(For yet another update on Psychopath's Sobol sampler, as well as significantly better LK hashes, please see the next post in this series: Building a Better LK Hash.)

Shortly after I wrote my last post about Sobol sampling, I got in contact with Brent Burley, who created the hash-based Owen scrambling used in the paper Progressive Multi-Jittered Sample Sequences. He was extremely kind, and spared some time to chat with me about his Sobol sampler. He has also now published a paper about it:

Practical Hash-based Owen Scrambling, by Brent Burley

Unsurprisingly, it goes beyond what I had figured out on my own, and improves upon existing Sobol samplers in multiple ways. It's really an amazing paper, and I highly recommend giving it a read.

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One of the tricky things about a Manuka-style rendering architecture is that you need to store your shading information really compactly, since it will be stored at every micropolygon vertex.

Storing surface normals seems like a fairly solved problem at this point, and I recommend the paper Survey of Efficient Representations for Independent Unit Vectors by Cigolle et al. if you haven't already read it.

Color, on the other hand, still seems like a bit of an open problem. For something like Psychopath, ideally I want a color format that meets these criteria:

• Compact (ideally 32 bits or less).
• Fast to decode (I want to use this at runtime while rendering, potentially decoding on every ray hit).
• Covers the entire gamut of human-visible colors.
• Has sufficient dynamic range to capture day-to-day natural phenomenon (e.g. the sun) without clipping.
• Has sufficient precision to avoid visible banding.

I took a few detours, but I believe I've come up with a format that meets all of these criteria. And I call it FLuv32.

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This post will walk you through a particular approach for efficiently importance sampling huge numbers of lights in a scene. I call the approach "Light Trees".

This post has been a long time coming. I actually wrote about this technique (tersely) back in 2014 on ompf2.com. But I never got around to writing about it properly on this blog. So I'm fixing that now!

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(For an update on Psychopath's Sobol sampler, please also see the next post in this series: Sobol Sampling - Take 2.)

Up until recently I was using Leonhard Grünschloß's Faure-permuted Halton sampler as my main sampler in Psychopath. I even ported it to Rust when I made the switch from C++. And it works really well.

I've also had a Rust port of Grünschloß's Sobol sampler in Psychopath's git repo for a while, and from time to time I played with it. But it never seemed notably better than the Halton sampler in terms of variance, and it was significantly slower at generating samples. This confused me, because Sobol seems like the go-to low discrepancy sequence for 3d rendering, assuming you want to use low discrepancy sequences at all.

However, I recently stumbled across some new (to me) information, which ultimately sent me down a rabbit hole implementing my own Sobol sampler. I'd like to share that journey.

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During my time working on Psychopath, I've slowly gained a better understanding of color science, color management, and other color related topics. I'd like to jot down some notes about my current understanding of these topics, because the angle I learned them from is slightly non-standard. My hope is that this may help other people gain a better understanding of the topic as well.

I don't know how many entries in this series there will be. Maybe this will be the only one! Who knows, I'm lazy sometimes. But my hope is to make additional posts about this in the future. I have a lot that I'd like to write about.

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