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 G1 , 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 G2 construction and various possible extensions of the method.

• Type: Journal
• Year: 2007
• Where: ADCM
• Authors: Pavel Chalmovianský, Bert Jüttler
• Keywords: ADCM 2007, Adjacent Points, Corresponding Normals, Limit Curve