Conchoid surfaces of quadrics

The conchoid surface FdFd 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 R3R3 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.