Circle inversion of two-dimensional objects with mathematica

Abstract

One of the most interesting and less known two-dimensional transformations is the so-called circle inversion. This paper presents a new Mathematica package, CircleInversion, for computing and displaying the images of two-dimensional objects (such as curves, polygons, etc.) by the circle inversion transformation. Those objects can be described symbolically in either parametric or implicit form. The output obtained is consistent with Mathematica's notation and results. The performance of the package is discussed by means of several illustrative and interesting examples. © Springer-Verlag Berlin Heidelberg 2005.