In the article "What is a LUT," you mentioned that the 1D function must simultaneously calibrate gamma and white balance. However, when calibrating white balance to meet the white point, wouldn't this lead to clipping in the RGB channels? Consequently, after the signal passes through the 1D function and enters the 3DLUT, some nodes in the 3DLUT would remain unused and be wasted.
If the 1DLUT ignores white balance and only handles gamma, it won't affect the 3DLUT. However, this wastes hundreds or thousands of calibration points from the 1D LUT intended for white balance, shifting that responsibility to the 17 gray scale points in the 3DLUT (assuming a 17^3 3DLUT).
How does the color space manage this trade-off? Or am I overthinking it—couldn't the RGB max values in the 3DLUT be dynamically set to match the 1DLUT's output max? Must they be strictly 0-1?
Thank you so much for clarifying this for me.

Your suppositions are wrong.
Correcting the white point doesn't cause clipping, unless you attempt to maintain the same peak white luma value.
See Peak Luma vs. Peak Chroma in LUT generation.

You also need to read the info on LUT Order issues.

Steve

Steve
Thank you for your reply.
Forgive my ignorance, but I'm not quite grasping your explanation.
Let me illustrate my confusion with an example.
Suppose my monitor displays a white point at (255,255,255) with a color temperature of 8000K. but I need D65. During calibration, wouldn't the 1DLUT only map (255,255,255) to (240,255,230)? In that case, the code values entering the 3DLUT for the R/B channels would be capped at 240 and 230 respectively, unable to reach 255. This would cause the 3DLUT to lose some of its node functionality.

That is not clipping.
That is the correct input triplet value for D65 white for the monitor.
For R/B to not therefore reach 255 is irrelevant/correct, as that would then be the wrong colour.
This is exactly how the 1D - 3D LUT combination would/should work.
(You appear to be confusing triplet values with actual colour values?)

Steve

Steve
Thanks for the reply.
Well, I expressed myself poorly. It shouldn't be called "clipping," but rather the correct adjustment for grayscale.
I understand that a 1DLUT doesn't correct mixed colors; it only corrects grayscale gamma and grayscale color temperature. Only a 3DLUT can correct other colors.
But as in my example, if a 1DLUT corrects grayscale color temperature, it significantly reduces the difficulty of color correction required by the 3DLUT (less nonlinearity). However, since the 1D correction limits the maximum values for R/B output, doesn't that reduce the number of usable nodes in the 3DLUT? For instance, nodes like (250, 255, 250) and (255, 255, 255) would receive no signal at all, as they are clipped by the 1D LUT.
If the 1D LUT doesn't correct color temperature, it would use the current 8000K white point as reference and only calibrate gamma. This wouldn't shrink the R/B channels, so (255,255,255) would still map to (255,255,255). In this case, the 3D LUT can capture all code values. However, for grayscale color temperature correction, it would rely solely on the 3D LUT's limited 17 grayscale points.
This is the contradiction I'm trying to express.

Upon reflection, I believe a solution exists: if the maximum values for the three RGB channels in the 3DLUT could match the maximum output of a 1DLUT, this issue would be resolved. The 3DLUT could redefine the 17 nodes by applying (0-240)/17 for the R channel, (0-255)/17 for the G channel, and (0-230)/17 for the B channel. This approach would prevent any nodes from becoming unusable.
While casually reviewing a cube 3DLUT file, I noticed a domain parameter (as shown in the image) that appears to define the maximum values for RGB channels. However, when I asked AI ChatGPT about this, it informed me that standard 3DLUTs uniformly distribute values from 0 to the maximum without compressing the three RGB channels.
This leaves me puzzled about how colorspace handles this.

No - a 1D LUT 'alters' all colours.
But it's main function is to alter the grey scale, as that is it's primary focus.
What it cannot do is alter 'colours' separately to the grey scale adjustments.

You appear to be confusing the input to output function of a LUT.
If the 1D LUT correct the grey scale, as your first example, then the 3D LUT needs to do nothing for the grey scale.
The input values are simple passed through the 3D LUT unaltered.

But, the volumetric colours will need to be adjusted, and may need to be adjusted beyond the restriction of the 1D LUT if the display has non-linear volumetric errors.
And as you have no idea what the 1D LUT will be doing you cant 'range adjust' the 3D LUT to match.
(Ignoring the fact you can't change the R/B axis of a 3D LUT separately to G, or each other)

Steve

Steve
Thank you for your reply.
I believe I understand the function of pre-1D. It primarily corrects grayscale, but since 1D is non-decoupled, its conversion is global and naturally affects all colors. Although other colors aren't its primary focus, they are generally influenced in a direction of reduced nonlinearity. Because grayscale and color temperature become more accurate, RGB levels typically improve as well, leading to better performance across all colors.

"And as you have no idea what the 1D LUT will be doing, you can't 'range adjust' the 3D LUT to match."
As you mentioned, so does this mean some nodes in the 3D LUT might become unusable? Since it doesn't know how much the 1D LUT will limit, it can only treat all nodes from 0-255 as input?

But in a professional LUT box like the AJA Colorbox, within the full 1D+3D+1D workflow, the color space should generate all three LUTs at once, right? The color space should know how much the signal is clipped after passing through the Pre-1D stage, and it should also know how much it's clipped after passing through the 3D stage, since it's an integrated process.

No - you cannot say a 1D LUT would do anything specific for non grey sale colours, as you have no idea what their display errors are.
With your example, Green primary would not really be affected, while Red and Blue would.

Beyond that, there are always areas of the theoretical 3D LUT volume that are not brought into play.
Nothing different there are all, as for all the LUT volume to be in use the display would have to perfect, and need no calibration at all...

And as before, there is no clipping.
And no, for the best result you would NOT profile everything at once for a 1D+3D+1D LUT workflow.
See the User Guides.

Steve