That's why integrals are boring. My question was a real game math one, the answer is also searchable. If you do look it up, be sure to understand the pieces of the puzzle, because you can build many things with that math.

This here is why I hate doing math.

Computers do the tedious parts. All you have to do is ask it the right questions.

I...half agree.

Integrals are boring.

Derivatives, however, are quite fun, and analyzing them can tell you a lot about how games are designed. Unfortunately, such math doesn't really help with LoL, because everything that scales, scales either linearly (such as base stats and their rate of change against champion level), or scales irregularly (such as end stats, the function of base + bonus from items/masteries/runes). Linear scaling is boring (though admitedly effective in LoL's setup), and irregular scaling, especially this kind of irregular scaling, is extremely difficult to analyze.

For example, as great as Final Fantasy 7 is, there's a pretty huge fallacy in its damage over play-time scaling: Physical damage scales as a roughly-cubic function of character level, while magic damage scales linearly. As a result, by the time most players finally have Ultima, its damage pales in comparison to basic attacks, especially 2xCut and 4xCut. This is partially solved via scaling spellpower values, but it's also the reason why you can overload physical damage over the MAX_INT value, but not magic damage.

Math degrees + insomnia - intellect loss because it's almost 3AM =

From L looking at P, we have vector A=(1/|P-L|) (P-L) where A is for at, and |P-L| is the length of vector P-L
let zHat be a unit vector in the up direction
so right is A x zHat, where the x is vector cross product.

Although if you're being fully general and the camera and location aren't in the same z plane, you need to normalize your right vector.

Ahem Griftix...
http://www.youtube.com/watch?v=m_mDTLphIVY

Very close, your UP isn't orthogonal to A and your right vector. You clearly get the idea though, so I'll chalk it up to poor question wording.

Now...

Find the distance from a point P to a line segment defined by end points L1 and L2. You do this and you are half way to many capsule intersection tests

Ahem yourself. http://www.progmofo.org/

Well played...

Under the assumption that P = (0,0,0) and L = (x,0,0) to keep all math simple, your three vectors are as follows:

Look At: <-x,0,0>, or <-1,0,0> for the unit vector (AKA -i)
Up: <0,0,z>, or <1,0,0> for the unit vector (AKA j)
Right: <0,y,0>, or <0,1,0> for the unit vector (AKA k)

From here, it should just be a "simple coordinate transformation" from my system to your cameras. QED :P

(For anyone confused as to what I did, I assumed point L was my eyes, and P was an object on a screen or monitor. Up was the top of the monitor, and right was the right of the monitor. the "simple coordinate transformation" is the entire question that was just asked, getting us nowhere.)