A Phong shader represents a Phong-like reflector. Its bidirectional reflection/transmission distribution functions are as follows:

At a given point x, let c_d be the diffuse color (components R, G, B) at that point, α the alpha-component of the diffuse color and c_t the transparency color. For each color component, set

c^α_t = 1 + α (c_t - 1)

Let c_s be the specular color and n the shininess exponent. Let r be the reflection coefficient as computed by Fresnel equation.

Now if interpolatedTransparency is true, set

• k_d = (1 - c^α_t) c_d

• k_s = (1 - c^α_t) c_s + r c^α_t

• k_t = (1 - r) c^α_t

Otherwise, set

• k_d = c_d

• k_s = c_s + r c^α_t

• k_t = (1 - r) c^α_t

The bidirectional reflection distribution function is

BRDF(x, ω_i, ω_o) = k_d / π + k_s (n + 2) max(cos β, 0)ⁿ / 2π

where β is the angle between ω_i and the direction of ideal reflection of ω_o. The bidirectional transmission distribution function is

BTDF(x, ω_i, ω_t) = k_t (η_t / η_i)² δ_ω⁺ (ω_i - T(ω_t))

where η stands for the index of refraction, T for the direction of transmission according to Fresnel's formulas, and δ_ω⁺ is the δ-distribution with respect to projected solid angle ω⁺.

The Phong shader supports:

1. `setDiffuse()` — sets the diffuse (reflected) component
2. `setTransparency()` — sets how much light is transmitted
3. `setSpecular()` — sets the mirror-like reflection for highlights
4. `setShininess()` — controls the size and sharpness of specular highlights
5. `setAmbient()` — ambient light scattering in the scene
6. `setEmissive()` — defines self-emission of light
7. `setInterpolatedTransparency()` — toggles interpolation of transmitted light

Below is an illustration of the effect of specular and shininess:

Note: In modern Phong shader implementations, roughness and glossiness replace specular and shininess.