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Algebraic equations for constant width curves and Zindler curves
Rochera, D.
(2022-03)
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 ...
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An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
Rochera, D. (2023-02-10)
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 ...
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Generalized plane offsets and rational parameterizations
Rochera, D. (2023-04-21)
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 ...
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Offsets and front tire tracks to projective hedgehogs
Rochera, D. (2022-07-25)
There are some known properties on curves of constant width and Zindler curves and their relationship with offsets and front tire-track curves in convex geometry. In this work, a generalization of all these concepts and ...
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On isoptics and isochordal-viewed curves
Rochera, D. (2021)
In this paper, some results involving isoptic curves and constant $\phi$-width curves are given for any closed curve. The non-convex case, as well as non-simple shapes with or without cusps are considered. Relating the ...
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Regular polygons on isochordal-viewed hedgehogs
Rochera, D. (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 ...
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Zindler-type hypersurfaces in R^4
Martinez-Maure, Y.; Rochera, D. (2022-09-08)
In this paper the definition of Zindler-type 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 ...