Talk:HSL and HSV/Archive 2

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HSL vs. HSI

HSI is different than HLS. HLS is sometimes known as HSL, not HSI. HSI is a cylindrical model, where H (hue) is an angle from 0 through 360 degrees, S (saturation) is the distance from the origin around which H rotates (normalized to range from 0 through 1), and I is intensity, which is distance along the vertical axis of the cylinder (again, ranging from 0 through 1). HSV (hue, saturation, value) and HSB (hue, saturation, brightness) are the same as each other, but are not the same as HLS. See Digital Image Processing by Kenneth R. Castleman, chapter 21, for a description of the HSI color model. Seaandsky 21:54, 3 October 2007 (UTC)

Can you give a better description? Maybe make a quick sketch image (or even ascii art would be fine :))? I'm not understanding the difference. --jacobolus (t) 21:46, 4 October 2007 (UTC)

I think the article should not say HLS and HSV are cylindrical. This is not correct. HLS is a double hexcone and HSV is a single hexcone. HSI is a cylinder. I will try to get back with some drawings if I can find any. :) Seaandsky 00:24, 9 October 2007 (UTC)

Here are some illustrations, but they don't quite align with how you're putting it. Dicklyon 04:45, 9 October 2007 (UTC)

No, mathematically they both are cylinders. But these can be thought of as simple transformations of cones or hexcones (or I suppose more accurately: topologically, cylinders, hexcones, and cubes are all the same, so HSV can be thought of as any one of the three, but the metric used is most straight-forward on a cylinder). I plan on explaining this more clearly, with pictures, but give me a few days to write the description. --jacobolus (t) 05:07, 9 October 2007 (UTC)

It's straightforward on a cylinder only if the saturation limit is fixed, independent of the lightness dimension. The other shapes more appropriately describe the saturation limits in different systems. Now if we could only be sure which is which... Dicklyon 05:13, 9 October 2007 (UTC)

The way it works is that the saturation limit *is* fixed, but a saturation of n is thought of as different “amounts” of saturation depending on the lightness (at least for HSV; s = (max - min) / max, where max = max(r, g, b), etc., so when any of r, g, b is 0, s is 1). Similarly, saturation is defined on a 0-1 scale regardless of hue, and "hue angle" in the "hexcone" is not really angle geometrically, but is rather defined as if each segment of the hexagon was warped into the corresponding arc. This is IMO best explained by showing the transformation from RGB cube to hexcone or double hexcone, and then further showing the transformation from hexcone to cylinder, with pictures. --jacobolus (t) 05:19, 9 October 2007 (UTC)

It would be great if this could be cleared up in terms of how HSV, HSL, HSB, HLS, etc. work mathematically and have graphical depictions of these as such 'as is', and discussing user-friendly visualizations in appropriate sections. For example, the cylindrical depiction of the HSV method has the description that it "might" be considered the mathematically most accurate depiction - I'd say drop the "might", as it simply is. An alternative depiction is given in the form of the tip-down cone - however this depiction implies that with decreased Value, the Saturation (distance from cone revolution axis to boundary) decreases as well, which in the HSV model referred to in this article (See also Dicklyon's comment for a page which describes there being two models named HSV) is not the case. Similarly, the only depiction given for HSL, "HSL arranged as a double-cone", does not fit the rest of the description nor the RGB to HSL conversion formula given. The article itself states that "a very pastel, almost white color can be defined as fully saturated in HSL". The depiction provided does not fit this claim. Mathematically, both would have to be cylinders to fit their descriptions. The conversion formula seems to fit this notion - a pale RGB color of [1.0,1.0,0.9] when fed through the conversion to HSL gives a Saturation of L = (1.0 + 0.9) / 2.0 = 0.95 : S(L>0.5) = (1.0 - 0.9) / (2 - 1.0 + 0.9) = 0.1 / (2 - 1.9) = 0.1 / 0.1 = 1.0 . The 'hexcone' depiction is even worse, in my opinion, as it implies a varying saturation level when going along the hue wheel (e.g. Red = [1.0,0,0] = 1.0, Orange = [1.0,0.5,0] = 0.866.., Yellow = [1.0,1.0,0] = 1.0) when measuring distance from the edge to the center axis (Edit: I understand that this is not how Saturation -is- determined within a hexcone, but without explanation that is not immediately clear.). I do understand that there are modifications to the two described in my comment as described in the article (ignoring the depictions) that may in fact fit the depictions and can be very useful; for example, the HSL method depicted (but not described) with a double-cone is superior to the cylindrical HSL when comparing two RGB values within such a space. A nearly-black RGB value RGB[0.01,0,0] in the cylindrical HSL results in the values HSL[0,1,0.005], which in terms of saturation places it nowhere near a black RGB value RGB[0,0,0] = HSL[0,0,0]; in fact, bright red RGB[1,0,0] = HSL[0,1,0.5] is a closer match within this method. The depicted double-cone HSL method does not suffer from this, to most observers (visual and mathematical), illogical behavior. On the other hand, the cylindrical method is much easier to work with visually and loses less fidelity code-wise (in limited bitdepth systems). I may certainly be entirely mistaken, but my excuse is the conflicting data both within a single article as well as from different sources cited. I look forward to jacobolus' edits and any further brainstorming/source citing/real world implementation conventions (not sure if the conical HSV, which may be the original, is what HSV should be described as, given that all the HSV implementations I'm aware of use a cylindrical HSV) ZeBoxx 00:04, 19 October 2007 (UTC)

Yes, you're on the right track; you've hit on the essential problem which is that conceptually these models describe a cone or double-cone (or hexcone/double-hexcone), but leave their values mathematically in a ([0°,360°), [0,1], [0,1]) range, which looks like a cylinder, when plotted in any reasonable fashion. I intend to make these distinctions clear (and with better pictures eventually) when I get around to rewriting this article, which I was planning to do sometime last week, but might not happen now for another week at least. --jacobolus (t) 00:47, 19 October 2007 (UTC)

For those who know German, the following page touches on many of the points made in other comments as well (RGB cube set on a corner, etc.). They, too, conclude that it is frustrating that there are so many conflicting descriptions and depictions - while also noting that for end-users, it hardly matters which model is used and how, as typical color-picking utilities are plenty intuitive no matter which model is chosen. http://www.hrz.uni-dortmund.de/computerPostille/September1999/00.html ZeBoxx 00:36, 19 October 2007 (UTC)

Heh. Whereas my conclusion (like that of Charles Poynton), is that none of these is particularly useful anymore on modern computer hardware which can quickly compute RGB values for colors in more accurate and intuitive models such as L*u*v*, L*a*b*, etc. --jacobolus (t) 00:51, 19 October 2007 (UTC)

I think the authors' conclusion is based mostly on the notion that most color pickers are no longer just three numerical fields into which you enter data and out pops a color; which would make HSV fairly confusing indeed ("I desaturated my Red and now it's White - what the.."). But with the typical triangle/square/whatnot presentation on-screen, interactively changing any of the values (or just picking one from right within the chart), no such concerns really exist. Picking a 'yellow' that is perceptually the same brightness as red becomes an issue of how good the user's vision is (L*a*b* won't save a colorblind person) and picking the color rather than one of endlessly fiddling with numerical values. That said, CIE L*a*b* does tend to be a superior color space for most perceptually-important operations (there's a reason color likeness functions, from plain delta E all the way to the behemoth that is CIEDE2000, base themselves off of it), but I wouldn't go as far as Poynton to say that HSV/HSB/HSL/etc. should be abandoned altogether; the single parameter Hue alone sets them aside enough from any of the other color models to be indispensable. The many variations is just a little (understatement) overkill, however ZeBoxx 06:51, 19 October 2007 (UTC)

You've obviously never tried using a more perceptually-uniform/intuitive color picker, in comparison to an HSV/HSL one. ;) --jacobolus (t) 13:08, 19 October 2007 (UTC)

