If a paint droplet is made up of 100 pigments and the pigments have 1
of 2 colors, what is the apparent color in cmy of the paint droplet
given that n pigments have the cmy value of (c1,m1,y1) and (100-n)
pigments have a cmy of (c2,m2,y2)?
You should assume that the pigments are too small to be seen
separately. Here is an example: if the paint droplet is made up of 30
pigments that have cmy value of (50, 35, 1) and the remaining 70
pixels have cmy value of (100, 75, 12), what is the apparent cmy value
of the paint droplet? You should assume that the pigments are mixed together evenly.

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Clarification of Question by hmulling-ga on 04 Jan 2006 15:29 PST

Here is a reworded example: if the paint droplet is made up of 30
pigments that have cmy value of (50, 35, 1) and the remaining 70
pigments have cmy value of (100, 75, 12), what is the apparent cmy value
of the paint droplet?

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Request for Question Clarification by hedgie-ga on 04 Jan 2006 20:51 PST

Are you interested in optical properties of paint? 


  Paint consists of pigments and an oil or water-based binder 
  (the binder being the majority in volume).
http://www.diydata.com/materials/paints/paints.htm

or in color of a dry surface, covered with a some paint?

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Clarification of Question by hmulling-ga on 04 Jan 2006 21:41 PST

I'm interested in the optical properties of paint. It turns out that
acrylic paint is not transparent and so it doesn't matter what color
the surface is; you can only see the color of the paint.

A simplier way to ask the orignal question is "if you mix x onces of
paint with color C1 with y onces of paint with color C2, what color
paint will you get?"

What you have to remember is that the pigments of the paint do not
change their color when they are mixed. If you mix white paint with
dark blue paint you don't get the same color as if you started with
light blue paint. Light blue paint and dark blue paint are made from
different colored pigments.

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Request for Question Clarification by hedgie-ga on 05 Jan 2006 02:04 PST

I see.  There is a simple formula for additive mixing of light, where
cmy of light mixture can be derived from cmy's of components.

 Mixing of paints is more complex. There is no such simple formula for
this case (subtractive mixing). The color depends not only on color of
pigments and concetration but also on particle size and uniformity of
dispersion. Light  penetrates into the liquid, and part of it is
returned to the surface. Incident
light (illumination) and reflectance of the liquid creates impression of color.
  
 Would you accept as an asnwer a search  of theories and articles on
this issue (reflectance of dispersions) even if no simple and
universal will be found?

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Clarification of Question by hmulling-ga on 09 Jan 2006 18:31 PST

I'm sorry for the delay. This thread is a little confusing.
(The google answer UI allows me to post a clarification but 
it feels more like we asking each other questions.)


I'm not sure if you will find me a webpage that discusses a possible solution
if you will read such a webpage and write the solution.

I'm looking for an algorithm like:
To compute the appearent CMY do the following: 
c = (n*c1+(100-n)*c2)/100,
m = (n*m1+(100-n)*m2)/100,
y = (n*y1+(100-n)*y2)/100

This is a linear weighted averaging of the separate components.
If the computation were this simple, I would have expected to 
find it on the internet more easily. Do the color components 
average together separately? Is it linear?

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Request for Question Clarification by hedgie-ga on 14 Jan 2006 01:22 PST

hmulling-ga

Google has a refund policy and  rules about what
constitutes an answer.
http://www.googleguide.com/answers.html
http://answers.google.com/answers/faq.html

 Not only for this reason, researchers,
before they invest their time, want to know whether they
can live up to the expectations of the asker. We ask
you to clarify your question and/or your expectations for
an answer. 

The Clarification dialog, a series of RFC's (Requests of Clarifications)
can happen before or after the question is answered, or both.

I see this is your first use of GA.
I suggest you read a couple questions/answer cases to see
how it works. Here are few of mine.

Some questions can be answered directly e.g. 
http://answers.google.com/answers/threadview?id=430559
http://answers.google.com/answers/threadview?id=427820

Some folks ask for what is not possible - and we need to know whether
a  'negative answer' -i.e. reasons for it being impossible, is of interest
http://answers.google.com/answers/threadview?id=558992

Sometimes it is not clear what asker knows and wants
http://answers.google.com/answers/threadview?id=600240


Reread the comments and RFCs to your question. 
If you answer my questions, e.g. by saying 

 'I understand that subtractive mixing does not
  have a simple formula like additive mixing. 
  You may neglect particle size effects
 and I will accept as an answer a simple approximation'
then I will answer your question.

Or, you may say "I do not know what you mean by
 'additive and subtractive mixing' please explain"


Tthen I will answer your question.
The answer would be different in each case.

 You can also say 'hedgehogd do not understand paints'
 and I will let it to other researchers.

