  With the increasing availability of experimental and computational data
concerning the properties and distribution of grain boundaries in
polycrystalline materials, there is a corresponding need to efficiently and
systematically express functions on the grain boundary space. A grain boundary
can be described by the rotations applied to two grains on either side of a
fixed boundary plane, suggesting that the grain boundary space is related to
the space of rotations. This observation is used to construct an orthornormal
function basis, allowing effectively arbitrary functions on the grain boundary
space to be written as linear combinations of the basis functions. Moreover, a
procedure is developed to construct a smaller set of basis functions consistent
with the crystallographic point group symmetries, grain exchange symmetry, and
the null boundary singularity. Functions with the corresponding symmetries can
be efficiently expressed as linear combinations of the symmetrized basis
functions. An example is provided that shows the efficacy of the symmetrization
procedure.
