This will be a short post explaining why conjugation is rotation, and why the axis-angle formula works. If you didn’t see it, here’s part 1. To see why conjugation is rotation, it is helpful to expand the multiplication (assuming q is a unit quaternion): When multiplying vectors as quaternions, notice that since the real part is 0, To finish, we need to talk about parallel and perpendicular components of And now we can start using trig to get rid of those half angles: From here, you can see that the parallel component remains unchanged, as expected. Also, notice that next time: exponentials, logs, and slerp
Quaternions part 2
Why is conjugation rotation?
.
to
.
and
. Notice that
.
is just
rotated
around
, So you can see that the perpendicular part is being rotated around
by
.
Twisted Oak Studios offers consulting and development on high-tech interactive projects. Check out our portfolio, or Give us a shout if you have anything you think some really rad engineers should help you with.
Archive