  Frustration in nematic-ordered media (endowed with a director field) is
treated in a purely geometric fashion in a flat, two-dimensional space. We
recall the definition of quasi-uniform distortions and envision these as viable
ways to relieve director fields prescribed on either a straight line or the
unit circle. We prove that using a planar spiral is the only way to fill the
whole plane with a quasi-uniform distortion. Apart from that, all relieving
quasi-uniform distortions can at most be defined in a half-plane; however, in a
generic sense, they are all asymptotically spirals.
