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The authors show that a wave with any desired polarisation state can generally be generated in any direction with respect to two crossed dipoles, and a closed-form expression is provided for the complex ratio of the required drive voltages. The authors also provide a simple projection method for the polarisation ellipse in the case where the dipole centres coincide. For achieving the authors' aim of exploiting closed-form equations to generate circularly polarised (CP)/elliptically polarised (EP)/linearly polarised in any direction, two orthogonally placed dipoles resonating at 1 GHz each are designed. By selecting complex feed solutions, which are provided from the proposed closed-form equations, it is realised precise polarisation states in a number of directions. Four separate such cases to generated CP and EP were investigated, and in all of them the numerical simulations and experiments validated the proposed theoretical predictions.