I've had to work with the strangest colorpickers (from RGB straight up to a LogLuv one for HDR colorpicking, they all have their pros and cons. HSV/etc. aren't so bad, as long as you get the visual charts to go with them so that you can see what does what; that was the point.. the colorspace/model doesn't matter so much in colorpickers as you get direct feedback/etc. anyway.. yes, RGB will still be more intuitive than, say, CMYK when working on a computer - but anybody who's only used to RGB can happily work with a colorpicker set to CMYK. Offer then only four value controls, one for each channel, and no graphical feedback, though, and they're far more likely to get stuck. In that sense, I don't think the colorspace/model matters too much for the purpose of colorpickers. For purposes of matching colors in any standard way, finding complementary colors, storage accuracy etc. - that's where the spaces/models are a more important element. ZeBoxx 01:29, 20 October 2007 (UTC)

I've been waiting to see the updated page before I made any more comments, but I do hope it will come soon because at the moment it may be a little unintentionally misleading. It's important to interpret saturation in the equations for conical HSV and HLS in terms of something along the lines of a percentage of the maximum for the particular value or lightness. Saturation of 1 means the color is on the surface of the cone. However, the distance between the surface of the cone and the vertical axis varies as value or lightness increases or decreases (for a cone, but not for a cylinder). So a saturation of 0.6 at one lightness is further away or closer to the vertical axis than at some other lightness, for the conical models. This is distinctly different than the cylindrical model, in which the saturation can be interpreted literally as a normalized distance from the vertical axis. The equations for each are different and the results are distinctly different when you see them displayed. At lightness = 1 in the double hexcone HLS model, you will see white. However, in a cylindrical model, at lightness = 1, you may still see some hue, depending on the saturation. (Note: you must also pay attention to whether the equations refer to a hexcone or a cone where the surface has been "warped" so that it is round.) Here's a link to some of the more basic equations for HLS, HSV and HSI: http://www5.informatik.tu-muenchen.de/lehre/vorlesungen/graphik/info/csc/COL_23.htm#topic22. I look forward to your updates. Seaandsky 17:03, 19 October 2007 (UTC)

I did not find any better illustrations than those mentioned by Dicklyon above on the web. The book and chapter I mentioned above, by Castleman, has an illustration of cylindrical HSI. Below, you say you are looking for references. There is also a book by Alan Watt, titled 3D Computer Graphics, published by Addison Wesley, which goes into the HLS and HSV color spaces in chapter 14. I do find that on the web, HSV and HLS may sometimes be depicted as hexcones and sometimes are transformed into cylinders (by "warping", as you say, the segments of the hexagon). The hexcones, as you have already said, come from tipping the RGB cube up so that its neutral (black-to-white) diagonal lies along the z-axis. As Dicklyon says, the cylinder then comes about from using a saturation maximum that is fixed, independent of the lightness level. Seaandsky 13:27, 9 October 2007 (UTC)

Dick sent me a copy (via email) of Alvy Ray Smith's original paper, which explains the geometric intuition behind the models. I was planning to turn his explanation into some diagrams of my own; I don't really find any of the existing diagrams I've found online satisfactory. --jacobolus (t) 13:35, 9 October 2007 (UTC)

Some time later...

I would just like to comment that the particular geometric solid used to depict HSL, HSV, HSI, etc. doesn't really matter. It's a matter of preference, not mathematical accuracy. The models all use three parameters, and they can be applied to any function that also takes three parameters. They can be mapped to a cylinder, sphere, cone, cube, whatever. There's also the hexcone. The use of the sphere in some form or another dates back to at least 1810 (see the image here, the image is described here). For instance, Also, the square color picker can be seen as either a slice (e.g., a partial cross-section) of a cylinder or a cross-section of a cube. The triangular color picker can be seen as a slice of a cone. SharkD (talk) 06:19, 13 January 2008 (UTC)

I think if you'll look more closely you see how the shape of the solid is important. First of all, I think we all agree that hue has to be arranged in a loop (circle or hexagon); now in HSL white is a unique L=1 top point; that is, when L is 1, S must be 0. This relationship is lost if you distort the space to a cylinder; for a sphere it can still work, perhaps, but it works most naturally with a bi-cone. Both HSL and HSV have a similar point at black. Why would anyone use cylinders for this? Dicklyon (talk) 07:57, 13 January 2008 (UTC)

That's not the case; luminance and saturation are independant of each other. A color can have any value for saturation; and, as long its luminance is equal to 1, it will be white. Also, this convergance upon a single point affects all the other colors, as well. Simply because the color white can only have one value for saturation—or is only a single color as opposed to a range of colors—doesn't mean it logically follows that all the other colors become less saturated (because of the slope) as they increase in luminance. SharkD (talk) 09:13, 13 January 2008 (UTC)

Not the case? Are you ignoring the defining equations and/or the limitation on the range of values? Getting L=1 requires min=max=1, so max-min is 0, so S is 0. They are not independent. The HSL model certainly does imply that colors become less saturated as L approaches 1; it's even logical, since L=1 means white, to say that all colors become less saturated as they approach white. That's the HSL model. HSV is different, being a cone, not a bicone. It all comes from the equations. Dicklyon (talk) 09:32, 13 January 2008 (UTC)

View this simple animation of the saturation changing and the color remaining white. SharkD (talk) 10:22, 13 January 2008 (UTC)

Yes, that's clear evidence that you are not the only one to ignore the definitions. It makes sense in such an interface to map nonsense coordinates back into real colors, which is why they do it. But does it help clarify the structure of the defined color model? No. Dicklyon (talk) 17:32, 13 January 2008 (UTC)

The formula I use to convert RGB to HSL sets the Hue to zero instead of "undefined" when min - max = 0. This is an arbitrary value necessary to keep the function from returning a range of values instead of only a single value. The same is true for Saturation when Luminance is equal to 0 or 1. Having the function return an "undefined" value would result in a nonsense RGB value that the computer could not interpret. Setting Hue or Saturation to zero is a necessity to keep computer applications from breaking, not due to mathematical accuracy. SharkD (talk) 19:09, 13 January 2008 (UTC)

Hue's no problem. The hue angle doesn't affect the geometry when it's at zero radius due to zero saturation. But the Saturation is defined as zero at black and white, not undefined. The shape of the solid is determined by the range of L and S values that you can get from the defined range of R, G, and B values. You can decide how to map L and S to height and radius or latitude or whatever, but no matter how you do it, you'll have something like a bi-cone, with white at the L=1 point where S can not be other than 0, and black at the L=0 point where again S can not be other than 0. You can't get a cylinder out of it. The only thing "undefined" is where the value has no geometric effect; there's no other place that blows up; and converting from HSL to RGB is not the issue; the domain (RGB) determines the range of HSL. Dicklyon (talk) 19:25, 13 January 2008 (UTC)

How about you do the reverse: use the HSL to RGB conversion formula and experiment with changing the Saturation values while keeping the Luminance 0 or 1. If these experiments lead to the results I describe, is this formula, then, also "wrong"? SharkD (talk) 19:30, 13 January 2008 (UTC)

What needs to be done

SharkD, you have some great 3D image making tools and abilities, but you've not applied them ideally, seems to me. For example, Image:HSL sphere color solid.png still has a misspelling and an incorrect indication of saturation as radius in the sphere; if you want to embed HSL in a sphere, you need to work out a mapping that works, and illustrate it correctly. As for the cylinders, I suggest we get rid of them, and instead illustrate the solid shapes that represent the range of HSL and HSV values that come from applying the definitions to the domain of RGB values. Agree? Other opinions? Dicklyon (talk) 19:36, 13 January 2008 (UTC)

No, I think the cylinders should stay, as they are the most uniform way of displaying the geometry used by the coordinate systems of the two models. Given the numerical mapping in use by HSL/HSV models, cones and double cones, whether hexagonal or circular, are extremely distorted. In other words, in a cylinder, changing e.g. *l* by 0.5 is a uniform movement, whereas in some other shape, the movement is unnaturally dependent on position in the shape. --jacobolus (t) 19:51, 13 January 2008 (UTC)

