Obscuration limits for the studied geometries. In blue we show the Θ_limit(i) curves for the elliptical torus, which determine the lower limit in Θ, below which no directly illuminated part of the elliptical torus is directly observable due to self-obscuration. From bottom to top, we show the cases of ρ/ρ_in = 1.001, 1.2, 1.4, 1.6, 1.8, 1.999, respectively. The dashed black line is the inverse of the function (A.1), i.e., Θ_limit, c(i) for the special case of a circular torus, which effectively spans through all ρ = ρ_c(Θ_limit)∈(1; 2) according to equation (1). In our geometrical assumption, such a general limitation to the parameter space due to self-obscuration does not appear for the cone and bowl geometries. In red we show the Θ_limit(i) curves for the cone geometry, which determine the lower limit in Θ, below which no part of the double-cone inner surface below the equator (at z < 0) is directly observable due to self-obscuration. From bottom to top we show the same cases of ρ/ρ_in = 1.001, 1.2, 1.4, 1.6, 1.8, 1.999, respectively, and the dash-and-dot line represents the ρ = ρ_c(Θ_limit) case according to (1). In brown we show the Θ_limit(i) curves for the cone geometry, which determine the upper limit in Θ, above which no part of the double-cone inner surface below the equator (at z < 0) is directly observable due to self-obscuration. From top to bottom we show the same cases of ρ/ρ_in = 1.001, 1.2, 1.4, 1.6, 1.8, 1.999, respectively, and the dotted line represents the ρ = ρ_c(Θ_limit) case according to (1). Equivalent red, brown, dot-and-dashed, and dotted curves for the bowl and torus geometries are nearly identical. We note that the axes of this figure nearly overlap with the extreme case of ρ/ρ_in = 1.001 in blue and brown colors.