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arXiv · 1111.1110

Conchoid surfaces of spheres

Martin Peternell·David Gruber·Juana Sendra
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Abstract

The conchoid of a surface $F$ with respect to given fixed point $O$ is roughly speaking the surface obtained by increasing the radius function with respect to $O$ by a constant. This paper studies {\it conchoid surfaces of spheres} and shows that these surfaces admit rational parameterizations. Explicit parameterizations of these surfaces are constructed using the relations to pencils of quadrics in $\R^3$ and $\R^4$. Moreover we point to remarkable geometric properties of these surfaces and their construction.

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Martin Peternell, David Gruber, Juana Sendra. 2011-11-04. Conchoid surfaces of spheres. https://arxiv.org/abs/1111.1110

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