The spherical depiction is just as "uniform" as the cylindrical depiction. A cube is uniform, as well. SharkD (talk) 20:46, 13 January 2008 (UTC)

That's certainly not true. If you increase s from, say, 0.3 to 0.7, you will always move 0.4 units in a cylindrical mapping. In a spherical mapping, s = 1.0 is defined relative to the edge of the sphere, so at the center (i.e. v = 0.5), you'd be moving 0.4 units, but halfway up (v = 0.75), you'd only be moving 0.4×√3/2 units. It is the complexity of the resulting arithmetic that makes a sphere a particularly inappropriate distortion of HSV: a double-cone or double-hexcone is a more comprehensible geometrical representation. --jacobolus (t) 21:07, 13 January 2008 (UTC)

I guess I don't understand what Jacobolus is saying about uniformity and the cylinder. Isn't it just height = l, radius from axis = s and angle = h? If so, then it's the same geometry as the cone and bicone, within the range of the defining functions, and an arbitrary filling in of values outside that range. Or is there some other mapping to cylinder coordinates that I've missed or that has not been stated? As to the sphere, I haven't seen a mapping to that, either, except for the one implied by the illustration, which is obviously "wrong" in that it gets the wrong saturation at the poles. Dicklyon (talk) 21:11, 13 January 2008 (UTC)

Take a closer look at the sphere again. The saturation remains constant for a given distance from the center, not the distance from the central axis. This is a common misunderstanding of lattitude. Lattitude is not a linear movement "up" or "down"—it's a rotation around the center. Imagine if the Earth expanded. The lines of lattitude and longitude would not move up or down linearly. They would scale with the changing radius, which would result in a non-linear vertical transformation. This is clearly evidenced if you take a look at the parametric equation for the sphere. SharkD (talk) 21:29, 13 January 2008 (UTC)

Right, and that's the problem. It implies that white and black have saturation of 1, while the definitions say the saturation of white and black should be zero. If you measured from the axis, instead of from the center, it would be possible to get those right, whereas with measurement of spherical radius it is not possible. Dicklyon (talk) 22:02, 13 January 2008 (UTC)

According to the article on the sphere, "In mathematics, a sphere is the set of all points in three-dimensional space (R3) which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere." The parametric formula for the sphere is,

$x=x_{0}+r\cos \theta \;\sin \phi \,$

$y=y_{0}+r\sin \theta \;\sin \phi \qquad (0\leq \theta \leq 2\pi {\mbox{ and }}0<\phi \leq \pi )\,$

$z=z_{0}+r\cos \phi \,$

I simply substituted H, S and L for theta, r and phi. E.g.,

$x=x_{0}+S\cos H\;\sin L\,$

$y=y_{0}+S\sin H\;\sin L\qquad (0\leq H\leq 2\pi {\mbox{ and }}0<L\leq \pi )\,$

$z=z_{0}+S\cos L\,$

I see. I mean, is that really what you did? Because it maps both white and black, and all grays for that matter, to the center of the sphere, and leaves other points on the axis undefined, which seems like a peculiar interpretation. If you could map the surface of the cylinder onto the sphere that way, but map the axis of the cylinder directly onto the axis of the sphere without collapsing it to the center point, so that you could preserve a representation of neutrals, that might work a lot better. The simplest way would be to just distort the distance from the axis of the cylinder to make a sphere, rather than starting from the kind of spherical parameterization you used. Dicklyon (talk) 04:17, 14 January 2008 (UTC)

Yes, this is what I did. You can confirm this by doing the mental math of inputting arbitrary values for H, S and L into the formula, visualizing the results and then comparing them to a reference image (this image is a bit better for the purposes of mental visualization, as individual colors are hard to distinguish apart in the ray-traced image). If you have access to POV-Ray, I could create a demonstration scene which would do a better job of showing this. Other points along the vertical axis are not undefined; they all have their corresponding H, S and L vectors. SharkD (talk) 06:21, 14 January 2008 (UTC)

OK, I was thinking of L as the height, still, like in the cylinder; I see that with the angle, the only real undefined point is the center, where all the neutrals map. That is, you've got an embedding where when s=0, you don't get to know anything about l. Dicklyon (talk) 06:48, 14 January 2008 (UTC)

Incidentally, in Phillip Otto Runge's mapping of H, S and L to a sphere (see the image in his biography article), L is the height. I don't understand why he did this. I don't understand the math behind it. SharkD (talk) 07:37, 14 January 2008 (UTC)

Here is the parametric formula for a cylinder:

$x=x_{0}+r\cos \theta \,$

$y=y_{0}+r\sin \theta \qquad (0\leq \theta \leq 2\pi {\mbox{ and }}0<z\leq h)\,$

$z=z_{0}+z\,$

Substituting H, S and L for theta, r and z results in the cylindrical depiction already present in the article.

Here is the parametric formula for a cone:

$x=x_{0}+(h-z)/h\,r\cos \theta \,$

$y=y_{0}+(h-z)/h\,r\sin \theta \qquad (0\leq \theta \leq 2\pi {\mbox{ and }}0<z\leq h)\,$

$z=z_{0}+z\,$

Substituting H, S and L in for theta, r and z results in a cone (but not a double cone).

Here is the parametric formula for a solid cuboid (the parametric formula for the surface, only, is a bit more complicated, as it requires additional logic):

$x=x_{0}+x\,$

$y=y_{0}+y\qquad (0<x\leq width{\mbox{ and }}0<y\leq length{\mbox{ and }}0<z\leq height)\,$

$z=z_{0}+z\,$

Substituting H, S and L in for x, z and y results in this image. SharkD (talk) 03:51, 14 January 2008 (UTC)

That cuboid doesn't respect the circular nature of hue, which is part of why it looks so bad. Dicklyon (talk) 04:17, 14 January 2008 (UTC)

Well, strictly speaking, the HSL model doesn't have a circular nature for hue. The values for H, S and L all increase linearly to some limit. The computer doesn't treat one value as especially "circular". Hue exists along a linear spectrum that extends into other wavelengths that can't be considered colors. Users simply find arranging hues into circles to be more "intuitive". I find the spherical depiction doubly "intuitive", as users don't have to switch from thinking along linear lines to circular ones for different parameters. You get whatever benifits there are from "circular" thinking for both parameters. But, this is just a preference. Some users will prefer the cube model. SharkD (talk) 06:44, 14 January 2008 (UTC)

Well, sure, for the benefit of the digitization, the circle is broken into a principal segment from 0 to 360; but since neighboring colors cross the cut, it's not a good idea to ignore the underlying circular structure. H is the only one that has this circular nature. As to some users maybe preferring that cube, that's hard to imagine, but out of a nearly infinite population of users, I guess anything's possible. Dicklyon (talk) 07:10, 14 January 2008 (UTC)

As I said, hue doesn't really have a circular nature. A circle is just the preferred method of visualization. SharkD (talk) 07:27, 14 January 2008 (UTC)

I'm not sure what you mean by "doesn't really have a circular nature". Hue ranges from [0, 360), where increasing the hue from a color of hue 359° by 1° yields hue of 0°. The shape made when we pick a particular s and l, allowing h to vary, is topologically equivalent to a circle. Whether you call this “circular” or not doesn't really change this mathematical reality. In some computer representations, the interval [0, 360) is actually represented as [0.0, 1.0), or [0, 256), etc., for convenience. --jacobolus (t) 12:25, 14 January 2008 (UTC)

The definition of a circle is all points equidistant from a central point. In physics, there is no "thing" that hues are oriented around. From the color wheel article: "A color wheel or color circle is an organization of color hues around a circle, showing relationships between colors considered to be primary colors, secondary colors, complementary colors, etc." The arrangement of hues around a circle is a human construction, designed for "usability" reasons (e.g., it's useful as a learning aid). It does not occur this way in nature. "In normal human vision, wavelengths of between about 400 nm and 700 nm are represented by this incomplete circle, with the longer wavelengths equating to the red end of the spectrum." Wavelength is a linear measurement of the distance between the peaks of a sinosoidal wave. The value for h can be normalized to any value. Its normalization to 0-360 degrees indicates a preference for a given visualization. SharkD (talk) 19:59, 14 January 2008 (UTC)

