vlen is the obvious way to measure distances in quake, but most of the time the result isn’t used directly, just compared to another distance. If you only use vlen in an inequality you can skip the function entirely.
The bit of maths you need for this trick is the dot product. The dot product is a function which takes two vectors and outputs a float. For vectors called a and b, the output is
a_x * b_x + a_y * b_y + a_z * b_z;
We can calculate it in QuakeC in a single operation:
a * b;
A bit of maths tells us the dot product is always equal to
vlen(a) * vlen(b) * cos(theta)
where theta is the angle between the vectors a and b.
What interests us today is taking the dot product of a vector with itself, which gives us
vlen(a) * vlen(a) * cos(0)
Since cos(0) is equal to 1, the dot product a * a is equal to vlen(a) * vlen(a) and we can swap one for the other.
If we started with code like
if(vlen(a) < 120)
PopUp(self);
Because we know vlen is never negative, we can safely change it to this:
if(vlen(a) * vlen(a) < 120 * 120)
PopUp(self);
To finish this off, we can do this:
if(a * a < 120 * 120)
PopUp(self);
I like leaving the constant on the right like that, so it’s easy to read what distance we’re actually comparing to – but does it matter for performance? The answer depends on which compiler you use. The original compilers would compute 120 * 120 each time, current ones will perform the multiplication at compile time, so there’s no impact on performance.
