so3_grid#

de_ebsd.index.spherical.so3_grid(bandwidth, device=None, dtype=torch.float64)[source]#

The equiangular SOFT SO(3) sampling grid for bandwidth L.

Returns the three 1-D angle vectors (alpha, beta, gamma) of the separable grid, each of length N = 2L + 2 (SOFT bandwidth B = L + 1):

  • alpha[j] = 2 pi j / N and gamma[p] = 2 pi p / N – equiangular in [0, 2 pi), the Fourier grids conjugate to the orders m', m (so the correlation is an inverse FFT over alpha and gamma);

  • beta[k] = pi (2k + 1) / (2 N) – the 2N-point equiangular colatitude grid in (0, pi) (no samples at the poles).

The cross-correlation returned by so3_cross_correlation() is indexed C[..., j, k, p] on this (alpha, beta, gamma) grid; grid_to_rotation() converts an (j, k, p) index to an orix Rotation.

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