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Many adaptive mesh methods explicitly or implicitly use equidistribution andalignment. These principles can be considered central to mesh adaption. AMetric Tensor is the tool by which one describes the desired level of meshanisotropy. In contrast a mesh redistribution method based on the Monge-Ampereequation, which combines equidistribution with optimal transport, does notrequire the explicit construction of a Metric Tensor, although one alwaysexists. An interesting question is whether such a method produces ananisotropic mesh. To answer this question we consider the general metric towhich an optimally transported mesh aligns. We derive the exact metric,involving expressions for its eigenvalues and eigenvectors, for a model linearfeature. The eigenvectors of are shown to be orthogonal and tangential to thefeature, and the ratio of the eigenvalues is shown to depend, both locally andglobally, on the value of the scalar density function. We thereby demonstratehow an optimal transport method produces an anisotropic mesh along a givenfeature while equidistributing a suitably chosen scalar density function.Numerical results for a Parabolic Monge-Ampere moving mesh method are includedto verify these results, and a number of additional questions are raised.

The Alignment Properties of Monge-Ampere based Mesh Redistribution Methods: I Linear Features