Simulation of powder spectra uses a summation of spectra calculated for N reference directions of external magnetic field. Usually, the directions are regularly or randomly distributed points on a sphere. Due to an excessive number of points with the same polar angle 𝜃 but with different azimuthal angles 𝜑, axial distributions produce jugged spectra, especially for spin systems with weak azimuthal anisotropy. To improve quality of obtained spectra, a triangulation and subsequent interpolation of resonance fields/frequencies for hundred additional directions between triangle vertices or average over a range of magnetic fields/frequencies (tent) are applied. Single spiral method with graduate steps on both 𝜃 and 𝜑 angles works better for systems with weak azimuthal anisotropy, but allows only few interpolation points along the spiral. Proposed bispiral approach combines best features of both spiral and triangular approaches: exact calculation for 𝑁 reference spiral directions, joining neighbor points of two spirals into a triangular net, and interpolation over hundred directions or the tent average. For systems with C1 symmetry the angular space between primary and complementary spirals is exactly equal to the phase space of magnetic fields (hemisphere). For systems with higher symmetry, the angular space can be significantly reduced by a choice of the 𝜑-shift for the second spiral, on a par with the space reduction for axial distributions. The bispiral approach with interpolation over triangles offers manyfold reduction of the calculation time for large spin or multi-spin systems with high ranks of spin-Hamiltonians in comparison with the single spiral grid.