scott wrote:
>> Because you can use it to determine which side of the line a point is on?
> 
> How?
> 
> Example: Line through (0,0) and (0,1), and points either side of the 
> line at (1,0) and (-1,0)

Suppose you have a line from point A to point B. Compute the vector AB, 

the dot product V . A and call it k.

Which side of the line is point X on? Well, take the dot product V . X, 
and subtract k. The result is negative on one side, positive on the 
other, and zero if X is on the line itself (or at least, parallel to it).

...so basically, it's a ray/plane intersection test, except the "plane" 
is a 2D slide - a line.

A = (0,0)
B = (0,1)
AB = (0,1) - (0,0) = (0,1) [already unital]
V = (0,1) * {(0,-1), (1,0)} = (-1,0)
k = (0,0) . (-1,0) = 0

X = (1,0)
X . V - k = (1,0) . (-1,0) - 0 = -1

Y = (-1,0)
Y . V - k = (-1,0) . (-1,0) - 0 = +1

QED.

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