c++ - OpenGL transforming objects with multiple rotations of Different axis

Question

I am building a modeling program and I'd like to do transformations on objects in their own space and then assign that single object to a group to rotate around another axis which the group rotates around. However, I'd also like to be able to do transformations in the object's own space when it's combined.

Manipulating the individual object, I pick the object's center.

glm::mat4 transform;
transform = glm::translate(transform, - obj.meshCenter);
glm::mat4 transform1;
transform1 = glm::translate(transform1, obj.meshCenter);
obj.rotation =  transform1*obj.thisRot*transform;

I then send this off to the shader,

glUniformMatrix4fv(modelLoc, 1, GL_FALSE, glm::value_ptr(obj.translation*obj.rotation*objscale);

I would now like to rotate this object around another axis, say an axis of (5,0,0) of 45 degrees.

I now have:

glm::mat4 groupR;
groupR = glm::rotate(groupR,glm::degrees(45.0f),glm::vec3(5,0,0));
obj.groupRotation = groupR;
glUniformMatrix4fv(modelLoc, 1, GL_FALSE, 
glm::value_ptr(obj.groupRotation*obj.translation*obj.rotation*objscale)

I've now moved the object from it's local space to the Group space. I'm having a bit of difficulty now operating tranformations in the object's own space when combined with the Group's rotation. I've had limited success when I set the groupR axis to (0,1,0) like so:

///Translating object in its own space///
glm::mat4 R = obj.groupRotation;
obj.translation = glm::inverse(R) * obj.translate * R;

the problem here is that this will only translate the object correctly in it's own space if the axis of rotation of R (Group's rotation) is equal to (0,1,0):

///Rotating object in its own space///
glm::mat4 R = obj.groupRotation;
obj.rotation = glm::inverse(R) * obj.rot * R;

Again, the rotations are incorrect. I'm thinking that maybe I have to undo the groupR's axis translation? and then re-apply it somewhere?

Answer 1

Let's assume we have an object that is moved, rotated and scaled, and we define a transformation matrix as follows:

glm::mat4 objTrans ...; // translation 
glm::mat4 objRot ...;   // roation 
glm::mat4 objScale ...; // scaling

glm::mat4 objMat = objTrans * objRot * objScale;

And we have rotation matrix that we want to run on the object. In this case we have rotation around the Z-axis:

foat angle ...; // rotation angle

glm::mat4 rotMat = glm::rotate( angle, glm::vec3( 0.0, 0.0, 1.0 ) ); 

We have several rotations we can do with this information. First we want to rotate the object on its local axis:

glm::mat4 modelMat = objMat * rotMat;

A Rotation around the worlds origin can be performed like this:

glm::mat4 modelMat = rotMat * objMat;

In order to rotate around the origin of the object in the world coordinate system, we must eliminate the rotation of the object:

glm::mat4 modelMat = objMat * (glm::inverse(objRot) * rotMat * objRot);

A Rotation around the worlds origin in relation to the object you have to do the opposite:

glm::mat4 modelMat = (objRot * rotMat * glm::inverse(objRot)) * objMat;

If you have a complete transformations matrix for an object and you do not know the rotation part, then it can be easily determined.

Note that a transformation matrix usually looks like this:

( X-axis.x, X-axis.y, X-axis.z, 0 )
( Y-axis.x, Y-axis.y, Y-axis.z, 0 )
( Z-axis.x, Z-axis.y, Z-axis.z, 0 )
( trans.x,  trans.y,  trans.z,  1 )

To generate a rotation only matrix you have to extract the normalized axis vectors:

glm::mat4 a ...; // any matrix
glm::vec3 x = glm::normalize( a[0][0], a[0][1], a[0][2] );
glm::vec3 y = glm::normalize( a[1][0], a[1][1], a[1][2] );
glm::vec3 z = glm::normalize( a[2][0], a[2][1], a[2][2] );

glm::mat4 r;
r[0][0] = x[0]; r[0][1] = x[1]; r[0][2] = x[2]; r[0][3] = 0.0f;
r[1][0] = y[0]; r[1][1] = y[1]; r[1][2] = y[2]; r[0][3] = 0.0f;
r[2][0] = z[0]; r[2][1] = z[1]; r[2][2] = z[2]; r[0][3] = 0.0f;
r[3][0] = 0.0f; r[3][1] = 0.0f; r[3][2] = 0.0f; r[0][3] = 1.0f;