Eye Coordinates?

Why are things like lighting normally done in eye coordinates? In my engine, I make sure to seperate the modelview matrix into a viewing matrix and a modelling matrix, and I do all my lighting calculations are done in world space, that is by applying only the modelling matrix.

This is a good question. It really depends on 
the space that's convenient for you. The 
important thing is to be very consistent in 
whatever space you choose.
For example, say you want to do your lighting in 
eye space. A typical calculation in any light 
model is the diffuse dot product
LdotN = (Le - Ve)  Ne
where Le is the light position, Ve is the vertex 
position, and Ne is the vertex normal, all in 
eye space. I've left out the normalization of 
Le - Ve for simplicity.
It is helpful to look at the transforms that put 
these vectors in eye space to begin with, then 
it will become clear why this works. 
To transform any vertex into eye space, we 
multiply it by the MV (Model and View matrix). 
To transform a normal, we multiply it by the 
inverse transpose of the same matrix. So our 
equation above would expand to
                 T                 T  -1T
LdotN = (Le - Ve) Ne = (CLw - CMVo) (CM) No
where C is the view matrix (camera C to avoid 
confusion with vertex V), M is the model matrix, 
Lw is the light position in world space, Vo is 
the vertex position in object space, and No is 
the vertex normal in object space.
Now, it really helps to know something about 
matrices at this point. 
LdotN = (Le - Ve) Ne                           eye space
                    T   -1T 
      = (CLw - CMVo) (CM)  No                  with transforms
            T   -1T           T   -1T
      = (CLw)((CM) No) - (CMVo)((CM) No)       transpose over sum
          T T -1T -1T       T T T -1T -1T
      = Lw C C   M   No - Vo M C C   M   No    reverse order law
          T  -1T       T
      = Lw  M   No - Vo No                     simplify
          -1         T	       
      = (M  Lw  - Vo) No                     simplify
(It's interesting to repeat this with everything 
in world space, you'll end up with the same 
This means that evaluating this equation 
is eye space is equivalent to moving the light
into object space and evaluating it there. This 
is intuitive really, you can move the object 
into world space with the light, or move the 
light into object space with the model, it's 
arbitrary. The important thing is to keep 
everything in the same space, or be very 
careful when mixing spaces. 
Hope this helps.


made a correction in a simplification

Yeah, I like keeping everything in “world space”, that is where (0, 0, 0) is the center of the “universe,” as opposed to “object space” where (0, 0, 0) is the “center of mass” or “eye space” where (0, 0, 0) is the center of the screen…

I’m well aware of the importance of keeping things consistent, though. If it works… why argue, right?

Right. I like world space too … it just smells better. :slight_smile: