12 citations · 12 across the 5 of their papers we have counts for
5 papers
A nice limaçon-like spiral
Alexey Kurnosenko
A limaçon-like curve, allowing 2π-transition with monotone curvature between concentric curvature elements, is presented. The curve is 4th degree algebraic, 4th degree rational, an…
Bounds for spiral and piecewise spiral splines
A. Kurnosenko
This note is the updated outline of the article "Interpolational properties of planar spiral curves", Fund. and Applied Math., 2001, Vol.7, N.2, 441-463, published in Russian. The…
On tractrices of planar curves
Alexey Kurnosenko
Tractrices of planar curves, in particular, a family of tractrices of a circle, are considered. Some new observations (including arc-length parametrization, Chezaro equation) and c…
Applying inversion to construct rational spiral curves
A. Kurnosenko
A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and p…
Around Vogt's theorem
Alexey Kurnosenko
Vogt's theorem, concerning boundary angles of a convex arc with monotonic curvature (spiral arc), is taken as a starting point to establish basic properties of spirals. The theorem…