Well, one thing's for certain: we have lots of tuning left to do on gimp-print. The good news is that a lot of it might just be parameter tuning rather than a massive overhaul.
Niels Gram Jeppesen forwarded me a photo of a friend's car. Now, said car is a beautiful red Alfa Romeo, and he was justly disappointed with the somewhat orange cast the car was taking on. He didn't notice (or took pity and didn't comment on) the rather strange color of the grass. I tried fiddling around, boosting the saturation and decreasing the yellow, and got slightly better results.
This morning I printed out a photograph of my wedding (the same photograph that's on my home page) to see how far things have come since 3.0 (or maybe an early 3.1, I don't know how long ago I printed it). Well, in terms of smoothness of dithering, we've certainly come a long way. However, it was definitely oversaturated, and had a somewhat yellow cast. Hmm.
Photograph mode has some hacks to improve color fidelity. These hacks hacks reduce the CMY levels in regions of fairly pure CMY (which is needed to prevent CMY from reaching saturation too quickly), and do some other things which appeared to reduce saturation (theoretically, they should have reduced saturation also; increasing the level of the least dominant ink will do so by definition). So I boosted the baseline saturation by 1.6 to compensate. Well, it appears that in practice that's going way too far. In fact, I got a really good print with saturation set to .625 -- the exact inverse of 1.6! So that suggests that no saturation boost at all is the right way to go. That's nice; it will speed things up too.
Anyway, with saturation at .625, yellow at .8, and overall gamma of .9 (that's also scaled from a printer and application specific baseline) I got some very nice prints. A brilliant sunset shot, unfortunately, is proving harder to fix.
What's really amazing me here is that reducing the saturation increases the perceived saturation of the color of the car. If I look at it very closely, though, the car isn't fully saturated at all; it's one of those perceptual quirks that makes it look like a brilliant, earth-shattering red. I don't have enough grounding in color theory to fully understand the details, but I think that what's going on is that cyan is the least dominant color in the output, so increasing the saturation decreases the cyan, which leaves only magenta and yellow. The end result is that the output looks slightly orange. Decreasing the gamma darkens the output, which also increases the perceived saturation.
What gimp-print really needs to do is to do everything in CMY space rather than RGB space, I think. That isn't going to magically solve anything, but it will at least make things consistent and hopefully easier to solve.
Of course, part of the story is that every printer is different. The 6 color Epson Stylus Photo EX is a more difficult printer to get light greens out of than a 4 color model; the result is that grass tends to look a bit brown. This isn't quite as offensive as one might think, because it's actually a fairly natural brown. When the saturation is less extreme, this is also less noticeable.
In any event, I think I'm probably going to rescale the saturation, since that's clearly wrong. The issue of yellow is very printer and lighting specific, and I think I'm going to leave it alone for now. Gamma is also a tough call, since every monitor's gamma is different.
I'm looking forward to khk's color management stuff for 4.1/4.2.