Strömgren radii and the radius-dependent H and He ionization fractions calculated with our 3d radiative transfer method (solid lines) compared to those from our spherically symmetric method. For the latter we use either the on-the-spot approximation (dashed lines) or a correct description of the diffuse radiation field (dotted lines). In the upper panels the ionizing source is a T = 30 000 K blackbody emitting 10⁴⁹ hydrogen-ionizing photons per second, representing a late O-type star (the temperature of the gas has been fixed to 7500 K), and in the lower panels a 65 000 K blackbody emitting 8 × 10⁵¹ hydrogen-ionizing photons per second, representing a VMS in the lower panel (the temperature of the gas has been fixed to a value of 10 000 K). The gas densities are n_H = 10 cm^-3 for the plots on the left and n_H = 10^-3 cm^-3 for those on the right.