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# Copyright 2021 The PlenOctree Authors.
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
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
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