📘 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
✔️ Types of Coordinate Systems
-
World Coordinates
-
Object Coordinates
- Local coordinates of an object
-
View (Camera) Coordinates
- Based on viewer’s position
-
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:
-
Orthographic Projection
-
Oblique Projection
✔️ Perspective Projection
- Projectors meet at a point
- Objects farther away appear smaller
👉 Used for realistic images
🔹 8. Viewing Pipeline in 3D
✔️ Steps
- Modeling
- Transformation
- Viewing
- Projection
- Clipping
- 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
-
Flat Shading
-
Gouraud Shading
- Smooth color interpolation
-
Phong Shading
🔹 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
- Define 3D graphics and its importance.
- Explain 3D coordinate systems.
- Describe types of 3D object representations.
- Explain 3D transformations with formulas.
- What is projection? Explain its types.
- Differentiate between parallel and perspective projection.
- Explain hidden surface removal techniques.
- Write short notes on shading methods.
- Describe 3D viewing pipeline.
- 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