I am trying to translate an object in world space after rotating it at the origin. The problem is, after I rotate an object while it's at the origin, its local coordinate system rotates as well, so its axes are not parallel with the world coordinate axes anymore. So, for example, if I needed to translate an object to the point (3, 0, 5) after rotating the object around the y-axis, I would not be able to do this since the object's local coordinate system isn't the same as the world coordinate system. For example:
glRotatef(45, 0.0, 1.0, 0.0);
glTranslatef(3.0, 0.0, 5.0);
glutSolidCube(1); // This won't be at (3,0,5) like how I need it
How can I overcome this?
This is not so much a property of OpenGL, but matrix math.
When you send in a vertex to the OpenGL fixed function pipeline, it gets transformed by the matrices modelview and projection, i.e.
v_eye = MODELVIEW · v
v_clip = PROJECTION · v_eye
Now the modelview matrix is composed of all those sub-transformations. And they're non commutative, i.e. order of operations matters. For example
MODELVIEW = T_0 · R_0 · R_1 · T_1 · S_1 · R_2
Now you can rewrite the v_eye calculation above as
v_eye = T_0 · ( R_0 · ( R_1 · (T_1 · (S_1 · (R_2 · v)))))
As you can see, the v is multiplied (just like the matrices) right to left onto the stack of matrices you composed modelview of.
However what happens in OpenGL is, that the one matrix "MODELVIEW" is calculated, and v is transformed only with that 4×4 scheme of numbers. OpenGL does not "re-execute" all the matrix multiplication steps.