I feel like this discussion is a pedantic semantic quibble, and like I'm talking past you, without making myself understood. I suppose you aren't willing to take my word for it that bright red is equivalent to bright red, and that the “hue” of HSL and HSV has been explicitly set up in the model to “wrap around” from one edge to the other (the topological definition of a circle). I'm not sure if there is anything I can say to convince you, other than suggesting you look again at the construction of HSV from the RGB color cube, where geometrically, this “wrap-around” aspect seems pretty obvious. If you really want to have a philosophical argument about the meaning of “circle”, I suggest you look elsewhere, as a discussion of the topic as it applies to HSL/HSV does not interest me. The article about color vision may help you understand the distinction between wavelength and hue. If you're still hung up about it, I can suggest some books which further explain the subject. --jacobolus (t) 20:44, 14 January 2008 (UTC)

Here is a nice article that describes how the arrangement of hues into circles was arrived at. It supports my argument that hues aren't arranged into circles based on physical properties of beams of light. Rather, it was designed to make geometric calculations easier—hence "usability". All arrangements of hue into a circle are descended from Newton's circle. Further, the functions provided in this article simply convert one set of vectors into another set of vectors. Though a circular mapping of hue was explicitely intended, as you say, how you map these vectors is really arbitrary. SharkD (talk) 22:26, 14 January 2008 (UTC)

I'm sorry if my arguments seem to come across as bothersome. I feel hesitant about getting into what is essentially a "popularity contest" about which depiction is most appropriate. SharkD (talk) 22:45, 14 January 2008 (UTC)

Newton thought there was something physical about closing the 1D wavelength parameter into a hue loop, but he was wrong. The circular nature of hue comes from psychophysics or physiology, not from physics. But it's very real; any kind of colorimetric representation has hue loops surrounding neutrals. You can always break the loop and show it as an open 1D parameter, but that's too much of a bastardization of HSL and HSV, and loses the important representation/topological property that was intended in defining in terms of angles. So let's just not go there; it has nothing to do with popularity. Dicklyon (talk) 23:17, 14 January 2008 (UTC)

I don't see how it logically follows that there is a circular property simply because some representations arrange hue in a circle. I agree that arranging hue in this fashion is useful for highlighting certain processes that occur within this domain. Also, I'm sure Newton was well aware that his arrangement of hue into a circle was not based on physical properties. SharkD (talk) 23:49, 14 January 2008 (UTC)

One other nifty thing about the sphere is that lightness and darkness are mapped as polar opposites. It kind of reminds me of this diagram. SharkD (talk) 22:11, 14 January 2008 (UTC)

As for SharkD's models, I have a few main problems with them: the misspelling is annoying (not to mention that L is not usually taken to stand for “luminance” at all, whatever the spelling; better I think to leave these labeled H, S, L, and V, particularly as S means something different quantitatively for each of the models), the shading applied to them is unfortunate, as it alters the relationship of the colors, and w.r.t. the sphere in particular, it seems quite unsaturated, the horizontal grid is distracting, the vertical axis line probably shouldn't cover the lower half of the sphere, I don't really like the curvature in the lettering, and it's not really a big deal, but I think I'd personally choose a different section to cut away. --jacobolus (t) 19:59, 13 January 2008 (UTC)

I used "luminance" because it is used in the Windows color picker. I can change this if the usage of the term is inappropriate (I think the article discusses this somewhere), though a Google search doesn't really show a great disparity in the usage of the two terms (hue saturation luminance = 30K+ hits, hue saturation lightness = 40K+ hits). As for the horizontal grid, it places the object within the coordinate system, which is important when trying to model the object (note the difference in position within the coordinate system between the sphere and the cylinder). The vertical axis passes through the bottom of the sphere because one of the lines of longitude passes through the center of the viewing plane. You see through the line of longitude to the other side. SharkD (talk) 20:46, 13 January 2008 (UTC)

I'm sorry about the mispelling. I will fix this soon. As for mapping Saturation to the radius— what exactly is wrong with this? It is done in the case of both the cone and cylinder depictions. SharkD (talk) 20:46, 13 January 2008 (UTC)

If you map things to a sphere, saturation is still radius w.r.t. a cylinder, that is, horizontal. The distance from the center of the sphere to a point is meaningless. --jacobolus (t) 21:02, 13 January 2008 (UTC)

It's really not clear what the right mapping is for a sphere, but distance from the axis will at least go to zero at the poles, unlike distance from the center, which does not. Dicklyon (talk) 21:11, 13 January 2008 (UTC)

OK, I goofed

On reviewing the defining equations for s, I see that I was wrong. Apparently in both HSL and HSV it does have a range out to 1 for all values of L or V, which is what Jacobolus and SharkD have been saying about the space being a cylinder. This is a disconnect from what I thought the definition was. I'll have to review the sources and see if there are different versions, or if I was just remembering wrong. And it makes some of my recent edits wrong, so I'll fix that. Sorry about the confusion. Dicklyon (talk) 21:19, 13 January 2008 (UTC)

Right, and that is what Alvy Ray Smith's formulae have as well, even though he calls them hexcones. But the geometrical intuition for the model of HSL for example is based on a hexcone created from the RGB color cube, and I want to create some diagrams which better display the progression from color cube → hexcone → cylinder, as I think that will clarify things for readers. --jacobolus (t) 04:31, 14 January 2008 (UTC)

Sphere

I'm responding here after a message on Wikipedia talk:WikiProject Mathematics#Help on parametric math. One way to find appropriate solids is to find which values of (h,s,l) give the same colour, ideally these are represented by a single point. In particular white (h,s,1) and black (h,s,0) should map to single points, giving the double-cone shape. From this double cone other shapes can be obtained. By pressing the top point downwards you get a single cone. By expanding the bottom point of this cone to a disk you can get a cylinder, with the base of the cylinder all black.

I'm fairly sure the sphere image is wrong. With that image if saturation is 0 you get the center of the sphere yet changing lumanance should give a range of colours from black to white. Note in the graphic to the right, in the bottom right image that all-points on the lower half of the axis give black. --Salix alba (talk) 11:12, 14 January 2008 (UTC)

Notice that Runge's sphere has nothing to do with HSL or HSV. I'm also not really sure what the question is about, which is listed at wikiproject mathematics. I have university mathematical experience which extends significantly beyond the issues in question here, if that is of any use, and should be able to answer any specific mathematical questions SharkD has. --jacobolus (t) 12:18, 14 January 2008 (UTC)

Runge's image shows a mapping of colors to a sphere based on their hue, saturation and lightness components. How does this not have anything to do with HSL? SharkD (talk) 20:26, 14 January 2008 (UTC)

I agree that in the cartesian coordinate system, the hue and lightness parameters of the color at point (0,0,0) of a sphere is undefined. However, this is not the case in the spherical coordinate system. In this system, each coordinate has a unique color. The same is true for the cone and double cone; e.g., colors coalesce to a single point (or two points in the latter case), and at these points (white or black), the saturation parameter is undefined. Additionally, at any point along the central axis the hue parameter is undefined. The spherical, cylindrical and conical depictions are simply mappings of the HSL cube to the spherical, cylindrical, and conical (if such a thing exists), double-conical (ditto) coordinate systems. Any limitations in these particular depictions are the same as you find in any depiction of these coordinate systems. SharkD (talk) 20:33, 14 January 2008 (UTC)

Can you make a sketch (pen and paper, or MS paint, or whatever, would be sufficient; doesn't have to be a masterpiece) of how you think this spherical organization of HSV is supposed to work? Because I don't have the foggiest idea what you're talking about in your description above. --jacobolus (t) 20:38, 14 January 2008 (UTC)

