Setting of the Dupin cyclide by three straight lines and sphere

Abstract

Over the past few years, interest in Dupin cyclides has re-emerged: they can be used both in mechanical engineering and in construction, for covering the spans of civil buildings and in temple architecture; the properties of the Dupin cyclide can be widely used in computer graphics. The article considers a method for setting of Dupin cyclides using three lines and a sphere, which greatly the possibilities for the construction of these surfaces, especially when it is necessary to cut compartments of a certain size from them and to dock them.