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 )

 The compiler-generated copy ctor, copy assignment, and dtor are OK.

      Re-adjust components to eliminate small deviations from |Q| = 1
      orthonormality.

      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