A non-linear circle-preserving subdivision scheme
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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 \(G^1\), 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.
Keywordssubdivision techniques fitting of algebraic curves
Mathematics subject classification (2000)65D17 68U05 53A04
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