Originally Posted by Scott_R_K
Probably a topic for stereomandan , or anyone actually , but is there a way to produce a 3D Plot of the CIE Diagram that would show the "Y" values for the Primaries and Secondaries and White Point ?
Do we know if the Calibrated "Y" value of any of the Primaries or Secondaries is a straight line to the D65 White Point or is it curved ? I'm assuming that if you have a linear CMS then this should be a straight line . Just curious . I'd like to see this as a 3D representation .
I'm trying to visually exactly what your question is, and I'm still not sure. So I'll try several answers, and maybe one of them is your real question.
Obviously, between any single primary/secondary color and D65 white, one could draw a straight line. After all, two points define a line. So that is probably not the question you are considering.
Between all the six 100% color points and 100% D65 white, in some sense, would the lines be coplanar? If one chose to calibrate by tuning all the Y values to match those predicted for a new gamut defined on the actual primaries, then all the lines should be coplanar. If one follows the advice of tuning each Y value to minimize the delta E relative to Rec709, when the actual primaries do not exactly match the Rec709 primaries in the x-y domain, then the lines are not coplanar. Rather one should see six triangles around the circle, where each triangle shares an edge with each adjacent triangle.
If the question is really about the intermediate saturation points, then I think these should be in a straight line in the x-y domain, provided the actual white point matches D65, and if one tuned the Y values to match a new gamut based on the actual primaries or if the actual primaries matched the Rec709 points. But where one tunes each Y value to minimize the dE of the actual point relative to the corresponding Rec709 point, I think it matters which triangle the CMS uses to generate the corresponding value for saturation point. So I would expect to see minor variation around the straight line in the x-y domain. This is where Dan's spreadsheet comes in, as it reveals the variation in the actual from a straight line in the x-y (u-v) domain.
As regards the Y aspect of the line through the saturation points, this line would be "flat" if the actual gamma matches that used to generate the data. In the discussion of the HCFR data to generate the AVSHD disk, it was determined that the saturation values were chosen to maintain a constant Y value at all the saturation measures assuming a display gamma of 2.2. So, for example, 100% yellow Y, 75% yellow Y, ... 0% yellow Y should all be equal giving a flat line. If one considers these lines for each of the six colors, each should be flat, but they should intersect the column at D65 at different heights. But the line starts varying from flat if the calibrated gamma does not match 2.2. Here, also, is where Dan's spreadsheet comes in. HCFR apparently treats the 100% color point Y values as correct, and displays the intermediate points relative to these. Dan wanted to compare these values, themselves, to the Rec709 Y values for each color, so the individual color 100% Y values could be higher or lower than the target. I contributed a separate spreadsheet to calculate what the target reference Y values should be, when the display gamma is flat but differs from 2.2.
So I can see why, whichever of these effects one wants to see, you would like to see this with some 3-D picture. For the saturation points, the HCFR charts with Dan's correction give this information in two 2D pictures, the shifts left and right of a straight line in the x-y plane, and the shifts above/below a flat line in the xy-Y plane.