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This paper reports a study of the influence of magnetization directions and ellipticity on the field strength and homogeneity of NdFeB-Halbach cylinders in three dimensions. For the calculations the author used the RADIA software package, which allows fast and accurate 3-D magnetostatic computations due to its semianalytical approach. Parameter variations were performed to find the magnetization angles and cylinder ellipticity which yield a maximum field at the center gap point or which result in maximum field homogeneity. By optimizing magnetization angles and ellipticity, the field strength and field homogeneity of a Halbach cylinder can be shaped and maximized without adding any additional magnetic material.