Hidden Lines and Surfaces

Hidden Lines and Surfaces

Hidden surface removal determines which parts of objects are visible and removes those that are behind other surfaces.

Why Needed?

• To create realistic images
• Avoid drawing unnecessary (hidden) parts

Back Face Detection Algorithm

Idea:

• Surfaces facing away from viewer are not visible

Method:

• Use surface normal vector (N) and view vector (V)

👉 If:

$$N \cdot V >$$

→ Surface is visible

👉 If:

$$N \cdot V$$

→ Surface is hidden (back face)

Advantages

• Simple
• Fast

Limitation

• Works only for closed objects

Depth Buffer Method (Z-Buffer)

Idea

• Store depth (Z value) for each pixel
• Compare and display closest surface

Steps

1. Initialize Z-buffer with large values
2. For each pixel:
   • Compare depth
   • Keep nearest pixel

Advantages

• Simple
• Works for all objects

Disadvantages

• High memory usage
• Precision issues

A-Buffer Method

Extension of Z-buffer that handles transparency and anti-aliasing

Features

• Stores multiple surfaces per pixel
• Supports partial visibility

Advantages

• Better image quality
• Handles transparency

Disadvantages

• More memory & computation

Scan-Line Method

Idea:

• Process image line by line (scan line)

Steps:

1. Take one horizontal line
2. Find intersecting polygons
3. Compare depth
4. Fill visible pixels

Advantages

• Efficient for polygons

Disadvantages

• Complex implementation

Basic Illumination Models

Purpose:

To calculate how light interacts with surfaces → determines brightness & realism.

A. Ambient Light

Idea

• Background light present everywhere

$$I = I_a K_$$

​Feature

• Independent of light position

B. Diffuse Reflection

Idea

• Light scattered equally in all directions

$$I = I_l K_d (N \cdot L$$

Feature

• Depends on angle between light and surface

C. Specular Reflection

Idea:

• Produces shiny highlights

$$I = I_l K_s (R \cdot V)$$

Feature:

• Depends on viewer position
• Controls shininess

D. Phong Illumination Model

Combined Model

$$I = I_a K_a + I_l K_d (N \cdot L) + I_l K_s (R \cdot V)^$$

Advantages

• Realistic lighting
• Widely used

Combined Approach

• Combines Ambient + Diffuse + Specular
• Produces realistic shading

Warn Model (Ward Model)

Improved illumination model for realistic surfaces

Features

• Handles rough surfaces
• Better specular reflection

Intensity Attenuation 

Idea

Light intensity decreases with distance

Formula

$$I = \frac{I_0}{a + bd + cd^2$$

​​Effect

• Distant objects appear dim

Color Consideration

Idea

• Light has RGB components

Process

• Apply lighting model separately for:
  • Red
  • Green
  • Blue

Result

• Realistic colored objects

Transparency

Ability to see through objects

Technique

• Alpha blending

$$I = \alpha I_1 + (1-\alpha) I_$$

​Example:

• Glass, water

Shadows

Dark regions where light is blocked

Types:

1. Hard Shadows

• Sharp edges

2. Soft Shadows

• Blurred edges

Techniques

• Shadow mapping
• Ray tracing

Final Summary Table

Topic	Key Idea	Advantage
Back Face Detection	Remove back surfaces	Fast
Z-buffer	Depth comparison	Simple
A-buffer	Transparency support	Accurate
Scan-line	Line-by-line rendering	Efficient
Phong Model	Combined lighting	Realistic

Concept Flow

Hidden Surface Removal → Rendering → Illumination → Color → Transparency → Shadows