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# how to rotate vector? been looking for two days

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I've been looking for two days, and before that, I came up with two ways that I cant preform corectly, and threw out the code for. Does anybody have C++ code for this?

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What do you want to use as the rotation to rotate the vector by? A matrix? a quaternion? a set of euler angles? An exponential map?

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anything including quaternions. Euler Angles might work, because im making modular stuctures that are just placed about, theres no physics needed right now on them and ill still be happy.

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For quaternions: vr = q * vo * q-1, where vo is the vector "transmogrified" into a pseudo-quaternion by adding a 0 as the fourth element.

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i think i understand that.

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Using regular trig, you can derive that if (a , b) is your original vector and t is the angle you want to rotate it by (anticlockwise), then to rotate around the origin you can use:

x = a*cos(t) - b*sin(t)
y = a*sin(t) + b*cos(t)

to obtain a new vector (x , y).

That may be wrong, because I just derived it myself on a scrap bit of paper.

I imagine for a 3d vector (a, b, c), if that's what you want, then you can use that as a rotation around the z axis, with the c value staying constant, for rotation around the y axis you'd want to subsitute y for z and b for c and keep b constant, and for rotation around the x substitute x for z and a for c and a is constant.

That may be completely wrong though, like I say. It shouldn't be too hard to derive the matrices from here, if you want them.

 ignore the stuff after rotation around z; I got it wrong.

Rotation around the y is:
x = c*sin(t) + a*cos(t)
z = c*cos(t) - a*sin(t)
and y = c

and to rotate around the x:
y = b*cos(t) - c*sin(t)
z = b*sin(t) + c*cos(t)
and x = a

Must remember to think rather than guess in future!

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I found some code in a vector class at www.planet-source-code.com that seems to involve all the required techniques, and it works well for me, and i know it works well because im rotating a whole collision structure with it, and so for placing objects around in different orientations, its fine, but could i run into the "gimbal lock" that ive heard about before?

heres the function that rotates an input vector by the Y axis by an input Degree:

#define DAX_PI 3.141592653589793238462643383279
#define PiOver180 DAX_PI/180
#define d180OverPi 180/DAX_PI

{
Vector3 _Vec0;
double sinCalc = (double)sin(_Angle * PiOver180);
double cosCalc = (double)cos(_Angle * PiOver180);

_Vec0.x = (_Vec1.x * cosCalc) + (_Vec1.z * sinCalc);
if((_Vec0.x < .00000000001) && (_Vec0.x > -.00000000001))
_Vec0.x = 0.0;
_Vec0.y = _Vec1.y;
_Vec0.z = (_Vec1.z * cosCalc) - (_Vec1.x * sinCalc);
if((_Vec0.z < .00000000001) && (_Vec0.z > -.00000000001))
_Vec0.z = 0.0;
return (_Vec0);
}

Beacause i want my robot to throw the scenery around with out having a rotation lock up on me.

Oh and to get the original source code vector class, search for MultiVector at www.planet-source-code.com.

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I believe gimbal lock is when your forward vector is parallel to your up vector? Actually I guess if any of your axes are parallel that would be bad. The way I usually combat this is simply checking to see if my forward vector dotted with my up vector is too close to 1 or -1. If it is, I rotate back by the amount I just tried to rotate...

Here's a quick example
void RotateZ(float fRadians){        // do all your normal rotation stuff    // now we're going to check to make sure our axes are ok    Vector globalUp(0.0f, 1.0f, 0.0f);    // this is just a guess, you may need to play around    // to find which epsilon value works the best for your case    const float fEps = 1e-3;    // just take the absolute value because -1 is just as     // bad as 1 in this case...    float dotValue = fabs( Dot( camera.ZAxis(), globalUp) );    // if our two axes are too close, rotate the opposite amount    // to get back to where we started... This could be done differently    // perhaps by using temp variables to calculate the rotations    // and then assigning them to the real variables ONLY if this statement    // isn't true-- you get the idea...    if( 1.0f - dotValue < fEps )    {       RotateZ(-fRadians);    }

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