3D Concepts

📘 3D Concepts in Computer Graphics — Exam Notes

---

🔹 1. Introduction

3D Concepts in computer graphics deal with representing and manipulating objects in a three-dimensional space using the X, Y, and Z axes.

👉 Unlike 2D graphics (flat images), 3D graphics add depth, making objects look more realistic.

---

🔹 2. Basic Definition

A point in 3D space is represented as: [ P(x, y, z) ]

Where:

• x → horizontal direction
• y → vertical direction
• z → depth (forward/backward)

---

🔹 3. Coordinate System in 3D

✔️ 3D Cartesian Coordinate System

• Three axes:

  • X-axis
  • Y-axis
  • Z-axis

• Intersection point = Origin (0,0,0)

---

✔️ Types of Coordinate Systems

1. World Coordinates

   • Global reference system

2. Object Coordinates

   • Local coordinates of an object

3. View (Camera) Coordinates

   • Based on viewer’s position

4. Screen Coordinates

   • Final display coordinates

---

🔹 4. Representation of 3D Objects

---

✔️ 4.1 Wireframe Model

• Object represented by edges and vertices
• Looks like a skeleton

Advantage: Simple Disadvantage: Cannot show surfaces clearly

---

✔️ 4.2 Surface Representation

• Represents surfaces using polygons (usually triangles)

---

✔️ 4.3 Solid Modeling

• Represents complete object (inside + outside)

---

🔹 5. 3D Transformations

---

🔸 5.1 Translation

[ x' = x + t_x,\quad y' = y + t_y,\quad z' = z + t_z ]

---

🔸 5.2 Scaling

[ x' = x \cdot s_x,\quad y' = y \cdot s_y,\quad z' = z \cdot s_z ]

---

🔸 5.3 Rotation

✔️ About X-axis

[ y' = y \cos\theta - z \sin\theta ] [ z' = y \sin\theta + z \cos\theta ]

---

✔️ About Y-axis

[ x' = x \cos\theta + z \sin\theta ] [ z' = -x \sin\theta + z \cos\theta ]

---

✔️ About Z-axis

[ x' = x \cos\theta - y \sin\theta ] [ y' = x \sin\theta + y \cos\theta ]

---

🔹 6. Homogeneous Coordinates in 3D

A 3D point is represented as: [ (x, y, z, 1) ]

👉 Used to perform transformations using 4×4 matrices

---

🔹 7. Projection (Very Important)

✔️ Definition

Projection converts 3D objects into 2D images for display.

---

🔸 7.1 Types of Projection

---

✔️ Parallel Projection

• Projectors are parallel
• No perspective distortion

Types:

1. Orthographic Projection

   • Front, top, side views

2. Oblique Projection

   • Shows depth at an angle

---

✔️ Perspective Projection

• Projectors meet at a point
• Objects farther away appear smaller

👉 Used for realistic images

---

🔹 8. Viewing Pipeline in 3D

✔️ Steps

1. Modeling
2. Transformation
3. Viewing
4. Projection
5. Clipping
6. Rendering

---

🔹 9. Visibility & Hidden Surface Removal

✔️ Problem

Some parts of objects should not be visible.

---

✔️ Solution Techniques

• Back-face culling
• Z-buffer method

---

🔹 10. Lighting and Shading

✔️ Lighting

Determines how light interacts with objects.

---

✔️ Types of Shading

1. Flat Shading

   • One color per surface

2. Gouraud Shading

   • Smooth color interpolation

3. Phong Shading

   • More realistic lighting

---

🔹 11. Important Terms

• Vertex: Corner point of object
• Edge: Line between vertices
• Face: Surface of object
• Rendering: Final image generation
• Projection: 3D → 2D conversion

---

🔹 12. Diagram Descriptions

✔️ 3D Axes

• Draw X, Y, Z axes from origin

---

✔️ Projection

• Show 3D object projecting onto 2D plane

---

✔️ Wireframe Model

• Draw cube using only edges

---

🔹 13. Applications of 3D Graphics

• Video games
• Animation movies
• Virtual reality
• CAD systems
• Medical imaging

---

📝 Likely Exam Questions

1. Define 3D graphics and its importance.
2. Explain 3D coordinate systems.
3. Describe types of 3D object representations.
4. Explain 3D transformations with formulas.
5. What is projection? Explain its types.
6. Differentiate between parallel and perspective projection.
7. Explain hidden surface removal techniques.
8. Write short notes on shading methods.
9. Describe 3D viewing pipeline.
10. What are homogeneous coordinates in 3D?

---

⚡ Quick Revision Summary

• 3D uses (x, y, z) coordinates

• Objects represented as wireframe, surface, solid

• Transformations: Translation, Scaling, Rotation

• Projection types:

  • Parallel (no depth effect)
  • Perspective (realistic)

• Hidden surfaces removed using Z-buffer

• Shading improves realism

---