Basic shading - DemoHut

In the simplest shading model, the outgoing radiance on a surface is the combination of diffuse radiance (following Lambert's law) and specular radiance of all light sources:

L_{o} (v) = \sum_{k = 1}^{n} (L_{diff(k)} + L_{spec(k)}),

L_{diff} = \frac{c_{diff}}{π} \times E_{L} \overline{\cos} (l, n),

L_{spec} = \frac{m + 8}{8 π} {\overline{\cos}}^{m} (h, n) c_{spec} \times E_{L} \overline{\cos} (l, n),

where

$v$ is the view ray pointing from surface to eye
$n$ is the number of light sources
$c_{diff}$ is the diffuse color
$\times$ is piecewise multiplication
$E_{L}$ is light irradiance/intensity, of RGB components
$\overline{\cos}$ is cosine value clamped to [0, 1]
$l$ is the normalized light ray pointing from surface to light source
$n$ is the normalized surface normal
$m$ is the smoothness of the surface
$h = \frac{l + v}{|| l + v ||}$ is called half vector
$c_{spec}$ is the specular color

There are different implementations of this shading equation, regarding the frequency of evaluation:

Flat (left): per-primitive normal, per-primitive evaluation
Gouraud (middle): per-vertex normal, per-vertex evaluation
Phong (right): per-vertex normal, per-pixel evaluation

Note that the "Phong" term above refers to "Phong shading", different from "(Blinn-)Phong reflection model", which describes a simplified shading equation and takes into account the ambient lights.