Algebraic Curves of Low Convolution Degree
AbstractStudying convolutions of hypersurfaces (especially of curves and surfaces) has become an active research area in recent years. The main characterization from the point of view of convolutions is their convolution degree, which is an affine invariant associated to a hypersurface describing the complexity of the shape with respect to the operation of convolution. Extending the results from [1], we will focus on the two simplest classes of planar algebraic curves with respect to the operation of convolution, namely on the curves with the convolution degree one (so called LN curves) and two. We will present an algebraic analysis of these curves, provide their decomposition, and study their properties.KeywordsCurve VersusAlgebraic CurfGeometric DesignRational CurfHermite InterpolationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.