It's not easy to fully answer some of the recent questions raised in recent posts, as the algorithms used within LightSpace when generating a calibration LUT from the profile data is key here, but that is not something we are going to explain in-depth, as this is what makes LightSpace work as it does... to use a recent description used by Zoyd, it is LightSpace's secret sauce!
But, Zoyd's answer above is not correct. LightSpace most definitely does NOT us a nearest neighbour local modification, and does NOT use "well-known color space transformations" at all.
ArgyllCMS is simply using standard ICC profile transforms to go from one colour space to another.
LightSpace is very different in the colour engine it uses, an no amount of inaccurate statements will change that fact.
When the LUT is made all points in the profile data are assessed and will influence the correcting for any given point - not just the reading from that point's measurement.
This is key, and is very, very unique, and requires a very high-level colour engine, which is at the heart of LightSpace.
It is the implementation of the final calibration LUT in any LUT box or DI program is the same for each and every LUT.
But it is the generation of the LUT that can be (and is, in the case of LightSpace) very different.
The colour engine within LightSpace is unique - and has no common operation with any other approach used in any other calibration system - simple fact.
A bit more info was posted here: http://www.avsforum.com/t/1461363/ee-colorbox-lightspace-and-3d-lut-calibration/120#post_23146650