I Question about subtractive color mixing

[JohnnyGui]

I think you have this the wrong way round. The chart is not based on the primaries; it started with the analysis curves of the eye. Those sensitivity curves were arrived at with a vast number of subjective tests using a range of monochromatic wavelength mixes and comparing the perceived brightness and 'colours' of combinations of mixtures. The curves came out of some complicated analysis of all the results (A load of simultaneous equations in effect). It was, of course, not possible to put a voltmeter on the outputs of the three sensors and just measure the response.

I would have expected your reading to have given you information about the way the CIE chart was arrived at but it was chosen to fit the eye's appreciation of colour and does its best to eliminate the Luminance factor and its scale is arranged so that the position of a perceived colour on a line between two other colours is given by a simple linear weighted combination of the relative brightnesses of the two mixed colours. This is analogous to the Centre of Mass of two masses on a light rod. Now move to a triangle.You cannot obtain a match outside a triangle of three chosen colours (which we could call Primaries). A colour outside a primary triangle can be only be obtained by adding another contribution, on the other side of the line.

Mechanical analogy: Imagine a large, massless plate with masses at the vertices of a triangle, drawn on the plate . You want to balance it on a point somewhere inside the triangle. You can do this by choosing the right combination of masses. To get it to balance on a point outside the triangle, you would need to LIFT one of the corners. This would correspond to a negative mass at that corner. Same with mixing primaries. But negative masses do not exist and neither is there a corresponding negative primary. It is just a bit of Maths.

Apologies for the late reply. I like your mechanical analogy a lot. It did help me understand this a bit better. The sources that I read don't really pay sufficient attention to how coordinates of the colors outside the RGB primaries are derived/calculated, and it was therefore hard for me to grasp the mathematical method since there are no negative primaries, like you said.

There are also no units as far as I understand regarding the "amount" of each primary of RGB used for each color. If there was, then colors outside the RGB triangle would have a certain "negative" amounts of those units (like "- kg" for example in your mechanical analogy) which can then be used to assign coordinates. I might be wrong about this though.

 

[sophiecentaur]

The sources that I read don't really pay sufficient attention to how coordinates of the colors outside the RGB primaries are derived/calculated,

There is a lot of stuff out there. Try including "Tristimulus" and "analysis" in your search terms.
Glad you liked the mechanical bit.
"how coordinates of the colors outside the RGB primaries are derived/calculated,"
I don't know why you are finding this so interesting because what would be the point in talking about producing colours additively when you would have to include subtraction? The sort of thing you seem to be suggesting would involve projecting two primaries through a subtractive filter, I think. What would be the point?
The fictitious (negative) coefficient of one of the primaries is obtainable using the same formulae as for colours within the triangle but there are many examples in Science where the result of a mathematical operation has no real meaning. Imo, there are enough real situations to solve.

 

[pinball1970]

Yes this is how do it in the lab, we choose say 3 4 or 5 dyes (3 usually enough) and this will give us a gamut of possible shades. Each of those individual dyes has an associated set of library dyeings, that is technically viable to produce from lightest to darkest given by a percentage of the weight of the substrate . The target shade say "Blue" is measured using a spectro and the software gives a recipe matching up the library of those dyes against the data generated from our Blue. If our Blue is very bright, brighter than the brightest blue in the library then the predicted recipe will give a negative Chroma value in the predicted outcome. The Flatter (duller) our library dye the greater the negative Chroma value (given as DC). So the software is telling us the colour is unobtainable. In this case this may be what JohnnyGui had in mind. How are the initial points in colour space set? By measuring each library of each dye, point one would be 0.0001% reactive red, this will have an absolute Chroma value (C) absolute Hue angle (H) and lightness Value (L) depending on what sort of software you use. Point 2 would be 0.0002% and so on.

 

[pinball1970]

Just to add this is the colour space we create using applicable colorants on a given substrate.

 

[sophiecentaur]

How are the initial points in colour space set?

Are you referring to the CMY values of three primary pigments?
But the detailed filter characteristic of a pigment must be known if you want to use it in a mixing process, surely. That's why I question the idea of those 'points' in colour space. Looking at it from an RF Engineering point of view, knowing only the centre frequency of a filter can never tell you the result of inserting it in a channel .
I take my hat off to 'colour engineers' in the world of CMY. I wouldn't know where to start to produce a matching procedure that didn't actually involve knowing the band pass characteristics of all the pigments.

 

[pinball1970]

I wouldn't know where to start to produce a matching procedure that didn't actually involve knowing the band pass characteristics of all the pigments.

Re Band pass - There isn't one. There are commercial tolerances but different equations and different weightings on the parameters. There is a useful one called CMC that dye houses use. Measure your target measure, your batch and if you get a value of 1.0 (called Delta E) or below there is a good a chance it is commercially viable. Where it gets interesting is when you split the numbers up into the respective components and then fiddle around with the recipe to see how each parameter varies.

 

[sophiecentaur]

Re Band pass - There isn't one.

We must be talking at cross purposes. I am referring to the frequency (wavelength) response of the filter. It will have a significant bandwidth and the pass band shape is important.

 

[pinball1970]

I take my hat off to 'colour engineers' in the world of CMY

I prefer technologist, we take our hats off to the guys who made predictions without the use of a spectro or colour software and to the guys that used colour space and library dyeings to come up with matching software. Where would the world be if we did not control colour? Chaos.

 

[sophiecentaur]

Where would the world be if we did not control colour?

In the 1970s !