## N-Arbitrary Rotations -> Euler angle shortcut?

Hello all,

I've tried looking through the posts that have already been made regarding the topic of Euler angles, but I'm not sure if Euler angles are the route to take for my current problem. My project has stalled for about two weeks, so I decided to consult the experts here...

I have an object that will be rotated an arbitrary number of times around the three principals axes, X, Y and Z, in no particular order. What I need is to extract the outcome from the resulting matrix and apply the transformation, preferably using glRotatef. (I have a somewhat older version of OpenGL, v. 2.0 I believe).

First off, I found Eberly's function for retrieving the Euler angles, which I'll list here:

Code :
```
GLfloat x = 0;
GLfloat y = 0;
GLfloat z = 0;
y = asin(m_matrix[2][0]);
if(y < PI/2)
{
if(y > -PI/2)
{
x = atan2(-(float)m_matrix[2][1],(float)m_matrix[2][2]);
z = atan2(-(float)m_matrix[1][0],(float)m_matrix[0][0]);
}
else
{
// not a unique solution
x = -atan2((float)m_matrix[0][1],(float)m_matrix[1][1]);
z = 0;
}
}
else
{
// not a unique solution
x = atan2((float)m_matrix[0][1],(float)m_matrix[1][1]);
z = 0;
}
x = x*180/PI;
y = y*180/PI;
z = z*180/PI;```

The matrix is:
|[0][0] [0][1] [0][2] [0][3]|
|[1][0] [1][1] [1][2] [1][3]|
|[2][0] [2][1] [2][2] [2][3]|
|[3][0] [3][1] [3][2] [3][3]|

They are all GLfloat values.

As far as I know, the angles that are being extracted using this function are the correct angles. I tested it by making single axis rotations, one at a time. At least as far as those tests go, the angles are correct.

In either case, once I have the Euler angles, I implement the transformation of the object using:

Code :
```glPushMatrix();
glRotatef(x,1,0,0);
glRotatef(y,0,1,0);
glRotatef(z,0,0,1);

// ... draw object
glPopMatrix();```

For as long as my series of arbitrary rotations are restricted to one axis (for instance, a bunch of rotations around the z-axis, say), this Euler angle approach works. As soon as I start adding rotations around the other axis, the object rotates incorrectly.

The first question I'd like to ask is a conceptual one: Is this the reasonable route to take to achieve the goal? The goal, to (hopefully) be clear, is: perform n-number of arbitrary X,Y,Z rotations, pull the Euler angles from the final matrix, and then use the Euler's angles to achieve the net result of the n-number of arbitrary rotations.

Your help will be greatly appreciated!