core/models/rendering/utils/sh_utils.py

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import torch

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,
]


def eval_sh(deg, sh, dirs):
    """
    Evaluate spherical harmonics at unit directions
    using hardcoded SH polynomials.
    Works with torch/np/jnp.
    ... Can be 0 or more batch dimensions.
    Args:
        deg: int SH deg. Currently, 0-3 supported
        sh: jnp.ndarray SH coeffs [..., C, (deg + 1) ** 2]
        dirs: jnp.ndarray unit directions [..., 3]
    Returns:
        [..., C]
    """
    assert deg <= 4 and deg >= 0
    coeff = (deg + 1) ** 2
    assert sh.shape[-1] >= coeff

    result = C0 * sh[..., 0]
    if deg > 0:
        x, y, z = dirs[..., 0:1], dirs[..., 1:2], dirs[..., 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


def RGB2SH(rgb):
    return (rgb - 0.5) / C0


def SH2RGB(sh):
    return sh * C0 + 0.5