This paper describes the Insight Toolkit (ITK) Conformal Flattening filter: itkConformalFlatteningFilter. This ITK filter is an implementation of a paper by Sigurd Angenent, et al., “On the Laplace-Beltrami Operator and Brain Surface Flattening”. This filter performs an angle preserving map of any genus zero (i.e. no handles) triangulated mesh to the sphere or, alternatively, to the plane. In other words, any given triangle in the resulting sphere will have the same angles as the corresponding triangle in the original mesh, though their areas may differ. In this paper, we describe our code and provide the user with enough details to reproduce the results which we present in this paper. This filter has a variety of applications including the flattening of brain surfaces, which was the initial motivation for this work.