1. Definition

Shading is the process of determining the color and brightness of a surface in a 3D scene based on light interaction.

It relies on two main components:

1. Illumination (Lighting Model) – How light sources contribute to the color at a point on a surface.
2. Surface Modeling – How the surface properties (like texture, reflectivity, and orientation) affect the way light is reflected.

---

2. Illumination Models

Illumination models define how light interacts with surfaces. They can be classified into:

A. Local Illumination Models

• Compute color at a point based only on direct light sources and surface properties.
• Ignore reflections from other objects (no global effects).
• Common models:

i. Ambient Lighting

• Uniform light everywhere; represents indirect scattered light.
• No direction; prevents completely black areas.
• Formula: $$I_{ambient} = k_a \cdot I_a$$ Where $k_a$ = ambient reflection coefficient, $I_a$ = ambient light intensity.

ii. Diffuse Reflection (Lambertian)

• Light scattered equally in all directions from a rough surface.
• Depends on the angle between surface normal $N$ and light direction $L$.
• Formula (Lambert’s Law): $$I_{diffuse} = k_d \cdot I_l \cdot \max(0, \mathbf{N} \cdot \mathbf{L})$$ Where $k_d$ = diffuse coefficient, $I_l$ = light intensity.

iii. Specular Reflection

• Light reflected in a preferred direction (shiny surfaces).
• Depends on view direction $V$, light direction $L$, and surface normal $N$.
• Phong model formula: $$I_{specular} = k_s \cdot I_l \cdot (\max(0, \mathbf{R} \cdot \mathbf{V}))^n$$ Where $k_s$ = specular coefficient, $n$ = shininess exponent, $R$ = reflection vector.

Total Local Illumination:

$$I = I_{ambient} + I_{diffuse} + I_{specular}$$

---

B. Global Illumination Models

• Consider light bouncing off other objects (reflections, refractions, shadows, caustics).
• Methods include ray tracing, radiosity, photon mapping.
• Produce more realistic images, but computationally expensive.

---

3. Surface Modeling

Surface modeling defines how surfaces reflect light. Types:

A. Surface Types

1. Matte / Diffuse surfaces – scatter light equally; appear soft.
2. Shiny / Specular surfaces – reflect light in preferred directions.
3. Transparent / Refractive surfaces – allow light to pass through, bending it according to Snell’s law.

B. Surface Representation

• Normals are essential for shading; computed per:

  • Vertex (for smooth shading)
  • Face (for flat shading)

• Texture mapping adds fine-grained details without increasing geometry.

---

4. Shading Techniques

A. Flat Shading

• Compute one color per polygon using the face normal.
• Quick, but produces faceted look.

B. Gouraud Shading

• Compute vertex colors using normals and interpolate across polygon.
• Smooth appearance, but can miss small specular highlights.

C. Phong Shading

• Interpolate normals across the polygon and compute color per pixel.
• Produces high-quality smooth highlights.

---

5. Summary Table

Aspect	Description
Shading	Determining pixel color based on light and surface properties
Illumination	Ambient, Diffuse, Specular (Local); Ray tracing, Radiosity (Global)
Surface Modeling	Matte, Shiny, Transparent; uses normals and textures
Techniques	Flat, Gouraud, Phong shading

---

Key Points:

• Shading combines light sources, surface orientation, and material properties to create realistic visuals.
• Phong model is widely used for per-pixel lighting in modern graphics.
• Surface modeling is crucial for defining how light interacts with objects, affecting realism.