  The onset of transformation optics has opened avenues for designing of a
plenitude of applications related to propagation of electromagnetic waves in
anisotropic media. In this paper, an algorithm is proposed using a coordinate
transformation and a piecewise function for the purpose of designing a three
dimensional cloak having an arbitrary geometry which could be convex or
non-convex in nature. The surfaces of the cloak as well as of the body under
consideration are assumed to be conformal to each other. For an arbitrary
geometry, the coordinate system needed to model the surface can be a
non-orthogonal system. For the purpose of verification of the algorithm, a ray
tracing process is carried out for an ellipsoid as well as for a concave
surface having axial symmetry. In order to solve the Hamiltonian equation for
the purpose of ray tracing, the process of finding the derivatives
analytically, for an arbitrary geometry as considered here, becomes very
cumbersome. Here, a numerical method is described which provides a better
approximation to the partial derivatives than the conventional finite
difference approach based on forward differences.
