I want to create a transformation matrix from the information I get from (trans, rot) =tf.TransformListener().lookupTransform('from_frame', 'to_frame', rospy.Time(0)). So that I can just have a matrix I can multply with a co-ordinate from one frame to another. I have been looking at how to make a homogenous transformatio matrix [[R,d][0,1]] where I use both the quaternion info(rot) and translation info(d) to make the matrix.Does any one know the right formula to make the 3x3 rotation part of the matrix? I was looking at this. But other sources give completely different formuli, I am also confused about the right arrangement of rot data, which element is w, is it rot[0] or rot[3].

As follow up, after I have made the correct 4x4 matrix. How do I set up what co-ordinate I wish to transform?I have the (x,y and z) but I need another element to make it 4 so that its possible to multiply it by the 4x4 transformation matrix.I dont know what the 4th element should be really, I'm assuming it has something to do with translation though.