In the previous post on reflections we covered the basic characteristics of direct (specular) and diffuse reflections. In this post I'd like to address three characteristics of direct reflections: direction, size, and intensity.
Direct reflections have a very definite sense of direction. In fact, on a plane reflective surface, the angle at which the light approaches the surface is exactly the same as the angle at which it leaves. This principle is most often stated as: the angle of incidence equals the angle of reflection. It can be extended to non-planar reflective surfaces using the tangent to the surface at the point of reflection. All of this is shown in the diagram below. This principle is very important and explains, among other things, why a light's placement can have a big impact on its apparent strength.
The size of the reflection will vary based on the curvature of the reflective surface. Compared to a reflection on a plane surface, convex surfaces will yield a smaller reflection and concave surfaces a larger one. For convex surfaces, such as spheres, a smaller radius of curvature will yield a smaller reflection. This is shown in the diagram below, where the grayed areas represent the reflection. The implications of this principle are numerous, and it explains why, for instance, a specular highlight on one's nose is much smaller than the one on the forehead.
The intensity of a reflection depends not only on the intensity of the source, but the size of the reflection. For instance, in the diagram above, the smaller reflection on the smaller sphere will be brighter than the reflection on the larger sphere. That is because both must reflect the same amount of energy, but must do so over differing surface areas. And, this explains why the that small specular highlight on the nose is brighter than corresponding hot spots on the cheeks or the forehead.
The next post will be a quick one on diffuse reflection, and then I'll try to bring it all together by applying these principles to real-world applications and examples.