A variational method for generating n-cross fields using higher-order Q-tensors

09/03/2019

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by   Dmitry Golovaty, et al.

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An n-cross field is a locally-defined orthogonal coordinate system invariant with respect to the cubic symmetry group. Cross fields are finding wide-spread use in mesh generation, computer graphics, and materials science among many applications. We consider the problem of generating an n-cross field using a higher-order Q-tensor theory that is constructed out of tensored projection matrices. It is shown that by a Ginzburg-Landau relaxation, one can reliably generate an n-cross field on arbitrary Lipschitz domains.