Short quaternions guide

[rich_27]

I did complex numbers early last school year, and it doesn't relate that much to quaternions...

Fizyk, when did you learn of them?

[Fizyk]

About quaternions? I have first heard of them a long time ago, they were briefly mentioned in a magazine about science for children. Also at the university they were mentioned once, but only as an interesting thing. So, almost all of my knowledge about quaternions I got from the internet They are not something that is taught in schools, because they are pretty much useless, the only field where they are really of use is 3D graphics.

[Remscar]

It helped my learn quaternions.

[Crenabea]

What are quaternions?

To explain it well, we need to start at what are complex numbers.
The regular numbers, that everyone is used to, are the real numbers. But they have a drawback - there are equations that don't have solutions in real numbers, like x^2=-1. There is no real number that squared gives -1. That's why people invented complex numbers. A number that when squared gives -1 is i, called an imaginary unit.

A complex number is a number like a+bi, where a and b are real. They have many great properties, but this is not the matter of this tutorial. To give you a quick feel how calculations on complex numbers work, here are a few examples:

Assume we have two complex numbers, z = a+bi and w = c+di (a, b, c, d are real). Then:

• z+w = a+bi + c+di = (a+c) + (b+d)i
• z*w = (a+bi)(c+di) = ac + adi + bic + bidi = ac + adi + bci - bd = (ac-bd)+(ad+bc)i
• z/w = (a+bi)/(c+di) = [(a+bi)(c-di)]/[(c+di)(c-di)] = [(ac+bd)+(bc-ad)i]/[(cc+dd)+(cd-cd)i] = [(ac+bd)+(bc-ad)i]/(c^2+d^2)

So the i is the imaginary and the product of a + b is being multiplied by the imaginary number. Is the imaginary number some number that will always solve things like x^2 = -1?

[Fizyk]

So the i is the imaginary and the product of a + b is being multiplied by the imaginary number

Only b is multiplied by i. It's a+bi, not (a+b)i (though (a+b)i is a complex number too, but it has real part equal to 0).

Is the imaginary number some number that will always solve things like x^2 = -1?

This is the definition of i: i is such a number, that i^2=-1. So yes, it will always solve things like x^2=-1.

[feha]

Is there any way to calculate exactly what constants is needed? I have trouble making it accurate enoguh to hit a popcan (not moving) with 100% accuracy over the whole map.

[Fizyk]

There are some ways to do that, but they are pretty complicated. Also, in most cases it will spazz out before the constants are enough to hit the popcan across the map. What you need is probably adding the I term to the code - if your turret is mounted to something, the mass center of the contraption is slightly off and it makes the turret aim a bit down; the I term can correct that (see my PID tutorial for details, I hope it will help).

[feha]

The thing is parented, and it is not that it aims slightly below my target, but it shakes a little (the sattelite is orbiting a planet probably the reason), which from shakuras to ninurta (planets in opposite corners) results in the hit pos being around 10 units in all directions from the actualy target position.

[Fizyk]

Sounds like you have too high proportional coefficient, and/or too low derivative coefficient. Try increasing the first and decreasing the second.

[Mendax]

wow, this guide helped alot. thanks.