Accurate angular quadratures are crucial for the numerical solution of three-dimensional (3D) radiative transfer problems, especially when the spectral line polarisation produced by the scattering of anisotropic radiation is included. There are two requirements for obtaining an optimal quadrature and they are difficult to satisfy simultaneously: high accuracy and short computing time. By imposing certain symmetries, we were recently able to derive a set of near optimal angular quadratures. Here, we extend our previous investigation by considering other symmetries. Moreover, we test the performance of our new quadratures by numerically solving a radiative transfer problem of resonance line polarisation in a 3D model of the solar atmosphere resulting from a magneto-hydrodynamical simulation. The new angular quadratures derived here outperform the previous ones in terms of the number of rays needed to achieve any given accuracy.

The tables mentioned in Sect. 4 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/645/A101