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The onset of transformation optics has opened avenues for designing of aplenitude of applications related to propagation of electromagnetic waves inanisotropic media. In this paper, an algorithm is proposed using a coordinatetransformation and a piecewise function for the purpose of designing a threedimensional cloak having an arbitrary geometry which could be convex ornon-convex in nature. The surfaces of the cloak as well as of the body underconsideration are assumed to be conformal to each other. For an arbitrarygeometry, the coordinate system needed to model the surface can be anon-orthogonal system. For the purpose of verification of the algorithm, a raytracing process is carried out for an ellipsoid as well as for a concavesurface having axial symmetry. In order to solve the Hamiltonian equation forthe purpose of ray tracing, the process of finding the derivativesanalytically, for an arbitrary geometry as considered here, becomes verycumbersome. Here, a numerical method is described which provides a betterapproximation to the partial derivatives than the conventional finitedifference approach based on forward differences.

Electromagnetic cloaking in convex and concave media with surface modelled as a parameterised function