Parametrization of the cone-shaped (green), torus-shaped (purple), and bowl-shaped (blue) reflectors. The sketch is in the meridional plane, and the reflecting structure is further rotated around the main axis and remains axially symmetric. We highlight in solid lines only the upper half of the reflecting surface above the equatorial plane in each geometry, although the model allows reflection from the bottom-half space of a mirror-symmetric surface to the equator to be taken into account. With the dashed purple line, we show the part of the inner walls of the torus, which may self-obscure some other reflecting part of the torus for a highly inclined observer, but is not directly illuminated by the source due to self-shadowing. We show in the dotted purple line the ellipse defining the torus-shaped reflector in both half-spaces from the equator. Similarly, we show in the dotted green line the corresponding straight edge of an off-centered geometrical cone in the meridional plane that defines the cone-shaped reflector in the upper half-space. Similarly, we also show in the dotted blue line the ellipse defining the bowl-shaped reflector in the upper half-space. The observer is inclined at an inclination i. Each reflecting geometry is fully described by its half-opening angle Θ, the inner radius ρ_in, and the maximal illuminated radius ρ. When i > Θ, the primary source is obscured for the observer.