A non-linear circle-preserving subdivision scheme

13 years 4 months ago

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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.

Pavel Chalmovianský, Bert Jüttler

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