Define: Specular Lighting

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Background

When we calculated ambient lighting the only factor was the strength of light. Then we progressed to diffuse lighting which added the direction of light into the equation. Specular lighting includes these factors and adds a new element into the mix - the position of the viewer. 

The idea is that when light strikes a surface at some angle it is also reflected away at the same angle (on the other side of the normal). If the viewer is located exactly somewhere along the way of the reflected light ray it receives a larger amount of light than a viewer who is located further away.

The end result of specular lighting is that objects will look brighter from certain angles and this brightness will diminish as you move away. The perfect real world example of specular lighting is metallic objects. These kinds of objects can sometimes be so bright that instead of seeing the object in its natural color you see a patch of shining white light which is reflected directly back at you. However, this type of quality which is very natural for metals is absent in many other materials (e.g. wood). Many objects simply don't shine, regardless of the where the light is coming from and where the viewer is standing. The conclusion is that the specular factor depends more on the object, rather than the light itself.

Let's see how we can bring in the viewer location into the calculation of specular light. Take a look at the following picture:

There are five things we need to pay attention to:

• 'I' is the incident light that hits the surface (and generates the diffuse light).

• 'N' is the surface normal.

• 'R' is the ray of light which is reflected back from the surface. It is symmetric across the normal from 'I' but its general direction is reversed (it points "up" and not "down").

• 'V' is the vector from the point on the surface where the light hits to the 'eye' (which represents the viewer).

• 'α' is the angle which is created by the vectors 'R' and 'V'.

We are going to model the phenomenon of specular light using the angle 'α'.

The idea behind specular light is that the strength of the reflected light is going to be at its maximum along the vector 'R'. In that case 'V' is identical to 'R' and the angle is zero.

As the viewer starts moving away from 'R' the angle grows larger. We want the effect of light to gradually decrease as the angle grows. By now you can probably guess that we are going to use the dot product operation again in order to calculate the cosine of 'α'. This will serve as our specular factor in the lighting formula.

When 'α' is zero the cosine is 1 which is the maximum factor that we can get. As 'α' is decreased the cosine becomes smaller until 'α' reaches 90 degrees where the cosine is zero and there is absolutely no specular effect. When 'α' is more than 90 degrees the cosine is negative and there is also no specular effect. This means that the viewer is absolutely not in the path of the reflected ray of light.

To calculate 'α' we will need both 'R' and 'V'. 'V' can be calculating by substracting the location of the point where the light hits in world space from the location of the viewer (also in world space). [LightPos]Since our camera is already maintained in world space we only need to pass its position to the shader. [FragmentPos]Since the image above is simplified, there is a single point there where the light hits. In reality, the entire triangle is lit (assuming it is facing the light). So we will calculate the specular effect for every pixel (same as we did with diffuse light) and for that we need the location of the pixel in world space. This is also simple - we can transform the vertices into world space and let the rasterizer interpolate the world space position of the pixel and provide us the result in the fragment shader. Actually, this is the same as the handling of the normal in the previous tutorial.

[Angle-of-Reflection]The only thing left is to calculate the reflected ray 'R' using the vector 'I' (which is provided by the application to the shader). Take a look at the following picture:

Remember that a vector doesn't really have a starting point and all vectors that have the same direction and magnitude are equal. Therefore, the vector 'I' was copied "below" the surface and the copy is identical to the original. The target is to find the vector 'R'. Based on the rules of vector addition 'R' is equal to 'I'+'V'. 'I' is already known so all we have to do is find out 'V'. Note that the opposite of the normal 'N' also appears as '-N' and using a dot product operation between 'I' and '-N' we can find the magnitude of the vector which is created when 'I' is projected on '-N'. This magnitude is exactly half the magnitude of 'V'. Since 'V' has the same direction as 'N' we can calculate 'V' by multiplying 'N' (whose length is 1.0) by twice that magnitude. To summarize:

Now that you understand the math it is time to let you in on a little secret - GLSL provides an internal function called 'reflect' that does exactly this calculation. See below how it is used in the shader.

Let's finalize the formula of specular light:

We start by multiplying the color of light by the color of the surface. This is the same as with ambient and diffuse light. The result is multiplied by the specular intensity of the material ('M'). A material which does not have any specular property (e.g. wood) would have a specular intensity of zero which will zero out the result of the equation. Shinier stuff such as metal can have increasingly higher levels of specular intensity. After that we multiply by the cosine of the angle between the reflected ray of light and the vector to the eye. Note that this last part is raised to the power of 'P'. 'P' is called the 'specular power' or the 'shininess factor'. Its job is to intensify and sharpen the edges if the area where the specular light is present. 

The above picture shows the effect of the specular power when it is set to 1:

the aboveshows a specular exponent of 32:

The specular power is also considered as an attribute of the material so different objects will have different specular power values.

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