by Julian
Last Updated June 05, 2019 11:18 AM

The MacAdam Ellipse is applied in the CIE Chromatic Diagram. I understand that humans distinguish some colors better then other colors (that's why the shape is eliptic / a horseshoe / inverted U-shape), and that the diagram is used to check wheter a specific color space is in or out of gamut.

The highest used y value is 0.84 (the top side of the ellipse ... it respresents 520 nanometers, green).

The lowest x value is 0.0 (the left bottom side of the ellipse ... it represents 380 nanometers, blue).
And, on the right, at the coordinates: x 0.73, y 0.64, the red hue 680nm is displayed.

**What I don't understand:**

Why is this diagram non linear?

Why is the highest y value 0.84 and not just at y = 1.0?

How was the CIE Chromatic Diagram "derived"?

Wolfram demonstrations page used for image in question

Derivation of diagram from original data - a rare reference.

They say:

- Published accounts of the calculations used to derive the CIE 1931 RGB chromaticity co-ordinates and color matching functions are at best sketchy and on occasions data has not been published. This paper, and the accompanying worksheet 1931CIE_RGB.xls, present in some detail the sequence of steps leading from the original experimental measurements of Wright and of Guild to the CIE 1931 RGB colorimetric system. It is not an easy story to unravel but the data presented here is probably a close representation of the actual calculations that were carried out by Guild just prior to the CIE meeting in Cambridge in 1931when the CIE 1931 standard observer was first specified. The further calculations transforming the RGB data into the XYZ of the CIE 1931 standard observer have been describes by Fairman, Brill and Hemmendinger8

**Related:**

How to ...: http://www.efg2.com/Lab/Graphics/Colors/Chromaticity.htm

http://selfpace.uconn.edu/class/percep/CIE1931.pdf

Interactive: http://www.biyee.net/color-science/cie-chromaticity-diagram/

*Why is this diagram non linear?*

The CIE Chromatic diagram is a transformed 2D map of the CIE standard observer color matching functions. Because the human eye responds in a non-linear way to to different ranges of wavelengths, and the transformation does not compensate for that, the Yxy diagram isn't linear either.

http://en.wikipedia.org/wiki/CIE_1931_color_space#Color_matching_functions http://hyperphysics.phy-astr.gsu.edu/hbase/vision/cie.html http://dba.med.sc.edu/price/irf/Adobe_tg/models/ciexyz.html

*Why is the highest y value 0.84 and not just at y = 1.0?*

The y value is calculated according to this formula:

When measuring 520nm at the standard observer color match chart, one can see that

- X = ~0.08
- Y = ~0.69
- Z = ~0.08

Thus, y = (0.69/(0.08+0.69+0.08)) = ~0.81

*How was the CIE Chromatic Diagram "derived"?*

That's the hardest part: First the CIE RGB Model is transformed to the CIE XYZ Model, distorting the color space. Then a "slice" through the color space (X+Y+Z=1) is calculated, and finally that slice is projected to the base surface so that Z does not change it (Z is basically Y).

One rather good explanation is Page 8 of "CIE Color Space" by Gernot Hoffmann

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