I've provided three diagrams already, as well as a formula. Should this not suffice? SharkD (talk) 22:02, 14 January 2008 (UTC)

I agree that your formulae and descriptions do make it clear; not sure why Jacobolus isn't getting it. But you haven't addressed the problem that several have pointed out: this embedding of HSL into a sphere does not preserve the different neutral colors as distinct points. Other embeddings could easily do so. Let me know if you'd like me to write you some equations. As to the Runge Farbenkugel, it's unclear what he took the parameters to be. HSL hadn't been invented, nor the RGB that it's defined in terms of; Runge's system is clearly based on RYB, but beyond that I don't know. Dicklyon (talk) 22:30, 14 January 2008 (UTC)

I've already agreed with the fact that pure unsaturated values are not represented as distinct points. Here's a pretty good description of Runge's color sphere. Also, I find it kind of ridiculous to say imply that Alvy Ray Smith invented the notions of hue, saturation and lightness. SharkD (talk) 23:42, 14 January 2008 (UTC)

Alvy Ray Smith certainly did not invent the notion of hue. He did however first describe these HSL/HSV transformations of RGB, which is what is being discussed in this article. --jacobolus (t) 01:27, 15 January 2008 (UTC)

Yeah, it's pretty silly to jump from the fact that he invented the HSL and HSV colorspaces as mappings of RGB to the strawman idea that he invented the notions of hue, saturation, and lightness. He didn't invent them, he adopted them, and made up the mappings that we call HSL and HSV. Dicklyon (talk) 04:14, 15 January 2008 (UTC)

How is this a strawman idea? You questioned the validity of Runge's model based on HSL and RGB not having been invented yet. If HSL and HSV are just transformations of RGB, then what relevance do they have to other parameterizations of hue, saturation and lightness, such as Runge's model? If HSL isn't a parameterization of hue, saturation and lightness, then why is it being compared to other parameterizations of color, such as RGB and CMYK? SharkD (talk) 05:35, 16 January 2008 (UTC)

“If HSL and HSV are just transformations of RGB, then what relevance do they have to other parameterizations of hue, saturation and lightness, such as Runge's model?” – they have none, except inasmuch as Alvy Ray Smith and his collaborators were inspired by other color models they had seen. HSL and HSV are just (modulo trivialities) 1:1 warpings of RGB into a shape intended to be more useful and intuitive for humans than a cube. They are nothing more, which is why I hesitate to call them “color spaces”, as the term is easy to misinterpret. --jacobolus (t) 10:44, 16 January 2008 (UTC)

From the article I linked to: "Each colour placed on the surface of the sphere can move in five directions: towards the colours to the right or to the left; up towards white; down towards black; and inwards to the pass the grey of the centre and continue in the direction of its complementary colour." This description is accurate for both models. Other aspects are different, however. SharkD (talk) 04:02, 15 January 2008 (UTC)

HSL (ack; correction: HSV) mapped to a sphere per SharkD's formulae (this is a vertical cross-section)

Sorry, I should have been clearer. It's not that I don't understand what your formulae say; it's that I don't think they are actually mapping HSL to a useful graphical description, and the mapping they do have doesn't match your diagram. Maybe a picture can help you understand what I mean. --jacobolus (t) 01:25, 15 January 2008 (UTC)

Your math is wrong. SharkD (talk) 03:01, 15 January 2008 (UTC)

J, are you sure that's not an HSV sphere? In HSV with V at the latitude, all the bright saturated colors come together at the North pole. I figured that's why SharkD had only done HSL. It might be nice to have a mapping that would work for both. It ought to be dead simple to instead start with the assumption that neutral axis of the cylinder maps to the axis of the sphere, linearly or otherwise, and then map the rest sensibly; one easy way is to replace the z-dependent radius factor in the cone formula with a factor that makes the cross section circular instead of triangular; there are probably other good ways; still, you probably don't want to do this for HSV, just HSL.

Ah, indeed. Blargh. Maybe I'll try to make a version properly showing HSL if I feel particularly ambitious. In any case, most of the problems with this direct spherical mapping apply to both equally, for instance having near-blacks sweep out an entire cone from the bottom of the sphere, collapsing all neutrals to a single point, and generally compressing unsaturated colors to a tiny fraction of the size they'd take in any perceptually-based representation. SharkD: how about this: You find a reliable source which uses such a spherical representation of HSL or HSV, and we'll mention it in the article. Otherwise, we'll take it out. --jacobolus (t) 04:26, 15 January 2008 (UTC)

I concur. The first few HSL spheres I found here have L on the axis; I doubt that anyone has ever done otherwise. Dicklyon (talk) 04:50, 15 January 2008 (UTC)

I created a diagram showing why mapping lightness to the vertical axis won't work. As you can see, the coordinates (0.9, 0.4), (0.8, 0.3) and (0.3, 0.2) don't exist in the diagram. If you move up a few units along the z-axis (lightness), the circles of radius (saturation) don't always intersect with them the lines. In order for the lines to always intesect the circles, they would have to be perpendicular to the tangent of the circles. If you look at the parametric equations for the cube, cylinder and cone you'll see that the z component is equal to a point along the z-axis. The z component of the parametric equation for the sphere is equal to the cosine of the angle phi. In order for lightness to be mapped to the z-axis in a sphere, the z component would need to equal a point along the z-axis, which would result in a cylinder. I think the mapping of lightness to the vertical axis in the articles is simply a mistake, and they meant to map it to the center. At least, they attempted to map HSL to a sphere. I believe this to be notable. SharkD (talk) 03:44, 16 January 2008 (UTC)

You could also argue that a cone doesn't work, for the same reason. But make it work; paraphrasing from your cone above:

Here is the parametric formula for a cone modified into a sphere:

$x=x_{0}+f(s)\,r\cos \theta \,$

$y=y_{0}+f(s)\,r\sin \theta \qquad (0\leq \theta \leq 2\pi {\mbox{ and }}0<z\leq h)\,$

$z=z_{0}+s\,$

$f(s)={\sqrt {1-s^{2}}}$

Substituting H, S, and 2L–1 in for theta, r, and s results in a sphere, or radius 1.

Try it? Dicklyon (talk) 05:34, 16 January 2008 (UTC)

Oh, and use $f(s)=1-|s|\,$ to make it a bi-cone. Dicklyon (talk) 05:38, 16 January 2008 (UTC)

Since the top of the cylinder is all white, and the bottom is all black, shrinking these surfaces to the poles reduces those colors to single points. That's why the bi-cone is a natural form, and the sphere ain't so bad, too. Dicklyon (talk) 05:41, 16 January 2008 (UTC)

Indeed, this is the sort of mapping I think most people who've ever tried to cram HSL into a sphere (or HSV into a hemisphere) have used. It's what I expected you meant, SharkD, before you specified otherwise (way up above in the discussion). I personally don't think it's particularly useful, as it isn't any closer to perceptually uniform or intuitive than the bi-cone version, and it adds some complexity to the arithmetic, so it is also less mathematically intuitive. But there certainly are sources which draw HSL in such an arrangement, such as the one Dicklyon linked to earlier. --jacobolus (t) 08:43, 16 January 2008 (UTC)

Your parametric function doesn't work. In your equation, the "radial" arcs all intersect the point on the sphere where lightness is greatest. A sphere is all points equidistant from a point. This distance is called the radius. The articles all specify that saturation proceeds with the radius of the sphere. Therefore, your model is not the one given in the articles. Further, in the model I provided, lightness does map roughly to the z-axis. The angle phi is measured in angles around the center of the sphere, starting from one pole and ending at the other. These points can be measured roughly along the z-axis. The colors do not get darker again as you continue along the circle, because the angle phi stops at 180 degrees. SharkD (talk) 04:25, 17 January 2008 (UTC)

