sh.py

# Spherical Harmonic helper functions, borrowed from svox library (Alex Yu)

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import jax.numpy as jnp
import jax

C0 = 0.28209479177387814
C1 = 0.4886025119029199
C2 = [
    1.0925484305920792,
    -1.0925484305920792,
    0.31539156525252005,
    -1.0925484305920792,
    0.5462742152960396
]
C3 = [
    -0.5900435899266435,
    2.890611442640554,
    -0.4570457994644658,
    0.3731763325901154,
    -0.4570457994644658,
    1.445305721320277,
    -0.5900435899266435
]
C4 = [
    2.5033429417967046,
    -1.7701307697799304,
    0.9461746957575601,
    -0.6690465435572892,
    0.10578554691520431,
    -0.6690465435572892,
    0.47308734787878004,
    -1.7701307697799304,
    0.6258357354491761,
]

@jax.partial(jax.jit, static_argnums=(0,))
def eval_sh(deg, sh, dirs):
    """
    Evaluate spherical harmonics at unit directions
    using hardcoded SH polynomials.
    ... Can be 0 or more batch dimensions.
    :param deg: int SH max degree. Currently, 0-4 supported
    :param sh: SH coeffs (..., C, (max degree + 1) ** 2)
    :param dirs: unit directions (..., 3)
    :return: (..., C)
    """
    assert deg <= 4 and deg >= 0
    assert (deg + 1) ** 2 == len(sh)
    assert sh[0].shape[-1] == 3 # 3 color channels

    result = C0 * sh[0]
    if deg > 0:
        x, y, z = dirs[..., jnp.newaxis, 0:1], dirs[..., jnp.newaxis, 1:2], dirs[..., jnp.newaxis, 2:3]
        result = (result -
                C1 * y * sh[1] +
                C1 * z * sh[2] -
                C1 * x * sh[3])
        if deg > 1:
            xx, yy, zz = x * x, y * y, z * z
            xy, yz, xz = x * y, y * z, x * z
            result = (result +
                    C2[0] * xy * sh[4] +
                    C2[1] * yz * sh[5] +
                    C2[2] * (2.0 * zz - xx - yy) * sh[6] +
                    C2[3] * xz * sh[7] +
                    C2[4] * (xx - yy) * sh[8])

            if deg > 2:
                result = (result +
                        C3[0] * y * (3 * xx - yy) * sh[9] +
                        C3[1] * xy * z * sh[10] +
                        C3[2] * y * (4 * zz - xx - yy)* sh[11] +
                        C3[3] * z * (2 * zz - 3 * xx - 3 * yy) * sh[12] +
                        C3[4] * x * (4 * zz - xx - yy) * sh[13] +
                        C3[5] * z * (xx - yy) * sh[14] +
                        C3[6] * x * (xx - 3 * yy) * sh[15])
                if deg > 3:
                    result = (result + C4[0] * xy * (xx - yy) * sh[16] +
                            C4[1] * yz * (3 * xx - yy) * sh[17] +
                            C4[2] * xy * (7 * zz - 1) * sh[18] +
                            C4[3] * yz * (7 * zz - 3) * sh[19] +
                            C4[4] * (zz * (35 * zz - 30) + 3) * sh[20] +
                            C4[5] * xz * (7 * zz - 3) * sh[21] +
                            C4[6] * (xx - yy) * (7 * zz - 1) * sh[22] +
                            C4[7] * xz * (xx - 3 * yy) * sh[23] +
                            C4[8] * (xx * (xx - 3 * yy) - yy * (3 * xx - yy)) * sh[24])
    return result