  Many adaptive mesh methods explicitly or implicitly use equidistribution and
alignment. These principles can be considered central to mesh adaption. A
Metric Tensor is the tool by which one describes the desired level of mesh
anisotropy. In contrast a mesh redistribution method based on the Monge-Ampere
equation, which combines equidistribution with optimal transport, does not
require the explicit construction of a Metric Tensor, although one always
exists. An interesting question is whether such a method produces an
anisotropic mesh. To answer this question we consider the general metric to
which an optimally transported mesh aligns. We derive the exact metric,
involving expressions for its eigenvalues and eigenvectors, for a model linear
feature. The eigenvectors of are shown to be orthogonal and tangential to the
feature, and the ratio of the eigenvalues is shown to depend, both locally and
globally, on the value of the scalar density function. We thereby demonstrate
how an optimal transport method produces an anisotropic mesh along a given
feature while equidistributing a suitably chosen scalar density function.
Numerical results for a Parabolic Monge-Ampere moving mesh method are included
to verify these results, and a number of additional questions are raised.
