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Topology of Frame Field Meshing
In the past decade frame fields have emerged as a promising approach for generating hexahedral meshes for CFD and CAE applications. One important problem asks for construction of a boundary aligned frame field with prescribed singularity constraints that correspond to a valid hexahedral mesh. We give a necessary and sufficient condition in terms of solutions to a system of monomial equations whose variables are in the binary octahedral group. Along the way we look at frame field design from an algebraic topological perspective, proving various results, some known, some new.