1. Definition

Phong shading is a per-pixel shading technique used to simulate realistic lighting on surfaces.

• It calculates color at every pixel by interpolating surface normals across a polygon and then applying the Phong illumination model.
• Produces smooth highlights and realistic appearance compared to flat or Gouraud shading.

2. Phong Illumination Model

The Phong model combines three components of light:

Where:

A. Ambient Component

• Uniform background light, direction-independent. $$I_{\text{ambient}} = k_a \cdot I_a$$
• $k_a$ = ambient reflection coefficient, $I_a$ = ambient light intensity.

B. Diffuse Component (Lambertian Reflection)

• Light scattered equally in all directions from a matte surface.
• Depends on the angle between surface normal $N$ and light vector $L$: $$I_{\text{diffuse}} = k_d \cdot I_l \cdot \max(0, \mathbf{N} \cdot \mathbf{L})$$
• $k_d$ = diffuse coefficient, $I_l$ = light intensity.

C. Specular Component

• Light reflected in a specific direction from shiny surfaces.
• Depends on surface normal $N$, light vector $L$, view vector $V$, and shininess exponent $n$: $$I_{\text{specular}} = k_s \cdot I_l \cdot (\max(0, \mathbf{R} \cdot \mathbf{V}))^n$$
• $k_s$ = specular reflection coefficient, $R$ = reflection of $L$ about $N$, $V$ = view vector, $n$ controls highlight sharpness.

3. Phong Shading Algorithm

1. Compute vertex normals for each vertex of the polygon.
2. Interpolate normals across the polygon for each pixel.
3. Compute color per pixel using the Phong illumination model.

• Produces smooth shading with correctly placed specular highlights, unlike Gouraud shading which interpolates color.

4. Comparison with Other Shading Methods

5. Advantages of Phong Shading

• Produces realistic lighting and smooth highlights.
• Correctly models specular reflections.
• Works well for curved surfaces.

6. Disadvantages

• Computationally more expensive than flat or Gouraud shading.
• Requires interpolation of normals and per-pixel calculations.

Key Points:

• Phong shading = interpolated normals + Phong illumination.
• Essential for high-quality graphics in games, simulations, and CGI.
• Controls like shininess exponent $n$ allow customizing surface glossiness.