An arbitrarily shaped cloak with nonsingular and homogeneous parameters designed using a twofold transformation

An arbitrarily asymmetrical cloak with nonsingular and homogeneous parameters is obtained by dividing an arbitrary N-sided polygonal region into N triangular regions, applying an independent twofold spatial compression, and smoothing the inner boundary of the polygonal cloak. In each triangular region, a small line segment is first stretched along one side of the triangle; this is followed by a second transformation along the other side which is carried out to create a pairing triangle. The inner boundary will thus be continuous and take a shape similar to the outer boundary. The proposed cloak is nonsingular and moreover each region of the cloak is composed of homogeneous materials.