3d vectors - calculating unit vectors?

[charlie_says]

Hi, I got an idea for a game, which requires a rotating cube.
I managed to get the cube rotation working quite well, until i realised that there was a problem with it (called gimble lock) which to those of you who may have looked into this will know means the order of the rotations will affect the outcome.
Solution to this problem was to use matrices. Job done, or so I thought until I realised that this rotation wasn't doing quite what I needed either - the rotation being through the world axes, and I needed the rotation through the local axes.
So, I part code a solution (I'd even say I've done the hard bit) but for the life of me I can't work out the last part.
UNIT VECTORS
Can anyone tell me how to calculate a Unit vector from a global x, y and z rotation? (and do I need 3 slightly different iterations for the 3 axes rotations)

[Ed Mack]

What do you mean by making a vector out of a rotation? Do you mean the axis of rotation?

You may also want to look into Quaternions, they are another good solution to the Gimble lock problem

[charlie_says]

well, as i understand it, and my a level maths was over half a lifetime ago, i need to represent the local axis of rotation by a unit vector. Even though I use the same function for each of the X,Y and Z rotations I imagine that I also have to update the unit vector after each rotation calculation.
I have this

code:

---

function rotArbAx(deg, X, Y , Z) {

	deg *= (Math.PI/180);

	SIN = Math.sin(deg);

	COS = Math.cos(deg);

	t = 1-Math.cos(deg);

	//

	arb = new Array();

	//

	arb[0] = [t*Math.pow(X,2)+COS, t*X*Y-SIN*Z, t*X*Z+SIN*Y, 0];

	arb[1] = [t*X*Y+SIN*Z, t*Math.pow(Y,2)+COS, t*Y*Z-SIN*X, 0];

	arb[2] = [t*X*Z-SIN*Y, t*Y*Z+SIN*X, t*Math.pow(Z,2)+COS, 0];

	arb[3] = [0, 0, 0, 1];

	//

	return arb;

}

---

and I call it like so

code:

---

transZRot = transform.rotArbAx(z, 0, 0, 1);

transYRot = transform.rotArbAx(y, 1, 0, 0);

transXRot = transform.rotArbAx(x, 0, 1, 0);

---

in this case where x,y and z are euler rotations (or if that's not the correct description, they rotate from the current position.)
In the function the rotational axis is represented by X, Y, Z and with the numbers as they stand I get rotation through the global axes, so I'm guessing that if instead of 0s and 1s being pushed to the function I would get rotation thru the local axes. BUt i can't figure it out, I'm pretty sure from the stuff I've read that it should be an iteration of sqrt(x^2+y^2+z^2) = 1
I do have the global rotations (which I accumulate from the euler figures_ stored in a separate variable, so I do know where the cube has been rotated to in order to calculate the numbers, but I'm just bangin my head against a wall.

[charlie_says]

I've tried, tried again and still not succeded, so here is the fla of where I'm at.
I'm pretty sure it's not far off the money, but I genuinely can't see what's wrong with this - if anyone cares for a quick look then please do. In case it's not clear I want to rotoate the cube through it's own axes of rotation (i.e through the faces)

Charlie

ps. In order to try to understand what was going wrong, in the top left corner you will see a representation of the axes - i think it may indicate (to someone) what is wrong, but I also think there is a problem with the way this is projected (try it you'll see.)

pps. in order to be honest this example is not completely my own, a lot of it is based on a FriendsOfEd example - i have left a lot of their original code in (i.e. single rotation about an axis) for transparency even though it isn't used, and there is also a good bit of my own added.

[Incrue]

I gess the solution is using quaternions, heard somewhere that with matrices you still have gimbal loop
There are a article by colin moock somewhere in the macromedia's site about it...is something like 'creating 3d classes' or wharever
This stuff is complicated as hell...i would like to understand but colin moock dont know how to explain