Last time I talked about basic ambient and diffuse lighting.  This is good for perfectly matt surfaces, but every real surface has some degree of specularity, which is when light is reflected off a surface to give a shiny appearance.  You may not think of most objects as having a shiny surface, but it’s a significant part of the look of almost any surface.  If you want to see for yourself, take a look at this article which shows you how to split up the light from any object into specular and diffuse components.

#### Specular from perfect mirrors

Light reflects off specular surfaces in exactly the same way as a mirror (because mirrors are in fact just very flat surfaces with pure specular reflection, and no diffuse lighting).  If you have a point light source, you can work out the reflection direction by reflecting around the surface normal.

Mirror reflections

When looking in a mirror, you see the reflection of the light at the point where the reflected light direction goes directly into your eye. If you work backwards you can see that each point on the surface of the mirror will reflect light from a different point in the world. Mirrors are the simplest case because they are completely flat, meaning that light from a point in the world will only be reflected towards your eye from one point on the mirror.

#### Imperfect reflections

Most surfaces aren’t perfectly flat, and so don’t have perfect mirror reflections. If a surface isn’t perfectly flat it means that the normals around a given point will be pointing in lots of different directions. On average the normals will all point directly away from the surface, but if you look close enough at a rough surface (e.g. tarmac) you’ll see lots of surface facets pointing in different directions.

When we’re far enough away from the surface, all of these surface facets will look small enough that they occupy just one pixel on the screen, or one receptor in our eye. However, the distribution of the normals still affects how it appears to us.

Reflections from rough surfaces

What we see in the diagram is that one pixel on a rough surface actually reflects light from lots of different directions. The strongest reflections are from the ‘mirror’ reflection direction, with the reflection strength tailing off the further you get from this (because on average more of the surface facets will be pointing in the normal direction). What this means is that if the light source is at A then you’ll get a very bright reflection because lots of the light is reflected towards the eye. If the light is at B then there will still be some reflection but it will be weaker. This is why shiny surfaces have sharp, bright highlights and rough surface have blurry, dim highlights.

#### Implementation

To calculate the specular highlights from a light source at a given pixel, we first need to find out how much the angles all line up. We need three pieces of information at each pixel:

1. View vector. This is the vector from the pixel to the eye, in world space. It is calculated in the vertex shader and interpolated for each pixel.
2. Normal vector. This is part of the data for each vertex in the mesh, and interpolated for each pixel. Normal maps can also be used to provide more detail (I’ll talk about those another time).
3. Light vector. This is the vector from the light to the pixel, and for distant light sources is constant for all pixels. For near light sources this is calculated in the vertex shader, the same as for the view vector.

Now we need to find the halfway vector, which is half way between the view and the light vectors.  To find this, simply work out (lightVecviewVec) and renormalise.

Then take the dot product of the halfway vector and the normal, which will give you a value for how aligned the two are. This value will be 1 if the vectors are perfectly aligned, and zero if they are at 90 degrees. It should never be negative (as this would mean you are viewing a surface from behind it) but it’s possible due to the way things are interpolated sometimes.

The next part is to come up with some simple way of simulating the rough surfaces, in particularly how all the normals reflect light from different directions.  Because the dot product is between zero and one, the simplest way is to just raise it to a power – higher powers cause the value to drop off quicker the further the halfway vector is from the normal, leading to a sharper highlight. The full specular equation is then:

spec = pow(dot(normalize(lightVecviewVec), normalVec), specularPower) * lightColour

Varying the specular power will change the sharpness of the highlight. Here are examples of just the specular lighting with powers of 2 and 20:

Specular power of 2

Specular power of 20

Add this to the other lighting and you start to get a more believable image:

Specular, diffuse and ambient lighting

#### Better specular

The problem with this method of doing specular highlights is with the simplicity of just taking a dot product and raising it to a power.  This method is chosen because it looks “about right” and is very cheap to calculate. It isn’t based on anything fundamental about the way light behaves, and because of this it will never produce photorealistic images.

In a future post I’ll talk about Physically Based Rendering (PBR), which boils down to a more complicated method of doing specular highlights, but a method that is based in the real-world behaviour of lights and surfaces. It is an advanced technique and has only been widespread in games for the last few years, but it given much nicer results (and the cost of being a lot more expensive to calculate).  Anyway, I’ll come back to this in a future post.

Next time I’ll talk about normal mapping, which allows much more detail to be put into lighting models.