A generalized transformation to convert an arbitrary perfect electric conductor into another arbitrary dielectric object

A generalized transformation is proposed to design an illusion device. The device can reshape an arbitrarily shaped perfect electrical conductor (PEC) into another dielectric object with arbitrary geometry. Such a device can evolve into an ideal invisibility cloak with non-conformal boundaries if the virtual space is filled with air. Furthermore, the validity of our proposed transformation is confirmed by two specific devices. One is to convert a regular polygonal PEC cylinder into a circular dielectric cylinder. Another one is to reshape a circular PEC cylinder into a regular polygonal dielectric cylinder.