Finding absolute coordinates from relative coordinates in 3D space <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>