====== Phong shader ======

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


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At a given point x, let c<sub>d</sub> be the diffuse color (components R, G, B) at that point, α the alpha-component of the diffuse color and c<sub>t</sub> the transparency color. For each color component, set

c<sup>α</sup><sub>t</sub> = 1 + α (c<sub>t</sub> - 1)

Let c<sub>s</sub> 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<sub>d</sub> = (1 - c<sup>α</sup><sub>t</sub>) c<sub>d</sub>

    * k<sub>s</sub> = (1 - c<sup>α</sup><sub>t</sub>) c<sub>s</sub> + r c<sup>α</sup><sub>t</sub>

    * k<sub>t</sub> = (1 - r) c<sup>α</sup><sub>t</sub>

Otherwise, set

    * k<sub>d</sub> = c<sub>d</sub>

    * k<sub>s</sub> = c<sub>s</sub> + r c<sup>α</sup><sub>t</sub>

    * k<sub>t</sub> = (1 - r) c<sup>α</sup><sub>t</sub>

The bidirectional reflection distribution function is

BRDF(x, ω<sub>i</sub>, ω<sub>o</sub>) = k<sub>d</sub> / π + k<sub>s</sub> (n + 2) max(cos β, 0)<sup>n</sup> / 2π

where β is the angle between ω<sub>i</sub> and the direction of ideal reflection of ω<sub>o</sub>. The bidirectional transmission distribution function is

BTDF(x, ω<sub>i</sub>, ω<sub>t</sub>) = k<sub>t</sub> (η<sub>t</sub> / η<sub>i</sub>)<sup>2</sup> δ<sub>ω<sup>+</sup></sub> (ω<sub>i</sub> - T(ω<sub>t</sub>))

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

The Phong shader supports:

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


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

{{ :tutorials:light-spec_vs_shiny.png?direct&450 |}}

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


====== References: ======

  * Phong BT, Illumination of Computer-Generated Images, Department of Computer Science, University of Utah, UTEC-CSc-73-129, July 1973.