So Im making a 2d space game and I have a bunch of spaceships that have turrets. Objects have a position and orientation, the ships being in world coordinates while the turrets are children and coordinates are relative to their parents.

How do I efficiently calculate the position of a turret in world coordinates (i.e. when it fires and I need to know where to place a bullet in the world)? Calculating the turrets orientation is trivial - I just add the turrets relative angle to its parents. For position though, I guess I could do a bunch of trigonometry but this MUST be a common problem with a good/fast general solution?

Should I be relearning how to do matrix math again? :)

btw - Im creating the game in javascript+canvas but its the math/algorithm im interested in here

Cheers, Greg