title: Updating local position/rotation/scale from global position/rotation/scale?
body: <p>Assuming I have a class that contains 3 vectors(one for position, one for scale and one for rotation) I can use them to generate a transform matrix that symbolizes the object's position, rotation and size in 3D space.Then I add parent/child relationships between objects and I multiply the child's local transform matrix by the parent's global one, I get the child's global one and this is the one I use for rendering objects, so when a parent rotates, a child rotates around it like an orbit.Now I need to be able to get a child's local transform(not the entire matrix, just the separate components).I know the child's global transform and I know the parent's global transform.</p>
  
  <p>I can get the child's local transform by multiplying the child's global transform by the parent's transform inversed.However I REALLY need to be able to do this specifically:</p>
  
  <p>1.To be able to get the child's local position, just by knowing it's global position and the parent's global position <em>WITHOUT</em> generating any matrices;</p>
  
  <p>2.To be able to get the child's local rotation, just by knowing it's global rotationand the parent's global rotation <em>WITHOUT</em> generating any matrices;</p>
  
  <p>3.To be able to get the child's local scale, just by knowing it's global scale and the parent's global scale <em>WITHOUT</em> generating any matrices;</p>