title: How do I compute a new basis (transformation matrix) from a 3D plane and known origin?
body: <p>Given a 3D plane and an arbitrary point on it that I want to consider the origin <code>(0,0,0)</code> of a new basis, it is possible to: (A) define a basis from this information?  And (B) create a transformation matrix that allows me to convert between world space and the new basis?</p>
  
  <p>I can assume the transformation is affine.</p>
  
  <p>Thanks very much!</p>