Conchoid surfaces of spheres

M. Peternell, D. Gruber, and J. Sendra


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 R3 and R4. Moreover we point to remarkable geometric properties of these surfaces and their construction.


    AUTHOR = {Peternell, Martin and Gruber, David and Sendra, Juana},
     TITLE = {Conchoid surfaces of spheres},
   JOURNAL = {Comput. Aided Geom. Design},
    VOLUME = {30}
      YEAR = {2013},
     PAGES = {35-44},