Lab Cross-Section

Press start to generate the cross-sectional visual Lab gamut points.
It may take a minute or two, but only needs to be done one time.
And, depending on your browser, this tab must remain on top during the process; if you want to browse in the meantime, open a new window.

Choose an RGB color space, then move the slider to see cross-sections of the Lab gamut at the indicated L value.
Press draw gamut to see the entire gamut.
On the canvas, the rectangle is the conventional -128 to +127 a or b range.
The gray outline is the visual Lab gamut (a  -165 to +145, b  -145 to +146).  Colors outside this range are not real.
ProPhoto has unreal green and blue primaries, and it is expected that its gamut would contain unreal colors; but note that because of the extent of their three-dimensional shapes, some of the other spaces contain unreal colors as well.