CIE & Its Diagrams: Four Projections of One Eye

A color is a point in 3D tristimulus space; a chromaticity is the direction of that point from the origin, ignoring intensity. Draw a plane across the cone of all visible directions and mark where each ray pierces it: that intersection pattern is a chromaticity diagram. rg uses the plane R+G+B = 1 in Wright–Guild primaries; xy uses X+Y+Z = 1; u′v′ tilts the plane to X+15Y+3Z = 1. Same cone every time.

Because all four are projective transformations of one another, straight lines stay straight (additive mixtures plot on lines in every diagram), but distances, angles, and areas are fair game. That freedom is exactly what the CIE spent 1931–1976 exploiting: keep the mixture geometry, bend the metric toward the eye.

Real primaries force negative numbers: the 1920s matches needed red added to the test side to match spectral cyans, so r goes negative (visible in the rg chapter where the locus crosses the r = 0 axis). Negative values were poison for 1931-era hand computation, so the CIE transformed to three mathematical primaries chosen outside the cone of real colors, making every visible chromaticity positive.

The transform bought three more conveniences: ȳ(λ) was set equal to the 1924 photopic luminosity function V(λ), so Y alone carries luminance and X, Z lie on the zero-luminance plane (the alychne); z̄(λ) collapses to zero above ~650 nm, shortening desk-calculator work; and equal-energy white lands at exactly (⅓, ⅓). XYZ is pure bookkeeping, deliberately clever bookkeeping.

The curved rim is the spectral locus: monochromatic light from ~400 to 700 nm. It bulges outward because no mixture of other wavelengths can reproduce a pure spectral color; every mixture falls inside, which makes the locus convex and every real gamut a shape inscribed within it.

The straight bottom edge is different in kind: the line of purples connects deep violet to deep red through colors that exist only as mixtures; no wavelength produces magenta. Everything a human can see lives inside this boundary; everything a display can make is a triangle (or polygon) strictly inside that. The gap between the two is the whole business case for wide-gamut displays (see Color Volume).

The Planckian locus is not part of the CIE system; it is physics imported into it. Feed Planck's 1900 radiation law through the color-matching functions and each temperature lands on one chromaticity point; sweep the temperature and you trace the curve. That computation was possible the day the 1931 system existed, and NBS lamp-standards work (Davis, 1931) was already correlating lamp colors to black-body temperatures the same year.

The real fusion is 1935–36: Deane Judd defined the nearest color temperature (the Planckian point closest to a test source in a perceptually uniform diagram) and published isotemperature lines mapped back onto the 1931 chart. The CIE later fixed the geometry in the 1960 uv diagram, where Judd-style isotherms sit exactly perpendicular to the locus; Kelly charted them (1963) and Robertson gave the standard algorithm (1968). Every CCT and Δuv readout since is that 1936 construction, frozen in 1960 coordinates.

The 1931 diagram never claimed equal distances meant equal differences, but users treated it that way until MacAdam measured the damage in 1942: thousands of repeated color matches around 25 chromaticity centers, with the scatter at each center forming an ellipse. In xy the ellipses vary in size by more than an order of magnitude (tiny in blue, enormous in green), so one number of "xy distance" can be invisible in one region and garish in another.

Turn on the MACADAM ELLIPSES overlay and switch chapters: uv shrinks the green ellipses dramatically, u′v′ rounds them further. But no projective transform can turn all 25 into equal circles; the residual is why color difference work left 2D diagrams entirely for CIELAB, CIEDE2000, and ICtCp (see MacAdam Ellipses and ΔE-ITP).

MacAdam's 1937 projective transform was chosen over Judd's 1935 triangle largely for arithmetic elegance: two short formulas from x, y. The CIE weighed it at the 1959 Brussels session and adopted it in 1960 as the official Uniform Chromaticity Scale. Its killer property: isotemperature lines meet the Planckian locus at exactly 90°, so "nearest black body" becomes a perpendicular drop.

That is why 1960 uv can never be deleted. CCT and Δuv (signed distance above or below the locus, green or magenta) are defined in this space, and definitions must not drift. The 1976 diagram superseded uv for judging uniformity, but every meter, every ANSI bin, every "3200 K, Δuv +0.002" still silently converts to 1960 coordinates first.

The 1976 revision is the smallest change on this timeline (v′ = 1.5v, nothing else) and the last chromaticity diagram the CIE ever issued. The same year it adopted two 3D color spaces, because industry could not agree on one: CIELUV kept the u′v′ diagram and its straight-line additivity for the light-emitting world (displays, lamps, TV), while CIELAB, with no usable chromaticity diagram at all, served surface colors in paint, ink, and textiles.

The split persists. Display and lighting people still draw u′v′ charts and quote Δu′v′; print and materials people compute ΔE in Lab and have no diagram to point at. Both camps trace to the same 1931 observer; the diagrams just stopped being the frontier.

xy (1931): reading and writing standards. Rec. 709, DCI-P3, and BT.2020 primaries are published as xy pairs; gamut coverage claims are drawn here. Never measure a color difference in xy. uv (1960): CCT and Δuv only; you will rarely draw it, but your instruments live in it.

u′v′ (1976): the working diagram, holding white-point tolerance circles (Δu′v′ of 0.002–0.004 is a typical broadcast window), calibration drift plots, and LED binning. And when 2D stops being enough (because chromaticity ignores luminance), you climb into the 3D spaces this series covers in Color Volume and ΔE-ITP. If it isn't measured, it isn't calibrated.