Why does the chromaticity diagram look like that?

That particular version of the chromaticity diagram makes it look like the colors missing from your display are various shades of laser pointer green as opposed to all the shades of red and blue that are missing because really saturated red and blue primaries are too dim (per unit of energy) to use.

See https://nanosys.com/blog-archive/2012/08/14/color-space-conf...

I learned a lot more about color management than I wanted to know in the progress of making red-cyan stereograms because I found when I asked for sRGB red I was getting something like (180,16,16) on my high gamut monitor which resulted in serious crosstalk between the channels.

Right now I am working with a seamstress friend on custom printed fabrics and I have a flower print where yellow somehow turned to orange in the midst of processing the image and I want to get it debugged and thoroughly proofed before I send out the order... I am still learning more than I want to know about color management.

Kinda related, but does someone maybe have a good set of links to help understand what HDR actually is? Whenever I tried in the past, I always got lost and none of it was intuitive.

There’s so many concepts there like: color spaces, transfer functions, HDR vs Apple’s XDR HDR, HLG vs Dolby Vision, mastering displays, max brightness vs peak brightness, all the different hdr monitor certification levels, 8 bit vs 10bit, “full” vs “video” levels when recording video etc etc.

Example use case - I want to play iPhone-recorded videos using mpv on my MacBook. There’s hundreds of knobs to set, and while I can muck around with them and get it looking close-ish to what playing the file in QuickTime/Finder, I still have no idea what any of these settings are doing.

I think the explanation is simple: Color is light and it is linear going from ultraviolet to blue to green to yellow to red to infrared. It's just a line.

In physical reality, there exists no purple light. Our minds make up all the shades of purple and magenta between blue and red when our eyes receive both red and blue light.

So in order to include the magentas, you need to draw another line between blue and red. Meaning you have to bend the real color line. And that's what we see in the chromaticity diagram.

It's probably good to start with XYZ, but we have much better colorspaces now that do a better job at correlating with our vision.

Mainly CIE 1976 L',u',v' and even more recently ICtCp from Dolby research.

Does anyone know of a nice "pedagogical" color space? That is, one optimized for teaching and learning, for correctness rather than for simple math? Where the space's highly-noticeable characteristics are actual features of human perception, rather than the usual mess of "nope, that too is a model artifact" (mostly from optimizing for computation). And full-gamut, well behaved out to spectral locus. And with at least somewhat linear hues and color combination. Sort of the Munsell niche, but full gamut, and this century.

I wasn't able to find anything even close, for a "maybe teach color better by emphasizing spectra?" side project, so I kludged. CAM16UCS as state-of-the-art for perceptual color, untwisted with Jzazbz for linear hues (it also sanity checked absolute luminosity), with a rather-unprincipled mashing down of CAM's IIUC-non-perceptual near-locus silly blue tail. Implemented as lookup tables. If there is any related work out there, I'd love to hear of it. Tnx.

I think a good explanation of color spaces might be starting at a camera sensor with a bayer array and how that’s processed.

Here's another really interesting exploration of color spaces https://ericportis.com/posts/2024/okay-color-spaces/

In my opinion, plotting chromaticity on a Cartesian grid — by far the most common way — is pretty misleading, since chromaticity diagrams use barycentric coordinates (and to be clear, I blame the institution, not the author). The effect is that the shape of the gamut looks skewed, but only because of how it's plotted; the weird skewedness of a typical XYZ chromaticity diagram doesn't represent anything real about the data.

Instead, a chromaticity diagram is better thought of as a 2D planar slice of a 3D color space, specifically the slice through all three standard unit vectors. From this conception, it's much more natural to plot a chromaticity diagram in an equilateral triangle, such as the diagram at [1]. A plot in a triangle makes it clear, for instance, that the full color gamut in XYZ space isn't some arbitrary, weird, squished shape, but instead was intentionally chosen in a way that fills the positive octant pretty well given the constraints of human vision.

[1]: https://physics.stackexchange.com/questions/777501/why-is-th...

Mostly correct, but I don't understand what the author is trying to do in the last section, where they try to fill the locus by generating spectra with two peaks and projecting it into the chromaticity diagram. Why do it like that?

This is how you should do it:

- You pick a Y value. This is going to be the luminance of your diagram.

- For each pixel inside the area bounded by the spectral locus (and the line of purples - the line connecting the two endpoints of the locus) you take its x, y coordinates.