Hope this helps.

hedgie

Greetings,

This seems closer to what you are seeking.  Maybe it can be of help to Hedgie:

http://www.answers.com/main/ntquery;jsessionid=5cnbk8kli9jqo?method=4&dsid=2222&dekey=CMYK+color+model&gwp=8&curtab=2222_1&sbid=lc05a&linktext=CMYK%20color%20model

(pasting the thread did work for me after I clicked on it in the Google text.)

At the bottom of the page, you can click on the second external link
and see hundreds of colors with the CMYK (K for black) percentages,
but it doesn't seem to have yours.
But at the bottom of the chart, there is an email address.

Good luck, Myoarin

I'm not sure what the rules are for this case. I would like an answer
and you're implying that there is no answer. I'm willing to pay $25
(via paypal) for your work so far but I'm not sure I should pay the
full amount. Is this acceptable?

Hmulling,
If your comment was directed to me, I did not mean to imply that that
there is no answer.  Not being a G-A Researcher, I cannot be paid and
do not expect to be.
It seemed that the link I posted was more in the terms of your question.
I was hoping that it might help Hedgie, who is a Researcher, to pursue
the matter further.  Having found that site, I began to understand the
question a little, but not like I could answer it, but now so that I
feel that it could be answered, perhaps by a description of what
happens if an actual color cannot be defined, or maybe an explanation
of why one cannot be.

                                      * * * *
Having looked around a bit more, I am beginning to wonder about your
original premise of a drop of paint made up of CMY(K) components.  As
I understand it, CMYK refers to the pigments used in four-color
printing, each pixel of color being applied separately so that in
combination the eye registers them as one hue. I found these
discussions of paint and CMYK, but in both cases they turn out to be
referring to printing or graphics, "paint (ink)", as appears on the
first site.

http://semmix.pl/color/extrans/etr10.htm
http://whatis.techtarget.com/definition/0,,sid9_gci211805,00.html

From the price you have put on your question, I am assuming you know a
lot more about what you're asking than I could find.  I was
anticipating finding a site that discussed mixing CMY pigments as you
suggest, but I was unsuccessful.  I did find this site, which
indicates that pigments come in many colors.  Cadmium yellow is  - I
believe -  the equivalent of Y, but the site doesn't suggest that
paints are just mixtures of CMYK as occurs in printing.
http://materials.globalspec.com/LearnMore/Materials_Chemicals_Adhesives/Chemicals_Raw_Materials/Pigments

Everything else that I found about paints agreed completely with Hedgie's posting.

Trying to get back to your question and acrylic paints, I suppose that
maybe one could find two acrylic paints that were equivalent in color
to the CMY combinations you mention and mix them 30/70 and having a
resulting acrylic paint of a color that could then be compared with a
CMY color chart (bigger than the one I found), and thus identify the
CMY combination for it.  There must be software that allows one to
adjust CMY proportions to match a given color.

As you can tell, I have moved on a ways in my thinking, so maybe I am
implying that what you have suggested is not possible  - or rather not
the way paint is made.

It has been very interesting.  If you do know, however, that there are
CMY composed paints, I would love to learn about it.
Regards, Myoarin

myoarin
        
      The link you posted does work, but I would not use it, since it
does confuse two things.
 1) coordinate systems for the color space. Like in geometry, there is several
of them, and they are equivalent (can be mathematicaly transformed
into each other. In addition there is a simple formula for composition
of light.
 2)  Physics of deriving color of either suspension or of multilayer
structure usually found in printing. As I said, that color depend on
other factors then colors of components or particles. Simple example
is milk (suspension of fat droplets in water) which is white, because
droplets (due to their size) scatter all visible light equally. Color
can be calculated, but there is no simple universal formula.


 Asker may expire the question and post different one for differnt
price. However, there is so much written about the problem two,
classical theory from 1930 and many current research papers, that $50
looks like a fair price to organize it.
The fact that asker is willing to pay $25 for few random link would be
encouraging; the fact that he is not responding to RFCs is
discouraging.

 I think I will let sit. May be some other GAR will pick it up.

Hedgie,
My only consideration is that I didn't find anything that suggested
that a drop of paint  - even one of paint as ink -  is physically a
mixture of CMY components.
I hope that I made it clear, that I defer to Hmulling's knowledge if
s/he knows better.  I just didn't find anything to support that
concept as I understood it, although at first  - and in consideration
of the price -  I assumed that it was valid.
Myoarin

Does this method get you what you want?
http://www.colorcube.com/articles/math/math.htm

Using your inputs, I end up with a result of C46 M34 Y5.

- Hammer

That is a great site, Hammer, but it seems that Hmulling's combination
(the clarification) would have to yeald a color with much more Cyan.
The site, however, relates to printing, not from the text but from its
basic reference  - the group of sites linked.  I still feel that this
doesn't apply to mixing pigments of acrylic paints.  I don't want to
be right about this, just can't find anything to support it.
Myoarin