OpenGL 2.1 rotation , Gimball lock

Question

I'm working on a little app for a school project , which should be manipulating 3D objects. And i'm stuck with the rotation , as i'm facing what i think is called the gimball lock ? here's a video I uploaded that clarifies my problem : https://youtu.be/MT8nTAkvD6k

Now , from what I have understood , multiple rotations change the orientation of the object , but keep the X , Y , Z axis fixed , is that it ? Without knowing a lot about openGL , i thought that some projections like these would be enough : say Alpha is the angle following the rotation around X; The new Y and Z (let's Call them Y' and Z')axis would have this equation :

Y'=cos(Alpha)Y+sin(Alpha)Z

Z'=-sin(Alpha)Y+cos(Alpha)z

Based on this , i wrote this code (this method displays the teapot)

void Teapot::PrintObj()
{
        glLoadName(_NameStack);
        glPushMatrix();
        Translated();
        RotatedX();
        RotatedY();
        RotatedZ();

glColor3ub(_Color.red,_Color.green,_Color.blue);
glutSolidTeapot(2);

if(_Selected){WiredTeapot();Guizmo();}

        glPopMatrix();
};

Now this is the RotatedX method :

void Object3D::RotatedX()
{
rotY.x=0;
rotY.y=cos((angles.x/180.0f)*3.141592);
rotY.z=sin((angles.x/180.0f)*3.141592);

rotZ.x=0;
rotZ.y=-sin((angles.x/180.0f)*3.141592);
rotZ.z=cos((angles.x/180.0f)*3.141592);

glRotated(angles.x,rotX.x,rotX.y,rotX.z);
}

all the variables are declared within the class : the rotX , rotY and rotZ are the 3 vector axis , every time the object undergoes a rotation , these axis are modified;

The RotatedY method now :

void Object3D::RotatedY()
{
rotX.x=cos((angles.y/180.0f)*3.141592);
rotX.y=0;
rotX.z=-sin((angles.y/180.0f)*3.141592);

rotZ.x=sin((angles.y/180.0f)*3.141592);
rotZ.y=0;
rotZ.z=cos((angles.y/180.0f)*3.141592);
glRotated(angles.y,rotY.x,rotY.y,rotY.z); 
}

Same thing , if this method is called it means that the object is rotated around the Y axis , hence the modification of the X and Z axis position.

and now the RotatedZ :

void Object3D::RotatedZ()
{
rotX.x=cos((angles.z/180.0f)*3.141592);
rotX.y=sin((angles.z/180.0f)*3.141592);
rotX.z=0;

rotY.x=-sin((angles.z/180.0f)*3.141592);
rotY.y=cos((angles.z/180.0f)*3.141592);
rotY.z=0;
glRotated(angles.z,rotZ.x,rotZ.y,rotZ.z);

I'm really struggling to make this work ; I've looked on the net and saw things like Quaternions (i don't even know what that is).

Thanks for helping me !

Answer 1

To avoid gimball lock you have to use quaternions. Since you are using the GLM library you already have code for that.

q1 = cos(a/2) + i ( x1 * sin(a/2)) + j (y1 * sin(a/2)) + k ( z1 * sin(a/2))

q2 = cos(a/2) + i ( x2 * sin(a/2)) + j (y2 * sin(a/2)) + k ( z2 * sin(a/2))

q3 = cos(a/2) + i ( x3 * sin(a/2)) + j (y3 * sin(a/2)) + k ( z3 * sin(a/2))

a = rotation angle
x1, y1, z1 = rotation axis 1
x2, y2, z2 = rotation axis 2
x3, y3, z3 = rotation axis 3

See http://glm.g-truc.net/0.9.4/api/a00153.html