- Together these 3 values specify your color in the CIE xyY color space. Converting from xyY to XYZ is trivial: X = Y / y * x, Y = Y, Z = Y / y * (1 - x - y)

- You map these XYZ values into your output image's color space (e.g. sRGB). If a given XYZ value maps outside the [0,1] interval in sRGB, then it's outside the sRGB gamut, and you may clip the values to the closest valid value inside the gamut.

I thought this might be a useful article because I've often had a similar question. But there's a diagram that has text:

More simply put: imagine that you have red, green, and blue light sources. What is the intensity of each one so that the resulting light matches a specific color on the spectrum?

...

The CIE 1931 color space defines these RGB color matching functions. The red, green, and blue lines represent the intensity of each RGB light source:

This seems very oddly phrased to me. I would presume that what that chart is actually showing is the response for each color of cone in the human eye?

In which case it's not a question of "intensity of the light source" but more like "the visual response across different wavelengths of a otherwise uniform intensity light source"?

... fwiw, I'm not trying to be pedantic, just trying to see if I'm missing the point or not.

I’ve been having problems studying this topic for years now, is there actually an official scientific field with official books and an official consensus on this ? Seems hard to know who to trust on this wide-but-niche topic

This is fantastic. It gave me an idea about colors, perception, and gamut.

Put simply, imagine that there is a combination of wavelengths of light that causes you to perceive the smell of ripe cheese, and another that causes you to think that there is a bear behind you. Now your diagrams must be filled in not only with colored pixels but also include a small picture of a cheese and a bear at the points where those specific perceptions occur.

I think, in real life, this is what magenta is: a non spectral color that’s more of a feeling or sensation that, in order for our brains to not get too overwhelmed, we simply perceive as another color. This is also, I believe, close to describing a real phenomenon for those living with varying degress of synesthesia or, if you will forgive a play on words, those on the synesthesia spectrum.

Bengtsson & Zyczkowski in the introduction (see p14-16) to their wonderful book make use of chromaticity diagrams to motivate their study of quantum states.

https://www.researchgate.net/profile/Karol-Zyczkowski/public...

In a way tradition suggests that colour theory should be studied before quantum mechanics, because this is what Schroedinger was doing before inventing his wave equation.

This page is also a beautiful explanation of color spaces, with chromaticity explained toward the end: https://ciechanow.ski/color-spaces/

Note that many of the diagrams are interactive 3d graphics (I didn't realize that at first, and it makes the page more interesting.)

I have a question for fellow color science nerds. I've been reading through Guild's original data: https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1932...

However, I'm having trouble understanding the meaning of the numbers in table 4. Does anyone understand all the columns there?

What I'm particularly interested in is finding the unnormalized coefficients from the color matching experiments, or some way to un-normalize those coefficients. (By "those coefficients," I mean the trichromatic coefficients u{a,b,c}_\lambda listed in table 3.) I don't know if that data is in table 4 so maybe those are two separate questions.

TL;DR: Imagine color space has 3 dimensions in polar coordinates.

- hue, the angle. your familiar red, orange, yellow, green, blue...

- saturation/chroma, radial distance from center. intensity of the pigment

- lightness, top to bottom, white to black

The XY diagram shows 3d color space, from the top, in XYZ.

XYZ is a particular color space that Nathan Myhrvold picked at Microsoft in the early 90s.

There is no privileged "correct" color space, they're developed based on A/B tests and intuition by color scientists.

However, there are more correct color spaces, in that color science matters and is a real field. Commonly agreed state of the art is CAM16.

It's a significant mistake that Oklab is the first space with significant mindshare since HSL, it was a quick hack by a ex-game developer to make something akin to CAM16 with just one matrix multiplication.

CAM16 conversions involve significantly more than one matrix multiplication. But, its ~400 lines of code, and you can do millions a second on modern hardware.

The lightness scale is _way_ off from scientific color spaces, and thus it can't be used to create simple rules like "40 delta L* ~= 3.0 contrast ratio, 50 delta L* ~= 4.5 contrast ratio". Instead you're still manually plugging colors into a contrast checker :(

Then again, its still a step forward. It's even more maddening HSL was used for so long: it's absolutely absurd, ex. lightness = average of two highest RGB components. Great for demo hacks in 1976, not so great in 2016.

What do you think a negative red light source means?

It means that the subject turned a dial to add red light to the color being matched.

Basically, you have an unknown color C, and then an R+G+B color. Sometimes, you can’t match it, so you try matching C+R = G+B. This results in “negative” R, because you’re adding R to the other side of the equation.

The same happens with green and blue, but to a lesser extent.

