title: Finding absolute coordinates from relative coordinates in 3D space
body: <p>My question is fairly difficult to explain, so please bear with me.  I have a random object with Forward, Right, and Up vectors.  Now, imagine this particular object is rotated randomly across all three axis randomly.  How would I go about finding the REAL coordinates of a point relative to the newly rotated object?</p>
  
  <p>Example:
  <img src="https://i.stack.imgur.com/LfEtJ.png" alt="enter image description here"></p>
  
  <p>How would I, for instance, find the forward-most corner of the cube given its Forward, Right, and Up vectors (as well as its coordinates, obviously) assuming that the colored axis is the 'real' axis.</p>
  
  <p>The best I could come up with is:</p>
  
  <pre><code>x=cube.x+pointToFind.x*(forward.x+right.x+up.x)
  y=cube.y+pointToFind.y*(forward.y+right.y+up.y)
  z=cube.z+pointToFind.z*(forward.z+right.z+up.z)
  </code></pre>
  
  <p>This worked sometimes, but failed when one of the coordinates for the point was 0 for obvious reasons.</p>
  
  <p>In short, I don't know what do to, or really how to accurately describe what I'm trying to do...  This is less of a programming questions and more of a general math question.</p>