[Algorithms] Re: D3DXQuaternionRotationYawPitchRoll

[Casey M. <gd...@fu...>]

I don't really understand what all the fuss is about.  Matrices and
quaternions are interchangable so far as rotation is concerned.  So why
would anyone be building a matrix of euler angle rotations and then
converting it to a quaternion?  If you want Yaw * Pitch * Roll, then just
build the quaternions and multiply them.  This will do the exact same
thing as compositing Yaw * Pitch * Roll matrices.  Even the order is the
same.  This is the whole concept behind quaternions for rotation in the
first place: they do the same thing as matrices.

To be more explicit, you have

   P = [Sin(Pitch/2), 0, 0, Cos(Pitch/2)]
   Y = [0, Sin(Yaw/2), 0, Cos(Yaw/2)]
   R = [0, 0, Sin(Roll/2), Cos(Roll/2)]

   Q = YPR

You can do this on the fly, or you can pre-compute what YPR is
algebraicly, and make something that builds the four elements of Q
directly from the input angles if you're concerned about the performance.
If you want an alternate Euler angle ordering, then just change the order
of multiplication.

Also note that I have not implied a sign or a handedness or any of that
here, and I arbitrarily chose the axes for each quantity to be expressed
in (you could freely permute the variables if your axes are different).

- Casey