- Updated constants for Owen scrambling, based on better optimization
criteria.
- Increased randomness for the higher bits in the Owen scrambling.
- A simple and efficient implementation of Cranley-Patternson rotation
for the Sobol sampler.
This produces identical results, but generates the direction
vectors from the original sources at build time. This makes
the source code quite a bit leaner, and will also make it easier
to play with other direction vectors in the future if the
opportunity arises.
1. Use better constants for the hash-based Owen scrambling.
2. Use golden ratio sampling for the wavelength dimension.
On the use of golden ratio sampling:
Since hero wavelength sampling uses multiple equally-spaced
wavelengths, and most samplers only consider the spacing of
individual samples, those samplers weren't actually doing a
good job of distributing all the wavelengths evenly. Golden
ratio sampling, on the other hand, does this effortlessly by
its nature, and the resulting reduction of color noise is huge.
The previous implementation was fundamentally broken because it
was mixing the bits in the wrong direction. This fixes that.
The constants have also been updated. I created a (temporary)
implementation of slow but full owen scrambling to test against,
and these constants appear to give results consistent with that
on all the test scenes I rendered on. It is still, of course,
possible that my full implementation was flawed, so more validation
in the future would be a good idea.
This gives better variance than random digit scrambling, at a
very tiny runtime cost (so tiny it's lost in the noise of the
rest of the rendering process).
The important thing here is that I figured out how to use the
scrambling parameter properly to decorrelate pixels. Using the
same approach as with halton (just adding an offset into the sequence)
is very slow with sobol, since moving into the higher samples is
more computationally expensive. So using the scrambling parameter
instead was important.
It has a slight color cast to it at the moment, I believe due to
incorrect color space conversions, not because of the upsampling
method itself. So Meng upsampling is still the active method
at the moment.
Tests random vectors, and makes sure that encoding/decoding
round trip only introduces precision errors below a certain
threshold.
Pretty confident that the implementation is correct now.
