I've been looking around the internet to get the formula for computing's the diffuse value of a given pixel in a raytracer (where a ray intersection has occurred of course).
The examples I found all involve multiplying colours by other colours. Nvidia's formula is as follows:
diffuse = Kd x lightColor x max(N · L, 0)
where:
- Kd is the material's diffuse color
- lightColor is the color of the incoming diffuse light
- N is the normalized surface normal
- L is the normalized vector toward the light source
- P is the point being shaded
The formula doesn't seem too hard to me, but when trying to program it I find that Kd x lightColour is the multiplication of 2 RGB values. This is confusing to me as, unless it's a case of just multiplying both R, G and B values together, there's no way to multiply values like this.
Similarly, the specular formula requires the RGB value to be raised to a power equivalent to the shininess factor of the material, which is again a multiplication of a 3-component data type by itself.
This is probably me just getting confused with the maths, but if someone could clear this up it'd be greatly appreciated.
Kd x lightColour is a component-wise multiplication:
a d a*d
[ b ] x [ e ] = [ b*e ]
c f c*f
In the formula for specular illumination (assuming you are talking about the phong or blinn-phong illumination model), there is no power operation on vectors.
specular = ks x lightcolor x (R · V)^a
The result of R · V is a float, thus the power is only applied to a single number.