IBM Journal of Research and Development
Parametric generalized offsets to hypersurfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Geometric Hermite interpolation with Tschirnhausen cubics
Journal of Computational and Applied Mathematics
Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
Polynomial/rational approximation of Minkowski sum boundary curves
Graphical Models and Image Processing
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Minkowski pythagorean hodographs
Computer Aided Geometric Design
Hermite interpolation by piecewise polynomial surfaces with rational offsets
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Problem Reduction to Parameter Space
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Rational hypersurfaces with rational convolutions
Computer Aided Geometric Design
Curves and surfaces represented by polynomial support functions
Theoretical Computer Science
On rationally supported surfaces
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Rational surfaces with linear normals and their convolutions with rational surfaces
Computer Aided Geometric Design
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
Computer Aided Geometric Design
On convolutions of algebraic curves
Journal of Symbolic Computation
MOS surfaces: medial surface transforms with rational domain boundaries
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Hermite interpolation by hypocycloids and epicycloids with rational offsets
Computer Aided Geometric Design
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
Reparameterization of curves and surfaces with respect to their convolution
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Exploring hypersurfaces with offset-like convolutions
Computer Aided Geometric Design
Reducibility of offsets to algebraic curves
Computer Aided Geometric Design
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Studying 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.