title: Calculate transformation matrix from three 3D points
body: <p>I have a 3D coordinate system of which I track the three outer points with a 3D camera.<br>
  So I have three points in (x,y,z) space.<br>
  Next frame I track these three points again.<br>
  I use the first three points as initial situation. Now I need to draft a transformation matrix  that gives me the translation, rotation and scaling of the second 3 points, in comparison with the initial position. </p>
  
  <p>Now I do not really know how to do this.<br>
  Is there a way to directly make the  the transformation matrix, or do I first have to work out the translation, rotation and scale matrix and than make a transformation matrix of these three? </p>
  
  <p>I work in c++ with opencv and qt. 
  Somebody got any suggestions? I do not necessarily need a full working example, anything that can get me on my way is appreciated. </p>
  
  <p>Thanks! 
  J</p>