Is there a formula for me to know the angle of an object with many rotates?

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.

Re: Is there a formula for me to know the angle of an object with many rotates?

Hey dolphonebublein.

What angle are you comparing it to (i.e. what are the vectors are referencing your line to)?

Also, are you referencing it to another line (or vector) or a plane?

Re: Is there a formula for me to know the angle of an object with many rotates?

The original angle isn't that important. If the object were a cuboid that pointed up (roughly up, approx 95 degrees) as seen here Edit this Fiddle - jsFiddle and your computer monitor were a clock how could you tell what time the object was pointing to?

Re: Is there a formula for me to know the angle of an object with many rotates?

It's hard to understand what you are saying. If the object is at 95 degrees to the x-axis, then it would be 95- 90= 5 degrees away from "directly up" and so would be pointing to (5/360)(60)= 5/6 of a minute before the hour. Your original question appeared to be asking about three dimensions and a clock face is only two dimensional.