Shading with a directional light source

A core component of a shading equation is the vector that points from the surface location towards the light source (s in previous examples). For lights that are extremely far away, there is very little variation in this vector over the surface of an object. In fact, for very distant light sources, the vector is essentially the same for all points on a surface. (Another way of thinking about this is that the light rays are nearly parallel.) Such a model would be appropriate for a distant, but powerful, light source such as the sun. Such a light source is commonly called a directional light source because it does not have a specific position, only a direction.

Note

Of course, we are ignoring the fact that, in reality, the intensity of the light decreases with the square of the distance from the source. However, it is not uncommon to ignore this aspect for directional light sources.

If we are using a directional light source, the direction towards the source...