Define terms; Phong intensity equation

i) Ambient light

Ambient light is the uniform background light from reflections off many surrounding surfaces. It has no direction and lights every surface equally. Contribution: I_amb = ka · Ia.

ii) Lambert's cosine law

The intensity of diffusely reflected light from a surface is proportional to the cosine of the angle θ between the unit surface normal N and the unit vector L to the light source:

I_diff = kd · IL · cosθ = kd · IL · (N · L)

A surface turned away from the light receives (and reflects) less light.

iii) Diffuse reflection

Diffuse reflection is the scattering of incident light equally in all directions by a rough, dull surface. The brightness does not depend on the viewing position but only on the light direction and the normal (Lambert's law).

iv) Specular reflection

Specular reflection is the mirror-like reflection from a shiny surface, concentrated around the direction of ideal reflection R, producing a highlight that moves with the viewer. Phong model: I_spec = ks · IL · (R · V)^n.

Phong illumination equation

Summing the three components for a point light source:

I = ka·Ia + kd·IL·(N·L) + ks·IL·(R·V)^n

with

• R = 2(N·L)N − L (reflection vector), V = unit vector to the viewer
• ka, kd, ks = ambient, diffuse, specular coefficients; n = shininess exponent

With distance attenuation and m lights:

I = ka·Ia + Σ f(d_l)·IL_l·[ kd (N·L_l) + ks (R_l·V)^n ], f(d) = min(1/(a0 + a1d + a2d²), 1)

Terms are set to zero when N·L < 0 or R·V < 0.