And yet, millions of people haven't complained about it, this problem you cite. LED TVs keep selling. sRGB is one industry standard; back before LEDs, color TVs had three different phosphors in the display and a somewhat different standard. Despite the problem you say is not resolved with standard color maps, lots of people bought color TVs then, as they still do now. Why don't more people complain about the colors on their TV?
Color in the first instance, is determined by what part of the EMS that falls on a body...secondly what part of that EMS is absorbed and what part is reflected.
Why a CIE 1931 color diagram/plot is an affine plane: --https://en.wikipedia.org/wiki/Affine_plane Compare the use of red and green in the xy "system" with different units/scaling along the axes . . . Although it's said that distances and angles aren't defined in an affine space, I can see a pair of lines intersecting at right angles, what gives? Is this "angle between red and green colors" completely artificial?/rhetorical_question
One other obvious thing about a CIE diagram such as the example I've posted, is that there are gradients in it, of intensity of single (spectral) colors. A gradient is a vector space. q.e.d. A spectral color is like a Dirac delta function in the time domain.
please stop using terms you don't understand. The gradient is differential operator acting on a scalar field that outputs a vector field. What scalar field do you have in mind? But the Dirac Delta only takes on meaning inside an integral. What exactly are integrating?
Intensities for each of the three colors range from 0-255 (i.e. digital intensity). The gradient is smooth though, because it's perceived to be smooth; we're talking about generating colors, mixing them together, and perceiving them. Perception is "lossy"; our visual system does a lot of approximation. But a monochromatic color or light source, might be a laser beam; this is something engineers can approximate (the power density spectrum of) with a Dirac delta. I'm pretty sure a little research into color models can explain this. Ordinary LEDs nowadays emit a fairly tight bandwidth centered on a frequency (or wavelength, if you want to ignore time). This as you most likely know, is another candidate for the delta function. And there is this from an online source: Please Register or Log in to view the hidden image! So now all you need to understand is what a color matching function is . . . p.s. the integral above is over wavelengths.
Yes, they do. Explicitly. "They" refers to the various theoreticians and modelers and engineers you linked and referenced. Wavelengths are not vectors, LEDs are not vectors, inks are not vectors, colors are not vectors, and so forth. Basis vectors are mathematical abstractions. This nails the lid shut: Until you realize that wavelengths are not colors, you will continue to post like that. Why, for example, would anyone need a "color matching function"?
This seems to be you deciding to remain tone deaf or blind, or both. Colors are defined as functions of wavelengths. One thing these functions do is "put" wavelengths into the time domain. Wavelengths don't come equipped with any dynamics, but you know that, right? What lid? What the hell are you talking about? You understand that a color standard can be perfectly understandable when it's defined as having 3, or n, wavelengths (all distinct) in it? The previous caveat still holds (why wouldn't it?); you need a time domain and wavelengths aren't in it. If wavelengths are not colors (whoda thunk?), why do you keep saying that engineers define colors "as wavelengths". Considering that . . they don't? Really, they just don't. Or is it that you think engineers don't really understand waves? Colors are defined as functions of wavelengths. Colors are defined as functions of wavelengths. Colors are defined as functions of wavelengths. Colors are defined as functions of wavelengths. Got it yet? Or would you like me to repeat that? If you want to know what a color-matching function is (as if), find out, there are plenty of references online. Hell, maybe you could do some experiments to see if you can match colors all by yourself . . . ? Here, I'll do my best to act like less of an asshole, and drop the handy hint that optical illusions, such as posted by you and James R, exist because there really are color-matching functions, in our neurobiological domain. It's the reason color TVs are designed a certain way, following a certain recipe, say. The brain has algorithms it runs when it receives color information (encoded in neural signals which, we don't understand very well). When it runs them on optical "illusions" they give a false reading, or interpretation, of the information.
