Conchoid surfaces of spheres

Authors:
Martin Peternell;David Gruber;Juana Sendra
Affiliations:
Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Austria;Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Austria;Dpto. Matemática Aplicada a I.T. de Telecomunicación, Univ. Politécnica de Madrid, Spain
Venue:
Computer Aided Geometric Design
Year:
2013

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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 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.