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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.9"
# dependencies = [
# "numpy",
# "openexr",
# ]
# ///
"""
Generate a DFG LUT (Look-Up Table) for PBR split-sum approximation.
This computes the pre-integrated BRDF for the GGX microfacet model,
storing scale and bias factors for the Fresnel term.
Output: DFG LUT as an EXR file with RG channels (scale, bias).
"""
import numpy as np
try:
import OpenEXR
import Imath
HAS_OPENEXR = True
except ImportError:
HAS_OPENEXR = False
def generate_hammersley_sequence(n):
"""Pre-compute Hammersley 2D sequence for n samples."""
i = np.arange(n, dtype=np.uint32)
# Reverse bits for radical inverse
v = i.copy()
v = ((v >> 1) & 0x55555555) | ((v & 0x55555555) << 1)
v = ((v >> 2) & 0x33333333) | ((v & 0x33333333) << 2)
v = ((v >> 4) & 0x0F0F0F0F) | ((v & 0x0F0F0F0F) << 4)
v = ((v >> 8) & 0x00FF00FF) | ((v & 0x00FF00FF) << 8)
v = (v >> 16) | (v << 16)
e1 = i.astype(np.float32) / n
e2 = v.astype(np.float64) / 0x100000000
return e1, e2.astype(np.float32)
def generate_dfg_lut(width=64, height=32, num_samples=512):
"""
Generate the full DFG LUT (vectorized).
Compatible with HLSL: float2 dfg_uv = float2(NoV, roughness);
X axis (U): NdotV (0 to 1)
Y axis (V): roughness (0 to 1)
"""
# Pre-compute Hammersley sequence
e1, e2 = generate_hammersley_sequence(num_samples)
phi = 2.0 * np.pi * e1
cos_phi = np.cos(phi)
sin_phi = np.sin(phi)
# Create coordinate grids matching HLSL UV layout
x = np.arange(width, dtype=np.float32)
y = np.arange(height, dtype=np.float32)
ndotv_arr = (x + 0.5) / width # shape: (width,) - U axis
roughness = (y + 0.5) / height # shape: (height,) - V axis
# Pre-compute roughness terms
m = roughness * roughness
m2 = m * m # shape: (height,)
lut = np.zeros((height, width, 2), dtype=np.float32)
for yi, (rough, rough_m2) in enumerate(zip(roughness, m2)):
# GGX importance sampling - vectorized over samples and NdotV
# cos_theta shape: (width, num_samples)
denom = 1.0 + (rough_m2 - 1.0) * e2[np.newaxis, :]
cos_theta = np.sqrt((1.0 - e2[np.newaxis, :]) / denom)
sin_theta = np.sqrt(1.0 - cos_theta * cos_theta)
# Half vector in tangent space
hx = sin_theta * cos_phi[np.newaxis, :]
hy = sin_theta * sin_phi[np.newaxis, :]
hz = cos_theta
# View vector in tangent space (varies per column)
ndotv = ndotv_arr[:, np.newaxis] # shape: (width, 1)
vx = np.sqrt(1.0 - ndotv * ndotv)
vz = ndotv
# V dot H
vdh = vx * hx + vz * hz
# Light vector (reflect view around half)
lx = 2.0 * vdh * hx - vx
lz = 2.0 * vdh * hz - vz
ndotl = np.maximum(lz, 0.0)
ndoth = np.maximum(hz, 0.0)
vdoth = np.maximum(vdh, 0.0)
# Visibility function (Smith GGX correlated)
vis_v = ndotl * np.sqrt(ndotv * (ndotv - ndotv * rough_m2) + rough_m2)
vis_l = ndotv * np.sqrt(ndotl * (ndotl - ndotl * rough_m2) + rough_m2)
vis = 0.5 / (vis_v + vis_l + 1e-8)
# Compute contribution
ndotl_vis_pdf = ndotl * vis * (4.0 * vdoth / (ndoth + 1e-8))
fresnel = (1.0 - vdoth) ** 5
# Mask invalid samples
mask = ndotl > 0.0
scale_contrib = np.where(mask, ndotl_vis_pdf * (1.0 - fresnel), 0.0)
bias_contrib = np.where(mask, ndotl_vis_pdf * fresnel, 0.0)
# Sum over samples
scale = np.sum(scale_contrib, axis=1) / num_samples
bias = np.sum(bias_contrib, axis=1) / num_samples
# Filament-compatible layout:
# R = bias (F0-independent term)
# G = scale + bias (reflectance when F0 = 1)
# Used as: lerp(dfg.x, dfg.y, f0) = bias + f0 * scale
lut[yi, :, 0] = bias
lut[yi, :, 1] = scale + bias
print(f"\rGenerating DFG LUT: {(yi + 1) / height * 100:.1f}%", end="", flush=True)
print()
# Flip vertically so V=0 (top) is high roughness, V=1 (bottom) is low roughness
return np.flipud(lut)
def save_exr(filename, lut):
"""Save the DFG LUT as an EXR file."""
if not HAS_OPENEXR:
raise ImportError("OpenEXR module not available. Install with: pip install OpenEXR")
height, width = lut.shape[:2]
header = OpenEXR.Header(width, height)
header['channels'] = {
'R': Imath.Channel(Imath.PixelType(Imath.PixelType.FLOAT)),
'G': Imath.Channel(Imath.PixelType(Imath.PixelType.FLOAT)),
}
r_channel = lut[:, :, 0].astype(np.float32).tobytes()
g_channel = lut[:, :, 1].astype(np.float32).tobytes()
exr = OpenEXR.OutputFile(filename, header)
exr.writePixels({'R': r_channel, 'G': g_channel})
exr.close()
def save_npy(filename, lut):
"""Save the DFG LUT as a numpy file (fallback)."""
np.save(filename, lut)
def main():
import argparse
parser = argparse.ArgumentParser(description="Generate DFG LUT for PBR rendering")
parser.add_argument("-o", "--output", default="dfg_lut.exr", help="Output filename (default: dfg_lut.exr)")
parser.add_argument("-W", "--width", type=int, default=64, help="LUT width (NdotV axis, default: 64)")
parser.add_argument("-H", "--height", type=int, default=32, help="LUT height (roughness axis, default: 32)")
parser.add_argument("-s", "--samples", type=int, default=512, help="Number of samples per texel (default: 512)")
args = parser.parse_args()
print(f"Generating {args.width}x{args.height} DFG LUT with {args.samples} samples per texel...")
lut = generate_dfg_lut(args.width, args.height, args.samples)
output = args.output
if output.endswith(".exr"):
if HAS_OPENEXR:
save_exr(output, lut)
print(f"Saved EXR: {output}")
else:
output = output.replace(".exr", ".npy")
print("Warning: OpenEXR not available. Install with: pip install OpenEXR")
save_npy(output, lut)
print(f"Saved NumPy array instead: {output}")
elif output.endswith(".npy"):
save_npy(output, lut)
print(f"Saved NumPy array: {output}")
else:
save_exr(output, lut)
print(f"Saved: {output}")
if __name__ == "__main__":
main()
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