In this tutorial, you have learned the following:

Specular lighting represents direct, mirror-like reflections from a surface. Specular highlights are mirror-like reflections directly from a light source. Adding weak specular highlights to even rough surfaces can increase visual realism.

The microfacet model of specular reflection means that, for a given surface area, there are many mirror-like surfaces. Each microfacet reflects perfectly in its direction. The average of the microfacets

The Phong and Blinn models of specular reflection use a power function based on how close the viewer is to perfect reflection to approximate a microfacet distribution.

A Gaussian statistical distribution can be used to more accurately model the distributions of microfacets on a surface.

Try doing these things with the given programs.

Change the shaders to use the diffuse color as the specular color. You may need to drop the specular color somewhat to keep from over-brightening the scene. How this all looks will be particularly evident with the colored cylinder.

As you might guess, this is far from the end on specular reflections and specular highlights. Accurately modelling specular reflection is very difficult; doing so while maintaining high performance is even moreso.

If you are interested in more accurate models of specular highlights, there is the Beckmann distribution. This is a particular statistical distribution of microfacets that is more physically based than a Gaussian distribution. It may or may not be a bit more computationally expensive than Gaussian; Beckmann lacks the inverse cosine, but has more other math to it. The two do have a roughness factor that has the same range, (0, 1], and the roughness has the same general meaning in both distributions.

If you want to go even farther, investigate the Cook-Torrance model of specular reflection. It incorporates several terms. It uses a statistical distribution to determine the number of microfacets oriented in a direction. This distribution can be Gaussian, Beckmann, or some other distribution. It modifies this result based on a geometric component that models microfacet self-shadowing and the possibility for multiple interreflections among a microfaceted surface. And it adds a term to compensate for the Fresnel effect: an effect where specular reflection from a surface is more intense when viewed edge-on than directly top-down.

`vec ` | vec I, |

vec N`)` ; |

Computes the vector that would be reflected across the normal `N`

from an incident vector `I`

. The vector result will be normalized
if the input vectors are normalized. Note that `I`

vector is the
vector *towards* the surface.

`vec ` | vec X, |

vec Y`)` ; |

Raises `X`

to the power of `Y`

, component-wise.
If a component of `X`

is less than 0, then the resulting value is
undefined. If `X`

is exactly zero, and `Y`

is less
than or equal to 0, then the resulting value is undefined.

`vec ` | vec X`)` ; |

Returns the inverse cosine of `X`

, component-wise. This returns
the angle in radians, which is on the range [0, π]. If any component of
`X`

is outside of the [-1, 1] range, then that component of the
result will be undefined. This is because the cosine of a value is always on [-1,
1], so the inverse-cosine function cannot take values outside of this range.

`vec ` | vec exponent`)` ; |

Returns the value of e^{exponent}, component-wise.