I'm not sure what you mean by radial arcs, but saturation maps linearly from the center to the maximum radius of the constant-L disc, as in the cone; the solid is still a sphere, or maybe a "ball". Which ref says saturation maps radial in the sphere? I've looked and have not found anything so specific. Where the one says "moving from the center of the sphere outward", that needs to be interpreted in light of the statement that "near the center of the sphere colors are desaturated," where by center they obviously mean the central axis, since they already said "In the middle of sphere, dark colors are at the base (black), and light colors (white) are near the top, with a range of grays in between." My parameterization fits their description. The other ref says saturation increases from the "central core" outward; think of an apple core. Dicklyon (talk) 05:46, 17 January 2008 (UTC)

I just created an image where I took the parametric version of the sphere and filled in the areas corresponding to non-vibrant colors, and it looks a lot more like an apple core. SharkD (talk) 01:46, 29 December 2008 (UTC)

No, you could not argue that the cone doesn't work for the same reason. I've created a diagram showing why. As you can see, the lines of height always intersect the lines of radius. You guys are really showing a lack of understanding of mathematics. SharkD (talk) 01:26, 17 January 2008 (UTC)

Sure, we know the cone works; my point was that for a cone or a sphere, or whatever, you can draw the picture that makes it work, and you can draw a picture that makes it not work. It's all about what parameterization you choose. Choose one that works, instead of a strawman that doesn't. Dicklyon (talk) 01:30, 17 January 2008 (UTC)

I've now removed the sphere image. As Dicklyon states most sphere reps have l running along the axis. Runge image predates the HSL colour-space and does not apply numeric quantities so that can not be used as a reference. A lack of WP:RS to colour system parametrised in this way means that the image classes as original research so should not be included. --Salix alba (talk) 10:23, 16 January 2008 (UTC)

I think that if the sphere can be recreated with L on the axis, then it should be restored, as an illustration of the mappings that are referred to in the refs I noted above, even though those don't get into detail of exactly how they completed the parameterization. Dicklyon (talk) 16:21, 16 January 2008 (UTC)

I think the lack of information would make this representation original research. SharkD (talk) 02:38, 17 January 2008 (UTC)

Well, it's true that the proposed parameterization is not unique in its correspondence to the descriptions here and here, but it's harder to imagine or describe the alternatives. The mapping I described has L mapped linearly along the axis (the simplest interpretation of what they say), and L constant in planes orthogonal to the axis (like in the cone mapping), and circles of hue as they say, and saturation mapping linearly to radius within the planes of constant L, again pretty much as they state. I don't think I did anything originally in writing down the equations for this most-obvious interpretation of how to embed HSL or HSV into a sphere; the only plausible alternative is to warp the surfaces of constant L, but why would you want to? Dicklyon (talk) 03:41, 17 January 2008 (UTC)

Well, regardless, the sources are ambiguous regarding how they map S to the sphere. Source #1 specifically says, "from the center of the sphere outward". Source #2 says, "from the center core outward". It's not clear what source #2 considers to be the "core" of the sphere, e.g. whether it is the common notion of the core of a spherical object, such as a planetary core or a solar core, or something else. I suggest these sources be removed from the article, as they do not support any statement made in the article.

As for Runge's and Munsell's spheres, Runge's sphere is obviously not parameterizable (going from the diagram presented in the article). Munsell's sphere, on the other hand, does use the system you describe. SharkD (talk) 06:52, 18 February 2008 (UTC)

Much later reply. I looked over the sources again, and I think it's pretty clear this time that they (except for Runge, whose model is broken, regardless) are referring to the model described in the article. I changed the text to better reflect this. SharkD (talk) 06:04, 29 June 2009 (UTC)

Hole in the middle

You know, I just considered that adding a small gap in the middle would eliminate the issues raised with the first sphere model. SharkD (talk) 01:27, 29 December 2008 (UTC)

Merge HSL and HSB/HSV articles into one

• These two color spaces are both simple transformations of some RGB space (more like other ways of representing the same space, than spaces of their own). Unlike XYZ, CMYK, Munsell, or CIELAB, they are all based on the same device-dependent additive RGB color model.
• They have a similar intent (make relationship between RGB colors a bit more intuitive), and much of the information about the two is overlapping. That is, explaining both isn't much more complicated than explaining one of them.
• The spaces are commonly confused, and referred to by each-others abbreviations, and putting them on one page allows the explanation of which is which to be made explicit and clear, preferably with comparative diagrams (I'm willing to make such a diagram).
• If left separate, each needs a lengthy "comparison to the other" section. (Indeed, most of the HSL article already consists of comparison with HSV!)
• The comparison of each of these spaces to other common color models is essentially the same.
• There isn't all that much to say about the combination of the two articles. Merging the articles together, and filling in the coverage gaps, won't make for an inordinately long article.
• Both articles need cleanup, and in the merge I think overall quality would improve.

So in general, I think it makes sense to combine them (titled “HSL and HSV color spaces” or similar). Additionally, the information should be summarized and put in a section of RGB color model. --jacobolus (t) 10:35, 16 September 2007 (UTC)

Is there really no one with an opinion about this? --jacobolus (t) 18:49, 4 October 2007 (UTC)

I agree to a merge. Thanks for pushing on it. Dicklyon 20:39, 4 October 2007 (UTC)

Well, if there are no objections soon, I'll hop to it. See the below section for my todo list for this article. --jacobolus (t) 21:44, 4 October 2007 (UTC)

Once these are merged, what's the best title for the article? I'm thinking just "HSL and HSV" might be appropriate. --jacobolus (t) 10:00, 5 October 2007 (UTC)

Okay, so the articles have been nominally merged. I left out a couple bits of the HSV article that I don't think are ultimately needed, for instance the distracting animated images (there was agitation for their removal on the HSV talk page anyway), and the section about complements, which better fits under the "motivation" section in the new article. In the next few days we can move to the todo list from the section below. --jacobolus (t) 13:07, 5 October 2007 (UTC)

I'm a bit late, I know. But, I think that merging the articles simply adds to the confusion. SharkD (talk) 20:02, 12 January 2008 (UTC)

The real problem is that I never did my planned rewrite, or moved the article title to something like HSV and HSL. But even in its current state, this article is much less confusing than the pair which came before, in my opinion. --jacobolus (t) 20:05, 12 January 2008 (UTC)

Well, the article should at least be renamed to reflect that it discusses both topics. Also, the article states that the two systems are related. They may be similar, but I'm not sure they're related, historically. SharkD (talk) 20:12, 12 January 2008 (UTC)

They're related in that they were both proposed by the same author, in the same paper. Dicklyon sent me a copy of the paper, and it's now been 3 months that I've been sort of meaning to rewrite most of this article. But I've gotten busy with one thing after another, and a proper rewrite is going to take several hours. --jacobolus (t) 21:08, 12 January 2008 (UTC)

That would be Alvy Ray Smith's "Color Gamut Transform Pairs," 1978. I can send a copy if anyone else wants to work on it. He proposes and constrast the HSV hexcone model and the HSL triangle model. I'd like to see better illustrations in terms of the actual 3D shapes of these spaces as defined, rather than warping them to cylinders or spheres. Dicklyon (talk) 23:19, 12 January 2008 (UTC)

rewritten intro, lowercase letters in formulae, todo for the next few days/weeks

I mostly rewrote the intro (and it's now in a form that should be easy to merge in HSV, which I'll try to do in the next few days, so raise any objections ASAP), to hopefully be a bit clearer and more accurate. I also lowercased the variable names in the formulae, which distinguishes coordinates from their corresponding axes, and looks cleaner, I altered some of the explanatory text between formulae, and I put the conversions under a single subheading. Still on the todo:

• Make some better images, that show the spaces as the cylinders they are defined as mathematically, and then show how those cylinders are deformed representations of cones or hexacones or spheres or whatever.
• Compare HSL/HSV to straight RGB, and better explain the motivation for expressing things by these color attributes instead of contributions of various primaries.
• Discuss the shortcomings of HSL/HSV, and compare to L*a*b* and Munsell systems, highlighting the trade-off of "fits in a nice box" and "easy to compute" and "based directly on RGB values from the screen" versus "perceptually-uniform". Explain that HSL/HSV co-opt the words "brightness", "lightness", and "value" (not to mention hue and saturation) to have different meanings than their usual technical definitions.
• Discuss the history of the use of HSL/HSV. I'm not too knowledgeable here so help would be appreciated.
• Prune out some of the cruft that's currently in the article
• Add some references—Help would also be appreciated with this one.

