The simulation of powder spectra involves summation of spectra calculated for N reference directions of the external magnetic field. Usually, the directions are given by regularly or randomly distributed points on a sphere. Due to an excessive number of points with the same polar angle \(\theta\) but with different azimuthal angles \(\varphi\), axial distributions produce jagged spectra, especially for spin systems with a weak azimuthal anisotropy. To improve the quality of the obtained spectra, a triangulation and subsequent interpolation of resonance fields/frequencies for hundreds of additional directions between triangle vertices or an average over a range of magnetic fields/frequencies (tent) are applied. A single spiral method with graduate steps for both the \(\theta\) and \(\varphi\) angles works better for systems with weak azimuthal anisotropy but allows for only a few interpolation points along the spiral. The proposed bispiral approach combines the best features of both spiral and triangular approaches: exact calculations for \(N\) reference spiral directions, joining of neighboring points of two spirals into a triangular net, and interpolation over hundreds of additional 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 the magnetic fields (hemisphere). For systems with higher symmetry, the angular space can be significantly reduced by choosing the \(\varphi\)-shift for the second spiral, on par with the space reduction for axial distributions. Spectra simulated for axial, random, and bispiral distributions with two-dimensional interpolation over triangles and for the semispiral grid with one-dimensional interpolation are compared.

粉末光谱的模拟涉及对针对外部磁场的N个参考方向计算的光谱求和。通常，方向由球体上规则或随机分布的点给出。由于具有相同极角\(\theta\)但方位角不同\(\varphi\)的点数量过多，轴向分布产生锯齿状光谱，特别是对于具有弱方位各向异性的自旋系统。为了提高所获得光谱的质量，对三角形顶点之间的数百个附加方向的共振场/频率或一系列磁场/频率（帐篷）的平均值进行三角测量和随后的插值。具有\(\theta\)和\(\varphi\)角的渐变步骤的单螺旋方法对于方位各向异性较弱的系统效果更好，但仅允许沿螺旋的几个插值点。所提出的双螺旋方法结合了螺旋和三角形方法的最佳特征：精确计算\(N\)参考螺旋方向，将两个螺旋的相邻点连接成三角网，并在数百个附加方向或帐篷平均值上进行插值。对于具有 C ₁对称性的系统，主螺旋和互补螺旋之间的角空间正好等于磁场（半球）的相空间。对于具有较高对称性的系统，可以通过为第二个螺旋选择\(\varphi\) -位移来显着减小角空间，与轴向分布的空间减小相当。比较了用三角形上的二维插值模拟轴向、随机和双螺旋分布的光谱，以及用一维插值模拟半螺旋网格的光谱。