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Index › Programming Questions & Help › OpenGL and 3D Libraries › 3D rotation of the coordinate system
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3D rotation of the coordinate system (Read 2851 times)
Pascal Wever
3D rotation of the coordinate system
Jul 20th, 2009, 3:42pm  
Hi everybody,
I would like to rotate the coordinate system (using rotateX, rotateY, rotateZ) so that a vector (generated from an accelerometer input) always points into the same direction (ie: down).

My initial thought was to figure out the angle between the input vector and the three axis, and basically 'undo' each with a counter rotations:

float angleX, angleY, angleZ;
PVector v = new PVector(2,4,3);

angleAroundX = atan2(v.y,v.z);
angleAroundY = atan2(v.x,v.z);
angleAroundZ = atan2(v.x,v.y);

rotateX(-angleAroundX);
rotateY(-angleAroundY);
rotateZ(-angleAroundZ);

After reading up on the problem online, I now believe that I can't do the rotation in three steps, since each step affects the basis of the next rotations. Since there isn't a single 'rotate(x_angle, y_angle, z_angle)' function, I am a bit at a loss.

Any thoughts and pointers are much appreciated.
Thanks // pascal
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dlp
Re: 3D rotation of the coordinate system
Reply #1 - Jul 21st, 2009, 6:00am  
What you'll need to do is take the cross product of your input vector
and the axis you want to point along the input vector.

Quote:
PVector axis = new PVector(0, 0, 1);
PVector crss = input.cross(axis);



The cross-product has the nifty property of being perpendicular to both your input vector and the z-axis. What this means is that you can rotate your coordinate system about crss, by the angle between your input and the z axis, and the two will then line up.

Quote:
float theAngle = PVector.angleBetween(input, axis);
crss.normalize();
rotate(-theAngle, crss.x, crss.y, crss.z);



Of course, you'll need this rotate function to rotate around an arbitrary axis (math from the OpenGL Red Book):
Quote:
void rotate (float r, float x, float y, float z) {
 float d = sqrt(x*x+y*y+z*z);
 float a = x/d, b = y/d, c = z/d;
 float t[][]={{a*a,a*b,a*c},{b*a,b*b,b*c},{c*a,c*b,c*c}};
 float s[][]={{0,-c,b},{c,0,-a},{-b,a,0}};
 float cosr=cos(r);
 float sinr=sin(r);
 float m[][]={{1,0,0},{0,1,0},{0,0,1}};
 for (int i=0; i<3; i++) {
    for (int j=0; j<3; j++) {
       m[i][j] = t[i][j] + cosr*(m[i][j]-t[i][j])+sinr*s[i][j];
    }
 }
 
 applyMatrix (m[0][0],m[0][1],m[0][2],0,
                     m[1][0],m[1][1],m[1][2],0,
                     m[2][0],m[2][1],m[2][2],0,
                     0,0,0,1);
}

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davbol
Re: 3D rotation of the coordinate system
Reply #2 - Jul 21st, 2009, 8:07am  
dlp wrote on Jul 21st, 2009, 6:00am:
Of course, you'll need this rotate function to rotate around an arbitrary axis (math from the OpenGL Red Book):


I think it may be missing from the reference, but an arbitrary axis rotate *IS* present in the Processing API, no need to roll your own.  :)
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Pascal Wever
Re: 3D rotation of the coordinate system
Reply #3 - Jul 21st, 2009, 10:47am  
This was exactly what I needed!
Thank you very much. All is working now.
Best regards // pascal
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dlp
Re: 3D rotation of the coordinate system
Reply #4 - Jul 21st, 2009, 7:30pm  
davbol wrote on Jul 21st, 2009, 8:07am:
dlp wrote on Jul 21st, 2009, 6:00am:
Of course, you'll need this rotate function to rotate around an arbitrary axis (math from the OpenGL Red Book):


I think it may be missing from the reference, but an arbitrary axis rotate *IS* present in the Processing API, no need to roll your own.  :)


Heh, oops. I've been using straight JOGL for so long I forget what the built in stuff does. :)
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alexarjuna
Re: 3D rotation of the coordinate system
Reply #5 - Jul 22nd, 2009, 8:05am  
I'm looking to do something similar (so that the Z axis always points to the camera) and I'd like to borrow this function. Can you give an example of what rotating around an arbitrary axis would look like using just the Processing language? (OpenGL and I are having a disagreement)

Much obliged - this could save me a huge headache.
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dlp
Re: 3D rotation of the coordinate system
Reply #6 - Jul 23rd, 2009, 2:25pm  
The built-in function works just like the function I've posted (which, by the way, doesn't use OpenGL anyways, the math is just from an OpenGL reference book).

rotate(float theta, float x, float y, float z)

Where theta is angle in radians, and x, y, and z are components of the arbitrary normalized vector to rotate about.
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