-jacobolus (t) 21:10, 4 October 2007 (UTC)

The required cruft pruning has been magnified about 3× by the merger. :) --jacobolus (t) 13:08, 5 October 2007 (UTC)

I found an interesting web site with some history of color models. The history of the Ostwald Colour System is here: http://www.coloracademy.co.uk/ColorAcademy%202006/subjects/ostwald/ostwald.htm#. Supposedly this was what the HLS model was based on (according to Alan Watt, 3D Computer Graphics, Second ed., 1993, Addison-Wesley Publishing Company, page 420), even though it is similar to HSV. History of the first 3D figures for the specification of color is here: http://www.coloracademy.co.uk/ColorAcademy%202006/classification/classification.htm, color terms like value and lightness and history related to color terms is here: http://www.coloracademy.co.uk/ColorAcademy%202006/subjects/parameters/parameters.htm, history of the Munsell color system is here: http://www.coloracademy.co.uk/ColorAcademy%202006/subjects/munsell/munsell.htm. These are all part of the web site of the "Color Academy" in the UK. They have other color system history and color science info as well. Their home page is: http://www.coloracademy.co.uk/ColorAcademy%202006/homepage/main.htm.Seaandsky 18:12, 20 October 2007 (UTC)

Rename

I think the article should be renamed to HSL and HSV color spaces to avoid confusion. SharkD (talk) 21:01, 13 January 2008 (UTC)

What confusion? I'm a bit leery of explicitly calling them “color spaces” (a term for which I have never seen a particularly precise definition) because they are properly simple coordinate transformations of RGB, with each RGB color space having its own unique corresponding HSL and HSV representations. --jacobolus (t) 04:27, 14 January 2008 (UTC)

The confusion resulting from readers not being informed that HSL and HSV don't refer to Hawaii State Library and Holden Special Vehicles. SharkD (talk) 06:00, 14 January 2008 (UTC)

Erm, why in the world would there be a single article about the two of those? And who would have any doubts about it after the first sentence? It's not like either HSL or HSV redirects here. --jacobolus (t) 12:17, 14 January 2008 (UTC)

Italicized HSV, etc.

Hi Dicklyon,

I had previously consistently labeled the components/axes of the space as H, S, V, L, etc. while consistently naming particular values (i.e. vector components) as h, s, v, l (and using italicized HSL, HSV, RGB, L*a*b*, etc. for those names). I think such naming is the best way to keep such distinctions clear. I noticed you changed upper-cased H, etc. for lower-cased h, etc. in a few cases, and otherwise removed a large number of my italics. I believe this to be a regression in article quality, though my naming convention is obviously less useful/clear than it would be had I completely rewritten the rest of the article, rather than just the introduction and formulae sections. --jacobolus (t) 12:36, 14 January 2008 (UTC)

Similarly, given that min and max are variable names, setting them in roman is misleading. I suppose greek letters or something could be used instead of min and max. I think though that the named variables make the formulae clearest. --jacobolus (t) 13:25, 14 January 2008 (UTC)

I think the H vs. h distinction might have something to it, but I see no precedent for italicizing the acronyms. As to the min and max, that was someone else's change, but I like it better than what we had before, where min appeared to represent m*i*n. There's no great way to mix computer-style naming with math-style. Dicklyon (talk) 16:04, 14 January 2008 (UTC)

I see RGB every where…

"These two color spaces are both simple transformations of some RGB space" I not agree with that. It seems to be a common idea and it's false. Models are independant at a first time. RGB space got only one white and one black, that why the double cone representation is well known. A true HSL space permit things that a RGB one doesn't. Decrease then increase light: in HSL a black can come from a red and return to this red; in RGB a black coming from red return to gray. HSL have choose a natural color space that can be fully converted to a RGB space but with data lost. HSL->RGB is non-injective and surjective. If it was a transformation of RGB, it would have been injective. (Or in another words, RGB->HSL would have been surjective.) As a digital painter, I'd like to have a software supporting a real HSL color space. RGB is a display color space. HSL could be a great creation color space. Lacrymocéphale

You are correct that it is not strictly a bijection, in that, in HSL, all points such that l = 0, and in HSV, all points such that v = 1, or v = 0, map to single points in the corresponding RGB space. However, given that all such points also represent a single color—and all other points, those which represent different colors, do map bijectively onto the corresponding RGB space—this is more a design flaw (i.e. they were designed for computational convenience, not theoretical elegance) with HSL/HSV, than it is an obstacle to thinking of them as a simple transformation of RGB. The rest of your statement is misinformed and garbled: black does not “come from” red, and HSL would not be no different for “creation” than RGB, because they are representations of the same model, transformed in a very rough way, and have little to do with human visual-perception: use something like L*a*b* instead, if you are looking for an intuitive color space. --jacobolus (t) 19:06, 14 January 2008 (UTC)

I think that Lacrymocéphale is clearly not a native English speaker. What he means is that, in HSL, colors can easily transition ("go to", "come from") between black and red. In other langauges, this is the proper usage. Also, I think the two of you have different definitions of "intuitive". From the end-user (e.g., artist's) standpoint, L*a*b* is the very definition of unintuitive. SharkD (talk) 03:33, 15 January 2008 (UTC)

No, from an human visual perception perspective L*a*b* is much more intuitive, at least in L*C_a*b*h_a*b* form (which basically has lightness, hue, colorfulness dimensions, but unlike in HSL/HSV they are actually consistent and meaningful). RGB has very little to do with human perception of colors. It's just that people have been taught models like RGB. This makes them learned, not intuitive. But quick, tell me what you get if you combine 30% R, 25% G, 80% B, and what's the relationship of that mixture to the same, but with 70% R instead. If you have to plug those into a computer or think hard about it to answer, that means the model isn't intuitive! If you tell me the number of a color in L*Ch or Munsell, I can picture that color in my head instantly. --jacobolus (t) 00:03, 18 February 2008 (UTC)

If L*Ch is simply a transformation of L*a*b* so that the input values correspond to Lightness, Chroma (Saturation) and Hue, then there is zero difference in intuitiveness. As for HSL and HSV not having meaningful values, they are in practice a transformation of sRGB space and are therefore no more or less device-independant than L*a*b*. SharkD (talk) 05:24, 18 February 2008 (UTC)

Duh … L*Ch isn't even really a transformation of L*a*b*, but just the same thing expressed in polar coordinates, an expression which is easier to visualize and grapple with; my claim is that L*a*b* is more intuitive than RGB. HSL/HSV lack meaning w.r.t. human vision because of their origin in RGB (whether sRGB or another space) and device-dependence or -independence has little to do with it. --jacobolus (t) 08:48, 18 February 2008 (UTC)

Open interval

The function for converting RGB to HSL could be rewritten in such a way such that the interval for Hue [0,360] is closed. I don't know where you got your function from. But, all the ones I've found on the Net only are closed. SharkD (talk) 18:16, 17 February 2008 (UTC)

I thought they all defined the hue of red as 0, not 360, meaning it's semi-open. Which ones allow for red to be 360? Dicklyon (talk) 23:19, 17 February 2008 (UTC)

Alvy Ray Smith's paper defining it has a half-open interval [0, 360), as does every other definition I've seen. I imagine the "ones on the Net" are just lazy. --jacobolus (t) 23:59, 17 February 2008 (UTC)

Ah, I thought an open interval meant that the function allowed values beyond 360, such as 720 or 1080. My mistake. SharkD (talk) 03:27, 18 February 2008 (UTC)

HSL definition

The text says that "Both models were first formally described in 1978 by Alvy Ray Smith". Unfortunately, reading through the article, it is clear that the HSL model the author is talking about is definitely not the HSL we are referring to in this page. Does anyone know any other source? --Prydeson (talk) 16:53, 21 March 2008 (UTC)

Actually as described in the paper, it's a generalization (allowing various other specific interpretations) of the model described in this article. I've been meaning for months to rewrite this to better explain that, but I'm not doing a very good job getting around to it, and am extremely busy for the next few weeks; grr.. --jacobolus (t) 20:30, 21 March 2008 (UTC)

Picture Window Pro

It's not very heavy, but the list of editors and which color models are used as tools by which should probably include "Picture Window Pro."* It is used by a number of professional photographers as well as may advanced amateurs.

