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import torch
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C0 = 0.28209479177387814
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C1 = 0.4886025119029199
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C2 = [
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1.0925484305920792,
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-1.0925484305920792,
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0.31539156525252005,
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-1.0925484305920792,
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0.5462742152960396
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]
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C3 = [
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-0.5900435899266435,
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2.890611442640554,
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-0.4570457994644658,
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0.3731763325901154,
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-0.4570457994644658,
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1.445305721320277,
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-0.5900435899266435
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]
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C4 = [
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2.5033429417967046,
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-1.7701307697799304,
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0.9461746957575601,
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-0.6690465435572892,
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0.10578554691520431,
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-0.6690465435572892,
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0.47308734787878004,
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-1.7701307697799304,
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0.6258357354491761,
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]
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def eval_sh(deg, sh, dirs):
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"""
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Evaluate spherical harmonics at unit directions
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using hardcoded SH polynomials.
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Works with torch/np/jnp.
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... Can be 0 or more batch dimensions.
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:param deg: int SH max degree. Currently, 0-4 supported
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:param sh: torch.Tensor SH coeffs (..., C, (max degree + 1) ** 2)
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:param dirs: torch.Tensor unit directions (..., 3)
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:return: (..., C)
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"""
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assert deg <= 4 and deg >= 0
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assert (deg + 1) ** 2 == sh.shape[-1]
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C = sh.shape[-2]
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result = C0 * sh[..., 0]
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if deg > 0:
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x, y, z = dirs[..., 0:1], dirs[..., 1:2], dirs[..., 2:3]
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result = (result -
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C1 * y * sh[..., 1] +
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C1 * z * sh[..., 2] -
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C1 * x * sh[..., 3])
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if deg > 1:
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xx, yy, zz = x * x, y * y, z * z
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xy, yz, xz = x * y, y * z, x * z
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result = (result +
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C2[0] * xy * sh[..., 4] +
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C2[1] * yz * sh[..., 5] +
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C2[2] * (2.0 * zz - xx - yy) * sh[..., 6] +
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C2[3] * xz * sh[..., 7] +
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C2[4] * (xx - yy) * sh[..., 8])
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if deg > 2:
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result = (result +
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C3[0] * y * (3 * xx - yy) * sh[..., 9] +
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C3[1] * xy * z * sh[..., 10] +
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C3[2] * y * (4 * zz - xx - yy)* sh[..., 11] +
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C3[3] * z * (2 * zz - 3 * xx - 3 * yy) * sh[..., 12] +
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C3[4] * x * (4 * zz - xx - yy) * sh[..., 13] +
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C3[5] * z * (xx - yy) * sh[..., 14] +
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C3[6] * x * (xx - 3 * yy) * sh[..., 15])
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if deg > 3:
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result = (result + C4[0] * xy * (xx - yy) * sh[..., 16] +
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C4[1] * yz * (3 * xx - yy) * sh[..., 17] +
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C4[2] * xy * (7 * zz - 1) * sh[..., 18] +
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C4[3] * yz * (7 * zz - 3) * sh[..., 19] +
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C4[4] * (zz * (35 * zz - 30) + 3) * sh[..., 20] +
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C4[5] * xz * (7 * zz - 3) * sh[..., 21] +
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C4[6] * (xx - yy) * (7 * zz - 1) * sh[..., 22] +
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C4[7] * xz * (xx - 3 * yy) * sh[..., 23] +
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C4[8] * (xx * (xx - 3 * yy) - yy * (3 * xx - yy)) * sh[..., 24])
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return result
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def eval_sh_bases(deg, dirs):
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"""
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Evaluate spherical harmonics bases at unit directions,
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without taking linear combination.
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At each point, the final result may the be
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obtained through simple multiplication.
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:param deg: int SH max degree. Currently, 0-4 supported
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:param dirs: torch.Tensor (..., 3) unit directions
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:return: torch.Tensor (..., (deg+1) ** 2)
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"""
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assert deg <= 4 and deg >= 0
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result = torch.empty((*dirs.shape[:-1], (deg + 1) ** 2), dtype=dirs.dtype, device=dirs.device)
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result[..., 0] = C0
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if deg > 0:
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x, y, z = dirs.unbind(-1)
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result[..., 1] = -C1 * y;
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result[..., 2] = C1 * z;
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result[..., 3] = -C1 * x;
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if deg > 1:
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xx, yy, zz = x * x, y * y, z * z
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xy, yz, xz = x * y, y * z, x * z
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result[..., 4] = C2[0] * xy;
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result[..., 5] = C2[1] * yz;
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result[..., 6] = C2[2] * (2.0 * zz - xx - yy);
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result[..., 7] = C2[3] * xz;
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result[..., 8] = C2[4] * (xx - yy);
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if deg > 2:
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result[..., 9] = C3[0] * y * (3 * xx - yy);
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result[..., 10] = C3[1] * xy * z;
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result[..., 11] = C3[2] * y * (4 * zz - xx - yy);
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result[..., 12] = C3[3] * z * (2 * zz - 3 * xx - 3 * yy);
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result[..., 13] = C3[4] * x * (4 * zz - xx - yy);
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result[..., 14] = C3[5] * z * (xx - yy);
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result[..., 15] = C3[6] * x * (xx - 3 * yy);
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if deg > 3:
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result[..., 16] = C4[0] * xy * (xx - yy);
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result[..., 17] = C4[1] * yz * (3 * xx - yy);
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result[..., 18] = C4[2] * xy * (7 * zz - 1);
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result[..., 19] = C4[3] * yz * (7 * zz - 3);
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result[..., 20] = C4[4] * (zz * (35 * zz - 30) + 3);
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result[..., 21] = C4[5] * xz * (7 * zz - 3);
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result[..., 22] = C4[6] * (xx - yy) * (7 * zz - 1);
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result[..., 23] = C4[7] * xz * (xx - 3 * yy);
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result[..., 24] = C4[8] * (xx * (xx - 3 * yy) - yy * (3 * xx - yy));
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return result
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