That link is so slow where I live that I had difficulty getting the site to work, but as far as I could judge it gives a rather nice and understandable explanation of what is a rather complex matter. It's in considerable contrast to those sections of my textbooks on color theory, they're so dry as to make one yawn, they're full of algebra, the complex operator and matrices with precious little other explanation of what it all means.

Some of the comments have already covered most of what I'd have mentioned so I won't dwell on them now, although I'd add that I reckon GrantMoyer is on the mark with his point about the inappropriateness of displaying chromaticity on Cartesian coordinates.

It's worth noting that understanding the intricacies of chromaticity and color theory is difficult to the extent that its 'opaqueness' has been used to protect trade secrets (and likely still is for reasons I'll mention in a moment).

Commercial lab printers that print masked color negative (neg film with the orange mask) to positives—color photos and color film print stock—go to great lengths to protect their matrices (precision resistor banks) against copying. Similarly, companies like Kodak do not publish the 'film terms' for their various emulsions ('film terms' being the unique matrix information for each film emulsion).

The reason for this that to reverse-engineer the matrix with enough accuracy for a single film is a complex job let alone do so for a multitude of different films. Moreover, it's imperative the matrix be accurate if good color balance is to be achieved. Keeping this info secret provided a competitive edge, selling or licensing the info is worth money.

I'd add that the destructive orange mask used in color negative film is a brilliant concept for reasons I cannot cover here, however what's relevant here is that the mask makes reverse-engineering the negative's film terms that much more complicated.

I'm a bit out of touch these days but no doubt the same applies with inkjet printers and the like (matching coordinates to specific inks etc). So there's a modicum of truth to statements from Canon, Epson and HP when they say not to use third-party inks because the colors won't match properly (mind you, that's never stopped me at the exorbitant and outrageous prices they charge for inks).

My point is that if it were possible to unravel and make this chromaticity stuff simpler to understand then many of these expensive commercial decisions would disappear.

Ahh but alas, we're suck with it.

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BTW, for those who've used scanner software like SilverFast the manufacturer provides a list of film emulsions to select from before the film is scanned. Selecting the correct emulsion type ensures the proper 'film terms' are used for the scan, this in turn ensures the color balance is optimal.

I'm a bit cynical about SilverFast's approach to the problem, they've a limited range of film emulsions to select from (many of the old and important color negative types are missing). SilverFast's literature suggests that if one's color negative type is not listed then to select one that best suits. I am at a loss how one does that except to just make a guesstimate, so much for calibration. Also, one has to wonder why SilverFast has such a limited range given they've been in the business since many of said emulsions were still in production.

There are similar issues with Hamrick's VueScan software but I've not time to address them here.

Again, all these issues further illustrate the practical complexities surroundibg the chromaticity diagram.

I say "cursed" because I have no idea what that means. What the heck is that shape??

Reminds me of frinklang.

"The most-commonly used, CIE 1931, is long known to be off by a factor of 7 from average human perception at short wavelengths, (compare it to the 1978 definition at 400 nm) and is arbitrarily truncated before the limits of human perception. In addition, no one perceptually-weighted curve is possible because the human eye is differently sensitive for photopic (bright-light, cone cells) and scotopic (dark-adapted, rod cells), or if the illumination occurs over narrower or wider fields. Many incremental improvements on these systems have been proposed, but none are part of the authoritative, oversimplified definition of the candela, making it useless for unambiguous definitions that can be agreed upon or binding to any party. Pronouncements of the CIE are in no way binding on the BIPM, nor vice-versa, and the CIE has a proliferation of "standard curves," which all disagree with each other. Agreements to use one curve or another thus have to be agreed outside the definitions of the SI, and, of course, parties can disagree on which curve to use. You can use CIE 1931, or CIE 1978, or the "CIE 1988 Modified 2° Spectral Luminous Efficiency Function for Photopic Vision" or the 2005 improvements by Sharpe, Stockman, Jagla & Jägle, or ISO 23539:2005(E), or something else..."

https://frinklang.org/frinkdata/units.txt

This article illustrates the theory and math that lead to the horseshoe diagram in a very approachable style that is as simple as possible without being too simple.

A Beginner’s Guide to (CIE) Colorimetry — Chandler Abraham

https://medium.com/hipster-color-science/a-beginners-guide-t...

The https://oklch.com color picker shows another way to represent colors:

- The 3D version looks like a mountainscape of colors

- L(ightness), C(hroma), and H(ue) are orthogonal 2d slices of this mountainscape

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And this software renders 3D chromaticity (gamut?) diagrams: https://youtu.be/FdFpJFSTMVw?t=679