  We propose a novel method of resolving the optimal anisotropy function. The
idea is to construct the optimal anisotropy function as a solution to the
inverse Wulff problem, i.e. as a minimizer for the anisoperimetric ratio for a
given Jordan curve in the plane. It leads to a nonconvex quadratic optimization
problem with linear matrix inequalities. In order to solve it we propose the
so-called enhanced semidefinite relaxation method which is based on a solution
to a convex semidefinite problem obtained by a semidefinite relaxation of the
original problem augmented by quadratic-linear constraints. We show that the
sequence of finite dimensional approximations of the optimal anisoperimetric
ratio converges to the optimal anisoperimetric ratio which is a solution to the
inverse Wulff problem. Several computational examples, including those
corresponding to boundaries of real snowflakes and discussion on the rate of
convergence of numerical method are also presented in this paper.
