The design of an arbitrary n-sided irregular polygonal transformed media is introduced in this paper. The generalized proposed optical transformation is based on a very simple Y-intercept transformation in the Cartesian coordinate system. In this method, the arbitrary shaped transformed media is decomposed into triangular segments. The permittivity and permeability tensors of the triangular segments are presented in an explicit closed-form expression. Based on the proposed method, the arbitrary irregular cloak, concentrator, superscatterer, and superabsorber are designed. Moreover, some simulations have been performed for verification of the proposed method. The numerical simulations prove the capability and universality of the proposed design method.