  We study a new formulation for the eikonal equation |grad u| =1 on a bounded
subset of R^2. Considering a field P of orthogonal projections onto
1-dimensional subspaces, with divergence bounded in L^2, we prove existence and
uniqueness for solutions of the equation P div P=0. We give a geometric
description, comparable with the classical case, and we prove that such
solutions exist only if the domain is a tubular neighbourhood of a regular
closed curve.
  This formulation provides a useful approach to the analysis of stripe
patterns. It is specifically suited to systems where the physical properties of
the pattern are invariant under rotation over 180 degrees, such as systems of
block copolymers or liquid crystals.
