We present a method for direction field design on surface and volumetric meshes supporting non-orthogonality. Our approach is a generalization of the representation of 3D cross fields in spherical harmonic basis. As such it induces a geometrically meaningful measure of smoothness, allows orthogonality control by a simple parameter and enables orientation constraints of a single direction. To the best of our knowledge this is the first work to propose non-orthogonal 3D frame field design. We demonstrate the applicability of our method to generate anisotropic quadrangular and hexahedral meshes which are particularly useful for remeshing CAD models.