Quaternion Rotations

A77e71b962cd6c7c3b885f0488452f1f
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tobeythorn 101 Nov 13, 2008 at 02:30

I tried quaternion rotations a long time ago, and never got it working. I’m trying it again, from scratch, but seem to be having exactly the same issue: not-so-circular orbits. As a test, I’m incrementing an angle theta each frame and then each frame, using quaternions, rotate a start point by that angle and set a mesh’s position as that point. What I want to happen is to see the mesh loop around in circles, depending on which axis i rotate about. I figure this way, I can’t possibly have problems with imprecisions accumulating. The thing is, my orbits look more like >’s or weird double loops. I’ve spent days days checking and rechecking, and am quite frustrated. If you aren’t familiar with Objective-C, the notation is [object method(well, message really): parameters].

Here is my relevant code:

//Rotation, done each frame

theta = theta+0.05;
    ZQuaternion* newRotation = [[ZQuaternion alloc] initWithValues: cos(theta/2.0): sin(theta/2.0): 0.0: 0.0];
    //ZQuaternion* newRotation = [[ZQuaternion alloc] initWithValues: cos(theta/2.0): 0.0: sin(theta/2.0): 0.0];
    //ZQuaternion* newRotation = [[ZQuaternion alloc] initWithValues: cos(theta/2.0): 0.0: 0.0: sin(theta/2.0)];
    
    //point to rotate
    ZQuaternion* qposition = [[ZQuaternion alloc] initWithValues: 0.0: 0.3: 0.1: 0.6]; 
    ZLeaf* mesh0 = [rootNode childAt: 0];
    ZVector3* position = [mesh0 localPosition];
    ZQuaternion* newQLocation = [newRotation multiply: [qposition multiply: [newRotation conjugate]]];
    position.x = newQLocation.x;
    position.y = newQLocation.y;
    position.z = newQLocation.z;

//Quaternion Class:

#import "zquaternion.h"

@implementation ZQuaternion
@synthesize w;
@synthesize x;
@synthesize y;
@synthesize z;

-(id) initWithValues: (float) a: (float) b: (float) c: (float) d {
    if ((self = [super init])) {
        w = a;
        x = b;
        y = c;
        z = d;
    }
    return self;
}

-(float*) getCArray {
    float* cArray = malloc(4*sizeof(float));
    *(cArray+0) = w;
    *(cArray+1) = x;
    *(cArray+2) = y;
    *(cArray+3) = z;
    return cArray;
}

-(ZQuaternion*) conjugate   {
    return [[ZQuaternion alloc] initWithValues: w: -x: -y: -z];
}

-(void) unitize {
    float magnitude = sqrt( (w*w) + (x*x) + (y*y) + (z*z) );
    w /= magnitude;
    x /= magnitude;
    y /= magnitude;
    z /= magnitude;
}

-(ZQuaternion*) multiply: (ZQuaternion*) q  {
    float a = (w*q.w) - (x+q.x) - (y*q.y) - (z*q.z);
    float b = (w*q.x) + (x*q.w) + (y*q.z) - (z*q.y);
    float c = (w*q.y) - (x*q.z) + (y*q.w) + (z*q.x);
    float d = (w*q.z) + (x*q.y) - (y*q.x) + (z*q.w);
    return [[ZQuaternion alloc] initWithValues: a: b: c: d];
}
@end

Thanks for your help,
-Tobey

3 Replies

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A8433b04cb41dd57113740b779f61acb
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Reedbeta 167 Nov 13, 2008 at 03:05

You’ve got a typo in your multiply routine:

float a = (w*q.w) - (x+q.x) - (y*q.y) - (z*q.z);

should have a * in the second term, not a +.

Besides that, all your code looks good to me.

A77e71b962cd6c7c3b885f0488452f1f
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tobeythorn 101 Nov 13, 2008 at 03:35

Reedbeta,
You are awesome, and much less lexdistic than I. I can’t freaking believe I didn’t catch that! It works perfectly now.

A8433b04cb41dd57113740b779f61acb
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Reedbeta 167 Nov 13, 2008 at 04:24

Glad to hear. Sometimes you just need a second pair of eyes; spend too much time looking at a piece of code and you start seeing what you think is there instead of what’s actually there. Happens to everyone. ;)