Shading is the process of altering the color of a surface, different shading models capture the process of light reflection on a surface, these models use the following variables in the computation

  • \(\mathbf{ray}\) (ray) - a ray emitted from a pixel, defined with an origin (\(\mathbf{ray_{origin}}\)) and a direction \(\mathbf{ray_{direction}}\)
  • \(\mathbf{p}\) (intersection point) - the intersection point of the surface and \(\mathbf{ray}\)
  • \(\mathbf{l}\) (light direction) - a unit vector pointing from the surface towards a light source, computed by normalizing the vector between the intersection point \(\mathbf{p}\) and the light source position \(\mathbf{l_s}\)

\[ \mathbf{l} = \frac{\mathbf{l_s - p}}{\norm{\mathbf{l_s - p}}} \]

  • \(\mathbf{v}\) (view direction) - a unit vector pointing from the surface towards the place the ray is emitted from, it's computed by normalizing the vector between the intersection point \(\mathbf{p}\) and the ray origin \(\mathbf{ray_{origin}}\)

\[ \mathbf{v} = \frac{\mathbf{ray_{origin} - p}}{\norm{\mathbf{ray_{origin} - p}}} \]

  • \(\mathbf{n}\) (surface normal) - a unit vector perpendicular to the surface at the point where the reflection is taking place
  • other characteristics of the light source and the surface depending on the shading model

References