• Digital Light & Color (http://dl-c.com/index.php?option=com_content&task=view&id=14&Itemid=28) was founded in 1993 by Jonathan Sachs -- the programmer who created the first version of Lotus 1-2-3 back in 1982.

Prof. Jewell (talk) 06:52, 29 April 2008 (UTC)

Picture Window Pro's use of HSL/HSV is now described a bit. :-) –jacobolus (t) 10:28, 12 March 2010 (UTC)

HSL to RGB Color Conversion

The article currently sates that for RGB to HSL conversion L=(min+max)/2... Shouldn't this be L=(R+G+B)/3? As it now sits, the RGB components (0,0,254) and (0,254,254) would both produce a luma value of 127. I do not believe this is correct... --Electrostatic1 (talk) 02:28, 8 September 2008 (UTC)

NM, I get it now... 0,0,255 would be fully bright and saturated blue, 0,255,255 would be fully bright and saturated cyan... —Preceding unsigned comment added by Electrostatic1 (talk • contribs) 02:38, 8 September 2008 (UTC)

You are right that (0,0,255) and (255, 255, 0) have significantly different luminance, lightness, etc. Realize that the L of HSL has only vague resemblance to physical or perceptual qualities. The HSL/HSV described in this article are historical artifacts from the 1970s whose usefulness has passed, but are still used because software devolopers are ignorant or lazy (mostly ignorant). —jacobolus (t) 06:18, 8 September 2008 (UTC)

I don't know... the L in such models as Lab or the Munsell system seem "fraudulent" somehow; kinda like someone else is deciding for you what the best values for lightness are instead of letting you decide for yourself. SharkD (talk) 15:57, 28 December 2008 (UTC)

Isn't that what a standard color space is supposed to do? Have someone else decide the coordinates for you, instead of a bunch of people making incompatible decisions for themselves? Dicklyon (talk) 18:06, 28 December 2008 (UTC)

Well, for the typical form of HSL the discrete steps for L are mapped more or less linearly to particular emissions of the phosphor diodes on a computer monitor (assuming all monitors share the same gamut). Since models like Lab are based on human perception, it's a lot harder to turn around and derive the original wavelengths of the source emissions based on a given tuple of coordinates. For example, let's say that a hypothetical color space interpolated across a range of wavelengths at intervals of 50nm. The calculations are a lot easier than if the color space instead interpolated at shorter intervals where human sensitivity is greater and longer intervals where it is less sensitive. I just personally feel that doing things like finding complementary colors and performing other color matching is a lot harder when the numbers themselves have been adjusted in some way. It's kind of like psychoacoustically-compressed audio: they offer better data compression for a given perceived quality of sound, but they don't affect how we perceive sound or how we manipulate the source frequencies. I can definitely see the advantages of Lab: it's inefficient to calculate or store colors that you can't see anyway, and it's better to offer higher fidelity where humans can see in greater detail. But this added difficulty is probably why Lab isn't in wider use. SharkD (talk) 22:17, 28 December 2008 (UTC)

“complementary colors” is not a particularly meaningful concept except w/r/t human perception, so using a non-perceptual space to compute them guarantees poor results. It’s physically impossible to derive the source emissions based on any finite tuple of coordinates. In typical HSL, the mapping is actually a gamma curve along each R, G, B coordinate, and this causes big problems in interpolation, etc. “Assuming all monitors share the same gamut” is an absurd assumption that will never be even close to true, even among displays of the same model number. And CIELAB’s advantage over RGB isn’t really about efficiency of calculation or storage (indeed, it’s less efficient for both). Finally, I don’t think this has anything to do with why perceptual spaces aren’t in wider use: that is much more an education problem than anything else. In 2009, the hardware limitations of the 1970s no longer apply. —jacobolus (t) 05:37, 1 July 2009 (UTC)

There is another problem in this section. We are given h, in [0,360), and then later given h_k = h/360 and told that h_k is in [0,1]. One of these statements is a lie: either h was in [0,360], h_k is in [0,1), or h_k is not h/360. Parabolis (talk) 13:01, 7 November 2009 (UTC)

Actually, it's not that much of a problem; if h is in [0,360), and h_k = h/360, then h_k is in [0,1), and also is in [0,1]. Fix the interval to be semi-open if it bothers you. Dicklyon (talk) 18:48, 7 November 2009 (UTC)

"such change of meaning should be accompanied by a source" (diff)

The original article text is unsourced and easily contradicted by reading the rest of the article. SharkD (talk) 03:24, 29 June 2009 (UTC)

I'll add some sources. SharkD (talk) 03:38, 29 June 2009 (UTC)

Thanks; correcting unsourced stuff with unsourced stuff is not generally a win. Dicklyon (talk) 03:42, 29 June 2009 (UTC)

"patch what's said about the RGB primaries back to what was intended" (diff) (newer diff)

"Values" would be a better word to use, since by themselves the R, G, and B primaries don't have a "color". I.e., colors need all three components; by themselves they have no meaning. SharkD (talk) 03:29, 29 June 2009 (UTC)

I'm not sure what "values" refer to there, but each primary color certainly does have a color. Dicklyon (talk) 03:41, 29 June 2009 (UTC)

I mean "value" in the same sense as "numerical value" or "value of the integer" (actually a float in this case). A color in the RGB model can't have just a R, G, or B value; it must have both of the other two values as well—even if they are set to zero. Also, using the word "color" makes it sound like the primaries could be something other than red, green or blue (which they of course can't). It's just a matter of choosing the right words for clarity. "Strength" might also be a good choice. I prefer "value" because it is used more often in mathematics and programming. SharkD (talk) 03:51, 29 June 2009 (UTC)

Those values have nothing to do with the intended meaning; the intended meaning is about what the three primary colors are; the R primary has a color (a red), the G primary has a color (a green), and the B primary has a color (a blue); exactly what colors the primaries are will affect what color is represented by and RGB triple and hence an HSV triple. Dicklyon (talk) 04:53, 29 June 2009 (UTC)

..."exactly what colors the primaries are will..." The primaries can only be *one* color. The phosphors or LEDs don't change color; they only get brighter or dimmer. I.e. they vary in intensity or strength, not in color. I don't disagree with the meaning; I disagree with the wording. SharkD (talk) 05:03, 29 June 2009 (UTC)

Sounds like you haven't understood the meaning yet. The "values" don't change the colors of the primaries; those are fixed, as you note. But fixed to what colors? Those are the primary colors being referred to here. Did you check the linked article on additive primaries at least? Dicklyon (talk) 05:12, 29 June 2009 (UTC)

Sigh... I was hoping to avoid getting into an English/grammar debate. I'll request an RfC. SharkD (talk) 05:19, 29 June 2009 (UTC)

I don't think it has to do with any language subtleties; just read what it says; it's very different from the concept you changed it to, which doesn't make a lot of sense, since the values of R, G, and B are completely determined by the values of H, S, and L. This is no ambiguity in the values, just in the colors that those values represent. Dicklyon (talk) 05:24, 29 June 2009 (UTC)

Sorry!!! I see the problem now. I completely glossed over the first sentence in the paragraph and neglected the fact that the paragraph was dealing with the device-dependent nature of color models with respect to color spaces. My mistake! SharkD (talk) 05:44, 29 June 2009 (UTC)