General boundary mapping method and its application in designing an arbitrarily shaped perfect electric conductor reshaper

A general boundary mapping method is proposed to enable the designing of various transformation devices with arbitrary shapes by reducing the traditional space-to-space mapping to boundary-to-boundary mapping. The method also makes the designing of complex-shaped transformation devices more feasible and flexible. Using the boundary mapping method, an arbitrarily shaped perfect electric conductor (PEC) reshaping device, which is called a "PEC reshaper," is demonstrated to visually reshape a PEC with an arbitrary shape to another arbitrary one. Unlike the previously reported simple PEC reshaping devices, the arbitrarily shaped PEC reshaper designed here does not need to share a common domain. Moreover, the flexibilities of the boundary mapping method are expected to inspire some novel PEC reshapers with attractive new functionalities.