Example: If I have a line rotated (at its center) by -45 degress on the x, y, and z axis what formula would I used to determine what angle that object is at if you put it back on a cartesian plane?
The higher level version is css transforms. Rotating is made easy but to handle mouse drag events I need to know what direction (on a cartesian plane) the object is pointing.
I would just use three-dimensional rotation matrices acting on a 3-d vector (where you start of assuming z=0), followed by dropping the z-coordinate. They should be easy to code (if they're not already pre-packaged) and would give you more flexibility. That's what the programmers would do when I worked on video games back in the day.