Specular Reflection

A second surface type is called a specular reflector. When we look at a shiny surface, such as polished metal or a glossy car finish, we see a highlight, or bright spot. Where this bright spot appears on the surface is a function of where the surface is seen from. This type of reflectance is view dependent.

At the microscopic level a specular reflecting surface is very smooth, and usually these microscopic surface elements are oriented in the same direction as the surface itself. Specular reflection is merely the mirror reflection of the light source in a surface. Thus it should come as no surprise that it is viewer dependent, since if you stood in front of a mirror and placed your finger over the refelection of a light, you would expect that you could reposition your head to look around your finger and see the light again. An ideal mirror is a purely specular reflector.

In order to model specular reflection we need to understand the physics of reflection. Reflection behaves according to Snell's laws which state:

• The incoming ray, the surface normal, and the reflected ray all lie in a common plane.
• The angle that the reflected ray forms with the surface normal is determined by the angle that the incoming ray forms with the surface normal, and the relative speeds of light of the mediums in which the incident and reflected rays propogate according to the following expression.

  Reflection is a very special case of Snell's Law where the incident light's medium and the reflected rays medium is the same. Thus we can simplify the expression to:

  

  Snell's law, however, applies only to ideal refelctors. Real materials, other than mirrors and chrome tend to deviate significantly from ideal reflectors. At this point we will introduce an empirical model that is consistent with our experience, at least to a crude approximation.

  In general we expect most of the reflected light to travel in the direction of the ideal ray. However, because of microscopic surface variations we might expect some of the light to be reflected just slightly offset from the ideal reflected ray. As we move farther and farther, in the angular sense, from the reflect ray we expect to see less light reflected.

  

  One function that approximates this falloff is called the Phong Illumination model. This model is purely empirical and has no physical basis, yet it is one of the most commonly used illumination models in computer graphics.

  

  The diagram below shows the how the phong reflectance drops off based on the viewers angle from the reflected ray for various values of n_shiny.

  We can compute the cos() term of Phong's specular illumination using the following relationship. The V vector in the unit vector in the direction of the viewer and the R mirror reflectance direction. The vector R can be computed from the incoming light direction and the surface normal as shown below. The following figure illustrates this relationship.

  Another approach for computing Phong's illumination uses the following equation:

  In this equation the angle of specular dispersion is computed by how far the surface's noraml is from a vector bisecting the incoming light direction and the viewing direction. On your own you should consider how this equation and the previous equation differ.

  The following spheres illustrate specular reflections as the direction of the light source and the coefficient of shineyness is varied.