Quality of Exported LUTs - explanation?

[Sofa Gas Rue]

Question:
In Affinity Photo "Export Luts" what does quality / "set the complexity" mean?

Issue/situation:
In Affinity Photo 'Export Lut' there is a Quality slider, where I only see a difference in the preview image once I go above 7 x 7 x7. The documentation is very sparse with its definition of what it actually does; "Quality—sets the complexity of the exported adjustment. Drag the slider to set the value."

Attachment:
Link to Affinity Photo Docs: https://affinity.help/photo/en-US.lproj/index.html?page=pages/Adjustments/export_3dLut.html?title=Exporting custom adjustments as LUTs

Operating system:
OSX Catalina 10.15.3

Affinity Photo:
Version 1.8.3

Any help or input on this matter is much appreciated. Thank you in advance.

PS: if this post is in the wrong forum, then please let me know, and I will submit it in another.

[Sofa Gas Rue]

It turns out James Ritson wrote an excellent introduction to LUTS and Affinity. So I'm just going to copy past the relevant part from his article below.

The article can be viewed here:
https://affinityspotlight.com/article/1d-vs-3d-luts/

I also enjoyed this introduction to LUTs:
https://www.bhphotovideo.com/explora/video/tips-and-solutions/introduction-luts

Quote

 

3D LUTs
3D LUTs are a different proposition entirely. They allow for complex colour operations, as opposed to the limitations of one-dimensional behaviour from 1D LUTs.

The way a 3D LUT is applied is also very different to a 1D LUT. Whereas a 1D LUT contains explicit input and output values based on the given bit depth (e.g. 1024 values for 10-bit), a typical 3D LUT will not contain values for every possible combination in the given colour space. As an example, let’s take the 3D LUT created in Affinity Photo you can see in the image. This LUT’s size is 64 (or 64x64x64), which means there are 64 input to output points for a value on each axis.

For a 64x64x64 3D LUT, we would calculate 64^3, which equals 262,144 values. That’s still not enough to cover the range of 10-bit footage, though—to get that number, we would calculate 1024^3, which equals 1,073,741,824. Quite a difference, and the resulting filesize of a LUT that contained this many values would be around 4GB. This is prohibitive for both storage and performance considerations, since caching and reading a LUT file this large would be difficult: therefore, a 3D LUT would never realistically contain this many values.

Even a LUT designed for 8-bit precision that contained every possible value would still need 16,777,216 values (calculated from 256^3), resulting in a filesize of around 65MB.

Since we don’t have the sheer range of values available needed to cover this range, it means that the values inbetween must be interpolated. The method of interpolation will vary depending on the software used (common methods tend to be trilinear, prism, pyramidal or tetrahedral interpolation). For example, these two mappings may be mandated by the LUT: 3464 3842 3476

The software would then have to interpret what the values would be inbetween these two mappings based on the relative relationship between the three axis.