A non-linear circle-preserving subdivision scheme

We describe a new method for constructing a sequence of refined polygons, which starts with a sequence of points and associated normals. The newly generated points are sampled from circles which approximate adjacent points and the corresponding normals. By iterating the refinement procedure, we get a limit curve interpolating the data. We show that the limit curve is G(1), and that it reproduces circles. The method is invariant with respect to group of Euclidean similarities (including rigid transformations and scaling). We also discuss an experimental setup for a G(2) construction and various possible extensions of the method.