For both textures, the experimental situations will be described in detail. For the flower texture, some visualization of the geometry of the different ellipses and confocal hyperbolae is presented. For the generation texture, some simulation has been made in order to understand how the layers are inside the sample. The aim is to visualize clearly the organization of the smectic layers which take the form of Dupin cyclides. A precise examination of the association of focal conic domains is needed. Note that these Dupin cyclides are useful in a great number of physical situations i.e. not only in the physics of liquid crystals, for more information, see .