
Algebraic equations for constant width curves and Zindler curves
(202203)An explicit method to compute algebraic equations of curves of constant width and Zindler curves generated by a family of middle hedgehogs is given thanks to a property of Chebyshev polynomials. This extends the methodology ...

An explicit characterization of isochordalviewed multihedgehogs with circular isoptics
(20230210)A curve α is called (ϕ, ℓ)isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine ...

Generalized plane offsets and rational parameterizations
(20230421)In the first part of the paper a planar generalization of offset curves is introduced and some properties are derived. In particular, it is seen that these curves exhibit good regularity properties and a study on ...

Offsets and front tire tracks to projective hedgehogs
(20220725)There are some known properties on curves of constant width and Zindler curves and their relationship with offsets and front tiretrack curves in convex geometry. In this work, a generalization of all these concepts and ...

On isoptics and isochordalviewed curves
(2021)In this paper, some results involving isoptic curves and constant $\phi$width curves are given for any closed curve. The nonconvex case, as well as nonsimple shapes with or without cusps are considered. Relating the ...

Regular polygons on isochordalviewed hedgehogs
(2022)A curve $\alpha$ is called isochordal viewed if there is a smooth motion of a constant length chord with its endpoints along $\alpha$ such that their tangents to the curve at these points form a constant angle. In this ...

Zindlertype hypersurfaces in R^4
(20220908)In this paper the definition of Zindlertype hypersurfaces is introduced in $\mathbb{R}^4$ as a generalization of planar Zindler curves. After recalling some properties of planar Zindler curves, it is shown that Zindler ...