Previously, we used precomputed Gaussian fits to the XYZ CMFs, performed
the spectral integration in that space, and then converted the result
to the RGB working space.
That worked because we're only supporting dielectric base layers for
the thin film code, so the inputs to the spectral integration
(reflectivity and phase) are both constant w.r.t. wavelength.
However, this will no longer work for conductive base layers.
We could handle reflectivity by converting to XYZ, but that won't work
for phase since its effect on the output is nonlinear.
Therefore, it's time to do this properly by performing the spectral
integration directly in the RGB primaries. To do this, we need to:
- Compute the RGB CMFs from the XYZ CMFs and XYZ-to-RGB matrix
- Resample the RGB CMFs to be parametrized by frequency instead of wavelength
- Compute the FFT of the CMFs
- Store it as a LUT to be used by the kernel code
However, there's two optimizations we can make:
- Both the resampling and the FFT are linear operations, as is the
XYZ-to-RGB conversion. Therefore, we can resample and Fourier-transform
the XYZ CMFs once, store the result in a precomputed table, and then just
multiply the entries by the XYZ-to-RGB matrix at runtime.
- I've included the Python script used to compute the table under
`intern/cycles/doc/precompute`.
- The reference implementation by the paper authors [1] simply stores the
real and imaginary parts in the LUT, and then computes
`cos(shift)*real + sin(shift)*imag`. However, the real and imaginary parts
are oscillating, so the LUT with linear interpolation is not particularly
good at representing them. Instead, we can convert the table to
Magnitude/Phase representation, which is much smoother, and do
`mag * cos(phase - shift)` in the kernel.
- Phase needs to be unwrapped to handle the interpolation decently,
but that's easy.
- This requires an extra trig operation in the kernel in the dielectric case,
but for the conductive case we'll actually save three.
Rendered output is mostly the same, just slightly different because we're
no longer using the Gaussian approximation.
[1] "A Practical Extension to Microfacet Theory for the Modeling of
Varying Iridescence" by Laurent Belcour and Pascal Barla,
https://belcour.github.io/blog/research/publication/2017/05/01/brdf-thin-film.html
Pull Request: https://projects.blender.org/blender/blender/pulls/140944
eaa5f63ba2