Concept

Diagram conventions — where it appears

The decisions built into a chromaticity diagram before any data are plotted: which coordinates, at what luminance, closed with what boundary. They are invisible in the picture and they decide every quantity read off it that is not a line or a membership.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

The 1976 uniform chromaticity diagram, with the unreachable region marked. The u′v′ diagram: the same spectral locus and the same sRGB primaries as the 1931 picture, projectively transformed. Straight lines stay straight, so mixtures and the gamut triangle survive; what changes is the distribution of area, and the green region that dominates the 1931 diagram is much reduced. 8% of the cells sampled inside the locus are reachable at Y = 0.55; the rest are hatched.

The diagram was replaced in 1976

The CIE knew the 1931 diagram was badly distorted and published a better one. Half a century later almost every chromaticity plot in print is still the old one, and both are still printed filled edge to edge with colours no display can show.

matching · Gamut

The locus and the triangle, drawn on one of the diagrams. The spectral locus and the sRGB triangle in CIE xy (1931) — the default of the discipline, and the default used here. The triangle covers 33.6% of the enclosed area here. Nothing about the observer or the display has changed between this picture and any other in the family; the coordinates have, and the coordinates are what an area is measured in.

The diagram has no area

A chromaticity diagram is a projective picture of a three-dimensional space, and the freedom colour matching leaves in the observer acts on it as a projective map. Straight lines and mixture ratios survive that; area, distance and angle do not — so half of what the diagram is used to say is a statement about the paper.

matching · Gamut $What share of the diagram the sRGB triangle covers, in twelve published coordinate systems. Each row is a chromaticity diagram somebody has printed, and each bar is the fraction of the enclosed visible area that the sRGB triangle covers in it. Every row describes exactly the same observer and exactly the same gamut. The answer runs from 8.5% to 38.4%, a factor of 4.52, because area is not preserved by the projective maps that carry one of these diagrams to another. The familiar "about a third" is a fact about CIE xy.$

Two thirds is not a property of the eye

It has been said from the beginning here that about two thirds of the chromaticity diagram cannot be shown on a screen. The figure is right, on the diagram it was measured on, and across twelve published diagrams the same triangle covers anything from 8.5 to 38.4 per cent of the same locus. Counting stimuli instead gives an answer that does not move.

matching · Gamut

Which of this collection's own claims survive a change of basis, and which are about the paper. Nine sentences this site says, sorted by whether they mean the same thing after the observer's three curves are replaced by a nonsingular combination of themselves. 5 of the nine do. The four that do not are not thereby wrong — they are statements about a chosen set of coordinates, and they are true of those coordinates. What they cannot be is statements about the eye, which is how every one of them is usually read.

Which of these is a convention

Nine ordinary sentences from this collection, put through one test — do they mean the same thing after the observer's three curves are replaced by a nonsingular combination of themselves? Five survive and four do not, and none of the four is wrong, because each is a statement about a set of coordinates being read as a statement about an eye.

limits · Limits

Named alongside it

The objects these essays reach for when they reach for this one.

Gamut Projective transformation Chromaticity plane Identifiability Invariance Chromaticity CIELAB Spectral locus Uniform chromaticity scale Additive mixture Assertion Colour vision deficiency

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