Specular Reflection

Specular Highlights

Specular reflection models shiny surfaces that reflect light in a preferred direction, creating bright highlights.

Phong Specular Term

$I_{\text{specular}} = I_l k_s \cos^n\alpha = I_l k_s (\mathbf{R} \cdot \mathbf{V})^n$

where:

• $k_s$ is the specular reflection coefficient
• $\mathbf{R}$ is the perfect reflection direction of the light
• $\mathbf{V}$ is the direction to the viewer
• $\alpha$ is the angle between $\mathbf{R}$ and $\mathbf{V}$
• $n$ is the Phong exponent (shininess)

Reflection Direction

$\mathbf{R} = 2(\mathbf{L} \cdot \mathbf{N})\mathbf{N} - \mathbf{L}$

Effect of Shininess $n$

Material	Typical $n$	Effect
Matte	1-5	Broad, dull highlight
Plastic	10-50	Moderate highlight
Metal	50-200	Sharp, tight highlight
Mirror	∞	Perfect reflection (delta function)

Higher $n$ concentrates the highlight around the mirror direction.

When Specular is Zero

Specular reflection is zero when:

• $\mathbf{R} \cdot \mathbf{V} \leq 0$: Viewer is on wrong side of reflection lobe
• $\mathbf{N} \cdot \mathbf{L} \leq 0$: Light behind surface (no illumination at all)
• $k_s = 0$: Surface has zero specular reflectance

View Dependence

Specular reflection is view-dependent:

• Highlight moves as the camera moves
• Must be recomputed every frame for animations
• Cannot be cached if camera changes

Physical Approximation

The Phong model is an approximation:

• Does not conserve energy
• Not physically based (BRDF is ad-hoc)
• But computationally efficient and produces plausible results

Summary

• Specular creates shiny highlights
• Intensity depends on angle between reflection and viewer
• Shininess $n$ controls highlight size
• View-dependent: must recompute if camera moves

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Past Paper Questions

2025 Paper 3 Question 3(e): How does the specular highlight differ from diffuse reflection in the Phong shading model? [2 marks]

2025 Paper 3 Question 3(d): Explain when the specular component becomes zero. [Part of 4 marks]