How to find a color within area in CIE 1931 color space

Question

Color should fall within an area defined with coordinates in CIE 1931 color space as stated in CIE 39.2 - "Recommendations for Surface Colours for Visual Signalling". The area is described with its corners - 4 pairs in the form of (x,y). So the question - how to find RGB or Pantone color matching this requirement?

Answer 1

CIE 1931 color space or "XYZ" has well defined transformation to sRGB in the definition of sRGB. You must

• use XYZ values which are scaled so that certain white D56 gives Y=1.0

• calculate R,G and B from X, Y and Z with linear transformation.

• correct the RGB values to proper sRGB display gamma

If the calculated R,G and B are all 0...1 the color can be converted to RGB. Multiply the numbers by 255 and round to integer to get the usual RGB values 0...255.

The math formulas are well presented in this Wikipedia article: https://en.wikipedia.org/wiki/SRGB

Programmers have also been interested in the subject. See this case from their site https://stackoverflow.com/questions/43494018/converting-xyz-color-to-rgb

The calculation of the linear (=non-gamma corrected) RGB numbers is presented there as three linear equations without matrix notation.

I guess you are interested in xyY version of XYZ color presentation. Scientists have noticed that XYZ system's Y-numbers are a good measure for the perceived luminance. In xyY system the color and luminance are separated. x and y contain hue and chroma in rectangular coordinates, Y is the luminance.

xyY is well described in the Wikipedia article about CIE 1931 system https://en.wikipedia.org/wiki/CIE_1931_color_space

Document "Recommendations for Surface Colours for Visual Signalling" by CIE is non-free stuff. I haven't it. If I had it I very likely would have no right to republish any part of its content. Sorry.

Pantone is a proprietary color system owned by X-Rite Inc. Pantone numbers must be considered as row numbers in an ink color list. Adobe and some other software suppliers have licensed conversion tables to RGB and CMYK and included them to their popular programs. The conversion work if the Pantone color happens to be possible in the used RGB or CMYK implementation (=in gamut). There's also numerous online tools available for this. Nothing guarantees their accuracy.

The power of Pantone lies in the same thing as in Munsell color system. Colors are available as printed cards from where one can select the wanted one and see its code. As extra Pantone has a proven mechanism to produce the wanted color as ink.

ADD due the comment:

We can try to find CIE1931 xyY values for your Pantone Red_032_C. We try converter site https://spektran.com/pantone/red-032-c It gives the following list:

There's no xyY presentation, but we can use formulas x=X/(X+Y+Z) and y=Y/(X+Y+Z). They are taken from the linked CIE 1931 Wikipedia article and can be seen also in many other sources.

The next Excel image shows how the calculated x and y values of the conversion result of Pantone Red 032 C and your limit points are placed on the xy-plane:

Red 032 C seems to be far away from the acceptable area.

Warning: The quality of the conversion of Red 032 C to XYZ is unproven. I would try more sources. Try to ask from Pantone. No idea, do they answer or not. The printhouse you use can also have the needed knowledge to decipher the case. I guess they should be able to properly measure the colors they produce.

My 2nd attempt gave this match in Pantone website:

Lab-numbers converted to XYZ gave these XYZ-values

XYZ = 41.079 ; 22.930 ; 7.345 ; (light D65/2°)

the Excel drawing:

This is the 2nd evidence for "it doesn't fit into the given range". But I would trust Pantone's conversions. You can try to find some acceptable Pantone colors if you take the midpoint of the acceptable area, apply different Y-values, convert to Lab-colors and let Pantone suggest something. Then you can check if their suggestion fits into the given range.

The allowed range is in so high chroma red area that I'm not at all sure it can be presented with any printed colors except with something that illuminates by fluorescence or is so dark that nobody believes it's numerically right.