Concept

Copunctal point — where it appears

The point where all of one class of dichromat's confusion lines converge, which is the chromaticity of the missing receptor's own response direction. Three such points supply six of the nine numbers colour matching leaves undetermined in the observer, and two of the three lie outside the diagram entirely.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

One observer's matching functions, in three of the bases the matches leave free. The three colour-matching functions after a change of basis 0.00 of the way from Hunt–Pointer–Estévez towards the set built from the dichromat confusion points. Every one of these triples predicts exactly the same matches as every other, because a match is an equality and a matrix applied to both sides of an equality changes nothing. What moves is where the peaks are and whether the curves go negative — these ones do not, and going negative is what the 1931 committee constructed XYZ to avoid.

The matches do not name the cones

Colour matching is the whole empirical basis of colorimetry, and it fixes the observer's three curves only up to a nonsingular 3×3 — nine numbers that no match, in any quantity, to any precision, can see. One particular choice of those nine is used throughout here, and it was made for a different purpose.

eye · Cones

Where a dichromat's confusions converge. Every pair of colours a protanope cannot tell apart lies on one of these lines, and all the lines meet at a single point — at (0.7465, 0.2535) for this class. The point is the chromaticity of the missing cone's own response direction, which is why it need not lie inside the diagram or correspond to any light at all. Two of the three do not. The three points between them carry six numbers, and six is two thirds of what the matching data leave undetermined.

A confusion point is a missing pigment

The nine numbers colour matching leaves free are fixed by three points on a chromaticity diagram, each of them the place where everything one class of dichromat cannot tell apart converges. Two of the three lie outside the diagram entirely, which is not a defect — a direction in tristimulus space need not correspond to a light.

eye · Cones

Where each published matrix puts the confusion points, whether or not it meant to. Every matrix from tristimulus values to cone responses commits itself to three confusion points, because the point is the direction the other two rows annihilate. The first row is the construction from the measured points and returns them exactly. The rest were chosen for other reasons and land elsewhere — Hunt–Pointer–Estévez, which this collection uses everywhere, misses the deuteranope's point by 1.28 in chromaticity. The worst here is 4.09.

The cones an appearance model uses

CIECAM16 adapts in three axes whose rows are labelled L, M and S, and they were fitted to corresponding-colour experiments rather than measured on receptors. Run the dichromat construction backwards on them and they commit to a deuteranope confusion point 1.45 away in chromaticity from the measured one — which is a test the axes were never asked to pass.

brain · Appearance

Named alongside it

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

Cone fundamentals Identifiability Colour vision deficiency Confusion line Degrees of freedom Dichromatic model The Bradford transform CAT16 Chromatic adaptation CIECAM16 Colour appearance Colour-matching functions

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