A methodology of designing an arbitrary transformation using transformation optics (TO) based on unitary vectors and Fermat's principle is presented. The TO equation is derived in terms of grid coordinates. The geometry of the transformed space is stored in the grid coordinates rather than the transformation functions. This allows the crafting of an arbitrary transformation by combining several transformation templates together. The touch interface is employed to intuitively apply the transformations. The resulting material parameters are calculated from the proposed method and verified using the anisotropic finite-difference frequency-domain method. Five examples are presented to demonstrate the capability of this method.