Rotation of object around World Axis OpenGL
<p>I'm trying to make a controllable ball in OpenGL. I'm using my own matrix class to transform the object matrix, but I can't seem to get the Rotation right. I always end up with the ball rotating around the local axis.
This is how it looks right now <a href="https://gfycat.com/LongKindBassethound" rel="nofollow">https://gfycat.com/LongKindBassethound</a> . The long line are the local axis.</p>

<p>So when the ball moves forward the next side movement will be wrong. Theres a function in the matrix class that allows rotation around any axis:</p>

<pre><code>Matrix&amp; Matrix::rotationAxis(const Vector&amp; Axis, float Angle) {
const float Si = sin(Angle);
const float Co = cos(Angle);
const float OMCo = 1 - Co;
Vector Ax = Axis;
Ax.normalize();

m00= (Ax.X * Ax.X) * OMCo + Co;
m01= (Ax.X * Ax.Y) * OMCo - (Ax.Z * Si);
m02= (Ax.X * Ax.Z) * OMCo + (Ax.Y * Si);
m03= 0;

m10= (Ax.Y * Ax.X) * OMCo + (Ax.Z * Si);
m11= (Ax.Y * Ax.Y) * OMCo + Co;
m12= (Ax.Y * Ax.Z) * OMCo - (Ax.X * Si);
m13= 0;

m20= (Ax.Z * Ax.X) * OMCo - (Ax.Y * Si);
m21= (Ax.Z * Ax.Y) * OMCo + (Ax.X * Si);
m22= (Ax.Z * Ax.Z) * OMCo + Co;
m23= 0;

m30= 0;
m31= 0;
m32= 0;
m33= 1;

return *this;
}
</code></pre>

<p>I think with this I can take the world direction vectors and transform them to the local space of the object and then rotate around the result. I don't really know how to do that though (matrix of the ball * world vector? That doesn't work). I would really like to avoid quaternions, but if I can't do that I would appreciate suggestions in that direction too.</p>

<p>EDIT: More Info</p>

<p>The transforamtion Code. As you can see I tried different methods that all do the same... So no surprise there that it doesnt work.</p>

<pre><code>Matrix transM, rotX, rotZ;
rotationX = straight;
rotationZ = side;
if (velocity != Vector(0, 0, 0)) {
    velocity.X = -0.0005 * DeltaTime;
    velocity.X = clamp(velocity.X, 0, FLT_MAX);

    velocity.Z = -0.0005 * DeltaTime;
    velocity.Z = clamp(velocity.Z, 0, FLT_MAX);
}

velocity.X += speed * -side * DeltaTime;
velocity.Z += speed * straight * DeltaTime;
transM.translation(velocity.X, 0, velocity.Z);

if (velocity.Z != 0 || velocity.X != 0) {
    //http://mathworld.wolfram.com/EulerAngles.html
    //http://gamedev.stackexchange.com/questions/67199/how-to-rotate-an-object-around-world-aligned-axes

    Vector localAxisX =  m_Ball * Vector(1, 0, 0);
    Vector localAxisZ = m_Ball * Vector(0, 0, 1);
    rotX.rotationAxis(Vector(1, 0, 0), 0.5* M_PI * straight * DeltaTime);
    rotZ.rotationAxis(Vector(0, 0, 1), 0.5* M_PI * side * DeltaTime);
    //rotX.rotationX(0.5* M_PI * straight * DeltaTime * 3);
    //rotZ.rotationZ(0.5* M_PI * side * DeltaTime * 3);
    //Matrix fullRotation.rotationYawPitchRoll(Vector(0,  0.5* M_PI * straight * DeltaTime, 0.5* M_PI * side * DeltaTime));
    m_Ball = transM * m_Ball * (rotX*rotZ);
}
else {
    m_Ball = transM * m_Ball;
}
</code></pre>

<p>Draw code with my previous attempt trying to use glRotatef (obviously commented out right now)</p>

<pre><code>void Ball::draw(float DeltaTime) {
  glPushMatrix();
  glMultMatrixf(m_Ball);
  if(rotationX)
    glRotatef(0.5* M_PI * rotationX * DeltaTime, 1.0, 0.0, 0.0);
  if(rotationZ)
    glRotatef(0.5* M_PI * rotationZ * DeltaTime, 0.0, 0.0, 1.0);
  g_Model_ball.drawTriangles();
  glPopMatrix();
  drawAxis();
}
</code></pre>