What is the range of L (lightness) when plotting HSL bi-cone colour space?

Hi,

I am trying to plot the HSL bi-cone colour space using Matlab.

From google search, there are many online HSL images look like below. Does the scaling look correct?

I assume L (lightness) is from 0 to 1, and S is also from 0 to 1. But purely based on the visual appearance of these online images, L from 0 to 1 is way longer than S from 0 to 1.

Or

I am wondering whether the colour experts here would agree with these online images in terms of scale, or should the HSL bi-cone look more like something more flattened like this?

Answer 1

[DGM]

In most implementations , L will be from 0 to 1, so yeah if you wanted to visualize it at uniform scale, it would be a squat bicone.

Bear in mind that these diagrams are all kind of loose interpretations that are convenient tor visualizing the transformation. The scale doesn't really matter as much as it would in a uniform color space.

Consider that from the user's perspective, we often tend to treat HSV/HSL, etc in a cylindrical fashion, despite the fact that one (HSV) or both ends (HSL) of this naive cylindrical interpretation actually collapse to a single color in RGB. Also, consider that it's often presented as a polygonal shape instead of a circular cone/bicone. A given hue step in HSV/HSL is a step along the perimeter of a hexagonal boundary, so not all hue increments are equal angular steps around the neutral axis of the RGB cube.

HSV/HSL aren't really their own color space, as you'd have with LAB/LUV/YUV, etc. As such, all of these takes on how it gets visualized are varied efforts to describe how RGB is transformed. The cylindrical interpretation describes how the model is treated by the user, the hexcone model describes how the RGB cube is transformed, and the circular bicone is some middleground. Each approach emphasizes some idea and misprepresents others. A conical diagram emphasizes the mapping of neutral extrema to the corners of the RGB cube, but it misrepresents S by illustrating it in a denormalized fashion.

All of this is to say that HSV/HSL are fair ground to play fast and loose with diagrams if you feel it makes it easier to communicate or fit into a plot box. I just plotted them as cylinders because I was lazy.

I'm not one of those experts, so anyone is free to tell me I'm wrong.

[DGM]

I think my commentary could have been a bit clearer, so let me add a bit of detail.

If you want a polar representation depicting the z-height of a point as L and the radius as S, then your model is a cylinder with height and radius of 1. The end faces of the cylinder would be undefined except for a single point in the center of each. Filling these faces with a constant black or white would be visually convenient, but it misrepresents how those regions are conventionally mapped.

If you want L and S to represent distances in RGB, then your bicone would have a height of sqrt(3) and at the primary-secondary locus, the radius would vary between sqrt(3)/2 (at the primary and secondary colors) and sqrt(2) (at the midpoints). The result would be a hexagonal bicone with height equal to the maximum diameter. This may explain the common fashion among illustrations, but it's obviously just another compromise and I think it can lead to confusion at least as much as any other.