Parametrizing 3-Webs of Circles on Darboux Cyclides

摘要

In 2012 Pottmann et al. presented full classification of 3-webs (hexagonal webs) of circles on Darboux cyclides into 5 types. We provide rational trigonometric bilinear parametrizations of these webs of circles in all cases except for the general case of type 3, which has a parametrization involving square root. As a direct corollary, analytic formulas for discrete 3-webs can be easily extracted from these parametrizations.