Joofa, you keep trying to show that the color [0, 0, 1] in Adobe1998 clips in the ProPhoto space.
I, and others, and photoshop say it doesn't. I even showed you the math. In ProPhoto that color is [88 36 241]. It doesn't clip.
So a simple question: are we wrong?
Seriously, this issue is less complicated then it has been made out to be. Chromatic adaption is not even an issue here. You will see below.
Lets deal this issue in two stages:
(A) There is a color with XYZ=[0.188185 0.075274 0.991108]; is that representable in Adobe RGB (D65) and PropPhoto RGB (D50)?. By representable we shall mean if the tristimuls values required to match these colors are in [0,1] range.
Both matrices from Bruce Lindbloom's website below:
Adobe RGB (D65):
===========
0.5767309 0.1855540 0.1881852
0.2973769 0.6273491 0.0752741 *
[0,0,1]' = [0.188185 0.075274 0.991108];
0.0270343 0.0706872 0.9911085
Since the trisimulus is [0,0,1], this color is representable in Adobe RGB (D65).
Prophoto RGB (D50):
=============
0.79767 0.13519 0.03135
0.28804 0.71187 0.00009 *
[0.183388 0.031393 1.201037]' = [0.188185 0.075274 0.991108].
0.00000 0.00000 0.82521
Since tristimulus value is [0.183388 0.031393 1.201037], where the blue component 1.2 exceeds one, so the color is not representable in Prophoto RGB (D50).
That is why in tho_mas' top figure it shows Adobe RGB (D65) ripping out through Prophoto RGB (D50).(B) Why doesn't Bruce Lindbloom and some others show Adobe RGB gamut ripping out through ProphotoRGB?
Because, after the chromatic adaption multiplication the gamut is changed from Adobe RGB (D65) to Adobe RGB (D50). In the
parallelepiped of Adobe RGB (D50), the color XYZ=[0.188185 0.075274 0.991108] is outside the gamut, so in all likelihood Bruce and others strip that and don't show it. So they only show the legal colors inside this new gamut which gets nice transformed to Prophhoto RGB (D50) gamut.
This situation is the second image of tho_mas. If you line both of them vertically you will notice that Prophoto RGB gamut volume visually looks the same but the Adobe RGB gamut has visibly shrunk in the blue area.Regarding your calculation that XYZ=[0.188185 0.075274 0.991108] in Adobe RGB (D65) gets mapped to XYZ=[ 0.14922403 0.06321976 0.74483862] in Adobe RGB (D50) after Bradford color transformation, that has nothing to do with it. Because the color XYZ=[0.188185 0.075274 0.991108] has not ceased to exist in the universe! It is still there but it is out of Adobe RGB (50) gamut, so does not get shown in conversion of Adobe RGB (D50) to Prophoto RGB (D50) which you have done essentially.
Hope that helps.
Joofa