class ROOT::Math::Quaternion

 ========== Constructors and Assignment =====================

Default constructor (identity rotation)

Construct given a pair of pointers or iterators defining the
beginning and end of an array of four Scalars

 ======== Construction From other Rotation Forms ==================

Construct from another supported rotation type (see gv_detail::convert )

Assign from another supported rotation type (see gv_detail::convert )

 ======== Components ==============

Set the four components given an iterator to the start of
the desired data, and another to the end (4 past start).

Get the components into data specified by an iterator begin
and another to the end of the desired data (4 past start).

Get the components into data specified by an iterator begin

Set the components based on four Scalars.  The sum of the squares of
these Scalars should be 1; no checking is done.

Access to the four quaternion components:
U() is the coefficient of the identity Pauli matrix,
I(), J() and K() are the coefficients of sigma_x, sigma_y, sigma_z

Overload operator * for rotation on a vector

Invert a rotation in place

Return inverse of a rotation

Distance between two rotations in Quaternion form
Note:  The rotation group is isomorphic to a 3-sphere
with diametrically opposite points identified.
The (rotation group-invariant) is the smaller
of the two possible angles between the images of
the two totations on that sphere.  Thus the distance
is never greater than pi/2.

Multiplication of an axial rotation by an AxisAngle