computer graphics.
2. What is a clipping window and viewport?
3. Explain point clipping with conditions.
4. Describe Cohen-Sutherland algorithm.
5. Explain Liang-Barsky algorithm.
6. What is polygon clipping?
7. Explain Sutherland-Hodgman algorithm.
8. What are types of text clipping?
9. Differentiate between clipping and windowing.
10. Solve a numerical on line clipping.

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⚡ Quick Revision Summary

• Clipping removes unwanted parts outside window
• Types: Point, Line, Polygon, Text
• Cohen-Sutherland → region codes
• Liang-Barsky → parametric method
• Sutherland-Hodgman → polygon clipping
• Condition for point: [ x_{min} \le x \le x_{max},\ y_{min} \le y \le y_{max} ]

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