OK. Some gamut compression charts.
We are rotating in 30-degree steps around the D65 white point xy coordinates, so each of these contains 12 groups of bands.
For each angle and Y luminance value:
- we take the xy coordinates at the edge of the Rec2020 gamut (this is determined via a simple search), and note its distance from the white point (
maxDistanceRec2020) - Then, we shorten that distance according to a fixed multiplier; each chart has its own, starting from 40% and going up to 100%, in steps of 10%. We treat this as a kind of ‘saturation’.
distance = saturation * maxDistanceRec2020 - Then we calculate the x and y of the unmapped pixel:
x = cos(alpha) * distance + D65_WP_x
y = sin(alpha) * distance + D65_WP_y - We convert this xyY into XYZ, then to Rec709RGB, and clamp the components to [0, 1], to demonstrate the naive approach. These values form the first line in the band.
- Then we take
maxDistanceRec709, the max. distance for the given angle for the Rec709 space (again, determined via a search). - We calculate
ratioToMax709Distance = distance / maxDistanceRec709 - We pass it through a curve that’s linear until 0.8, and smoothly converges to 1 above that. This gives us
compressedRec709RatioFromMax. - We calculate
compressedDistance = maxRec709Distance * compressedRec709RatioFromMax. If the original distance was less than 80% of the maximum, it remains unchanged; otherwise, it gets compressed more and more, but will never exceed the max. distance. - Then we calculate the x and y of the mapped pixel:
x = cos(alpha) * compressedDistance + D65_WP_x
y = sin(alpha) * compressedDistance + D65_WP_y - We convert this xyY into XYZ, then to Rec709RGB, and clamp the components to [0, 1]. These values form the second line in the band.
- The third line in the band is simply Rec2020 at 30% saturation, as that saturation never needs compression. It’s included as a hue reference.
- The fourth, monochromatic line indicates the extent of the compression,
1 - compressedDistance / distanceRec2020. Black means no compression.
Right. So, here are the charts (from 40%, as 30% needs no compression):
Rec2020 at 40% (only one of the greens needs some compression):
At 50%:
At 60%:
At 70%:
At 80%:
At 90%:
And at 100%:
If you have good wide-gamut (but not HDR, so Y should not exceed 1) input files, I’d appreciate them, to check how this behaves with real-world images. Flowers (maybe @ggbutcher ?), hummingbirds, whatever.
Thanks for reading, if you got here. 