Abstract:

The conchoid surface

*G* of a given surface

*F* with respect to a point

*O* is roughly speaking the
surface obtained by increasing the radius function of

*F* with respect to

*O* by a constant

*d*. This
paper studies real rational ruled surfaces in this context and proves that their conchoid surfaces
possess real rational parameterizations, independently on the position of

*O*. Thus any rational ruled
surface

*F* admits a rational radius function

*r(u, v)* with respect to any point in space. Besides the
general skew ruled surfaces and examples of low algebraic degree we study ruled surfaces generated
by rational motions.

Bibtex:

@article{peternell-cs-2011,
author = "Martin Peternell and David Gruber and Juana Sendra",
title = "Conchoid surfaces of rational ruled surfaces",
journal = "Computer Aided Geometric Design",
volume =28,
pages = "427-435",
doi = "http://dx.doi.org/10.1016/j.cagd.2011.07.005",
url = "http://dmg.tuwien.ac.at/dgruber/paper/paper_conch_ruled_surf.pdf",