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Fractional-order differential geometry of Gielis curves: chart regularization, Caputo curvature, and the fate of singularities
Gielis curves describe many natural shapes, and some of them have corners or cusps. We apply two recent ideas from the differential geometry of curves to Gielis curves: "regularizing" changes of metric and fractional curvatures based on the Caputo derivative. First, we show that the smoothness of a
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