The model shows an oblique conoid with a helix as the directrix. The directrix is parallel to the helix axis.

The surface normals through the self-shadow boundary of a screw tube surface create the accompanying ruled surface under general parallel illumination. Its directional plane is normal to the direction of the light. The directrix passes through the vanishing point of rotation of the light rays.

With illumination normal to the screw axis, the directrix through the vanishing point of rotation and the infinity line of the directional plane coincide, and the accompanying ruled surface is no longer embedded in a hyperbolic but rather a parabolic mesh. The projectivity along the infinity line is then induced by the ray thread of the screw.

If the light source is assumed to be at the far point of the screw axis, the accompanying ruled surface is a helical surface.