The model shows an oblique conoid with a directrix. The directrix is normal to the circular plane. The directrix is inclined at 45° to both the circular plane and the directrix. The area is of degree four and of the seventh Sturm type. In addition to the half of the directrix, a conic projecting onto the directrix is also given as a boundary." It is noteworthy that the generatrix segments are all of equal length and are bisected by the directrix.

Under certain assumptions, the presently presented controlled surface can be generated using parallel illumination of a special circular shear surface: Assume that the profile and directing circle are congruent and in mutually normal planes. Then, the double curve (hyperbola) of the circular shear surface decomposes into a pair of right-angled lines. The light source is placed at the far point of one of the lines. This becomes the directing line of the present controlled surface and coincides with the inner branch of the self-shadow boundary. The outer branch of the self-shadow boundary corresponds to the ellipse that bounds the present controlled surface model and is thus of a much simpler shape than the "general self-shadow boundary, which is of 8th order. The "general controlled surface is also of a significantly more complex shape than the present model.