“In the 19th century, the French geometer Charles Pierre Dupin discovered a nonspherical surface with circular lines of curvature. He called it a cyclide in his book, Applications de Geometrie published in 1822. Recently, cyclides have been revived for use as surface patches in computer aided geometric design (CAGD). Other applications of eyelides in CAGD are possible (e.g., variable radius blending) and require a deep understanding of the geometry of the cyclide.”