Doug Kerr
Well-known member
The HSV (sometimes called HSB) and HSL color spaces describe a color in terms of three coordinates that represent hue, something like saturation, and something like luminance. Thus, they are attractive at the human interface (for "picking" colors for drawing, etc.).
But unlike a color space that works in true hue, saturation, and luminance, the definitions of the coordinates here admit of simplified calculations in translating between these spaces and the RGB space in which the colors are usually actually held in computer memory, a substantial advantage at the time when these spaces were introduced (early in the era of computer graphics).
We often read that "[the gamut of] the HSV color space is [plots as] a cone (or a hexcone, a figure whose proper name is hexagonal pyramid)".
Similarly, we often read that "[the gamut of] the HSL color space is [plots as] a bi-cone (or a bi-hexcone)".
But what does that mean? The HSV gamut (which is identical to the RGB gamut) plots in the HSV color space as a (circular) cylinder. The HSL gamut (which is also identical to the RGB gamut) plots in the HSL color space as a (circular) cylinder. This (single) gamut plots as a cube in the RGB color space. In no color space we encounter in normal theoretical or practical colorimetry does this gamut plot as a hexcone or bi-hexcone. So what is going on here?
Well, it turns out that this gamut does plot as a hexcone or a bi-hexcone in two different (and peculiar) color spaces we never encounter in normal theoretical or practical colorimetry. What is the significance of these two spaces? Well, they make the RGB/HSV/HSL gamut plot as a hexcone and a bi-hexcone, respectively, that's what.
These color spaces have one coordinate that is the "lightness" coordinate of the color space of interest (V for HSV, L for HSL), but the other coordinates are not coordinates of the color space. Rather, they work in a plane defined by "rotation of the axes" from the coordinate system of the RGB color space. So these are in a sense "hybrid color spaces" (as if, for some reason, we decided to do something in the RGL* color space, or the xyZ color space, both of which I just now "invented"). (For "hybrid" you may wish to read "bastard".)
What does that gambit do for humanity? Well, authors often draw upon these portrayals (without even stating the color space in which they emerge) to illustrate certain "facts" about this gamut, or maybe about the HSV or HSL color spaces themselves. These facts are rarely clearly articulated, and if we can see through the fog and discern what the author seems to be trying to say, we often find that it is not exactly true, or not true at all, or is in fact not illustrated exactly, or at all, by the hexcone or bi-hexcone portrayal.
I will shortly be publishing an article in which this situation is explored more thoroughly, with extensive illustrations and supporting background.
But unlike a color space that works in true hue, saturation, and luminance, the definitions of the coordinates here admit of simplified calculations in translating between these spaces and the RGB space in which the colors are usually actually held in computer memory, a substantial advantage at the time when these spaces were introduced (early in the era of computer graphics).
We often read that "[the gamut of] the HSV color space is [plots as] a cone (or a hexcone, a figure whose proper name is hexagonal pyramid)".
Similarly, we often read that "[the gamut of] the HSL color space is [plots as] a bi-cone (or a bi-hexcone)".
But what does that mean? The HSV gamut (which is identical to the RGB gamut) plots in the HSV color space as a (circular) cylinder. The HSL gamut (which is also identical to the RGB gamut) plots in the HSL color space as a (circular) cylinder. This (single) gamut plots as a cube in the RGB color space. In no color space we encounter in normal theoretical or practical colorimetry does this gamut plot as a hexcone or bi-hexcone. So what is going on here?
Well, it turns out that this gamut does plot as a hexcone or a bi-hexcone in two different (and peculiar) color spaces we never encounter in normal theoretical or practical colorimetry. What is the significance of these two spaces? Well, they make the RGB/HSV/HSL gamut plot as a hexcone and a bi-hexcone, respectively, that's what.
These color spaces have one coordinate that is the "lightness" coordinate of the color space of interest (V for HSV, L for HSL), but the other coordinates are not coordinates of the color space. Rather, they work in a plane defined by "rotation of the axes" from the coordinate system of the RGB color space. So these are in a sense "hybrid color spaces" (as if, for some reason, we decided to do something in the RGL* color space, or the xyZ color space, both of which I just now "invented"). (For "hybrid" you may wish to read "bastard".)
What does that gambit do for humanity? Well, authors often draw upon these portrayals (without even stating the color space in which they emerge) to illustrate certain "facts" about this gamut, or maybe about the HSV or HSL color spaces themselves. These facts are rarely clearly articulated, and if we can see through the fog and discern what the author seems to be trying to say, we often find that it is not exactly true, or not true at all, or is in fact not illustrated exactly, or at all, by the hexcone or bi-hexcone portrayal.
I will shortly be publishing an article in which this situation is explored more thoroughly, with extensive illustrations and supporting background.