I just googl'd "color is a wavelength" to see what happens. Lots of articles bang on about how the colors we see have wavelengths, different wavelengths are the reason we see different colors. That's true, but not really very scientifically accurate (or all that useful). Kids can understand it though, especially when they get shown the visible spectrum in a nice straight line (with a Euclidean metric on it, i.e. on the domain of . . . wavelengths). Explaining that the bands of colors are not in a Euclidean domain is a little more involved (consider affine geometry first, say) . . . I came across this from hyperphysics Note the first sentence has "color is determined . . . "; the last sentence hands off the question "what is color" to the rest of the brain. It also has: "the eye is very much like a camera"; "visual information leaves the eye . . ." If we replace a human eye with a camera, what can we do with the visual information? (thinks hard).
Although the term "affine plane" isn't heard much below university-level maths or physics, once you know what one is you see they're used all the time in physics. The visible domain of wavelengths has this spectrum of colors (that we see) attached to it. Plotting wavelengths (in the x direction) versus colors (in the y direction) means you construct an affine plane. Please Register or Log in to view the hidden image! Roughly, the question is, how high does the colored band need to be? The answer is it has an affine height. The space is quotiented by an equivalence relation (each color is independent of how "tall" it is in the plane). More abstractly, if you're a color it doesn't matter what height you are in the diagram, all (nonzero) distances look the same. Lines of colors are parallel in the y direction (this need not be perpendicular to x), independently of the angle between the x and y axes in the affine plane. So now to the problem of a vector space, starting with this affine construction. It has no inner product for starters. How do we get from here to a CIE diagram and why would an engineer want to get there? We want a cone over this set of distinct-looking colors (at least, that's what Erwin S. wanted). Consider that a real (or a topological) line can have a Euclidean metric and so can be defined in terms of units of distance. Once you color a real line with a single color (red, say), all the points look the same. Any (red) colored distances (not zero) look the same because they . . . are an equivalence class of distances. First define a scaling function on the 1-colored line, so you have a gradient of intensities and take it from there. Do this with each color in the affine construction above and there should be a line of black at the highest (resp. lowest) y value (for the intensity function). The space now has a gradient defined on it (or . . . does it??).
Yep. That's the way they all do it, in your links - because if they started with the colors, they couldn't define a vector space or a distance measure or any of that stuff. You have to construct all that stuff over the EMR wavelengths, and then match the color names to the wavelengths (regardless of what humans perceive in various different circumstances). That means restricting your colors to one per wavelength or combination thereof regardless of human color perception, so you get a function, but it works for engineering purposes. I was just wondering if you understood what that implied - that the engineers are assigning color names to the wavelengths, one color per wavelength or combination thereof.
But starting with the affine plane of parallel colors (see above) you have an obvious distance between colors, a wavelength difference. It lives along the x axis (but you can see that, right?). The band of spectral colors has obvious discrete colors in it (or, you might restrict a color, say yellow, to a single wavelength or a very small section of the spectral line centered on a single wavelength). These discrete colors are not mixtures of other colors; mixing colors is another affine operation on pairs of colors which generates the interior of the affine cone over the spectrum. As explained earlier in this thread, any CIE diagram in some xy system, is a 2d slice through this cone at a constant illumination intensity. Note, Erwin Schrodinger did this affine cone construction a long time ago, CIE has a color standard dating back to about the same time, i.e. 1931. Well before color TVs existed (but, who's counting?).
I've been wondering actually, about what exactly your question is asking. Do I understand what assigning a name to a color implies? Engineers aren't the only ones doing this but you know that I assume? I assume, because you've posted stuff about cultures and color-naming. One thing I do know about naming colors is this: humans can distinguish a number of colors and that number is much larger than the number of words in any language (English is considered to be among the largest or actually the largest language). I know that Isaac Newton fudged things when he named a color indigo, which is actually a blue color; but he was possibly more interested in finding a color-symmetry and didn't consider an affine plane so much; but who can really say? Besides, we've advanced the science of color somewhat since the 17th century. I would say that these days the average electronics engineer isn't too concerned about what to call a fixed color; engineers deal with wavelengths (not in the time domain) and their corresponding frequencies (in the time domain, where reality is). So engineers replace colors with numbers and dynamical equations (for currents flowing through devices which all have a fixed impedance, etc.)
