Microfacet Interpretation

Microfacet Model

Surface reflection can be understood through the microfacet model: surfaces are composed of tiny mirrors (facets) with varying orientations.

Facet Distributions

Material	Facet Distribution	Reflection Behaviour
Diffuse (Lambertian)	Random in all directions	Scatter equally everywhere
Imperfect specular	Mostly aligned, some spread	Broad highlight
Perfect specular (mirror)	All co-planar with surface	One sharp reflection

Diffuse Surfaces

Facets randomly oriented in all directions:

• Light hits facets at all angles
• Light scatters uniformly
• No preferred reflection direction

Result: View-independent reflection (Lambertian).

Imperfect Specular Surfaces

Facets mostly aligned with the macro-surface normal, but with some angular spread:

• Most light reflects near the mirror direction
• Some spread creates a broad highlight
• Higher alignment = higher shininess $n$

Result: Phong-like specular with finite highlight size.

Perfect Specular Surfaces

All facets perfectly co-planar with the surface:

• All light reflects in exactly one direction
• No diffuse component
• Mirror-like reflection

Result: $n \to \infty$, perfect mirror.

Physical Insight

The microfacet model explains why:

• Metals have coloured specular ($k_s$ takes metal colour)
• Plastics have white specular ($k_s$ is light colour)
• Rough surfaces have broad, dim highlights
• Polished surfaces have sharp, bright highlights

Summary

• Microfacets model surfaces as collections of tiny mirrors
• Facet orientation distribution determines reflection properties
• Random facets → diffuse; aligned facets → specular
• Phong exponent $n$ models the spread of facet orientations