  Disclination lines in nematic liquid crystals can exist in different
geometric conformations, characterised by their director profile. In certain
confined, colloidal and even more prominently in chiral nematics, the director
profile may vary along the disclination line. We construct a robust geometric
decomposition of director profile variations in closed disclination loops based
on a quaternion description and use it to apply topological classification to
linked loops with arbitrary variation of the profile. The description bridges
the gap between the known abstract classification scheme derived from homotopy
theory and the observable local features of disclinations. We compare the
resulting decomposition of disclination loop features to a similar
decomposition of nematic textures on closed surfaces.
