Abstract:

The conchoid surface F"d of a surface F with respect to a fixed reference point O is a surface obtained by increasing the distance function with respect to O by a constant d. This contribution studies conchoid surfaces of quadrics in Euclidean R^3 and shows that these surfaces admit real rational parameterizations. We present an algorithm to compute these parameterizations and discuss several configurations of the position of O with respect to F where the computation simplifies significantly.Bibtex:

@article{peternell-2013-conchoid, AUTHOR = {Gruber, David and Peternell, Martin}, TITLE = {Conchoid surfaces of quadrics}, JOURNAL = {Journal of Symbolic Computation}, VOLUME = {59} YEAR = {2013}, PAGES = {36-53}, DOI = {http://dx.doi.org/10.1016/j.jsc.2013.07.003}, }