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 Subject: paint drop color calculation Category: Science > Physics Asked by: hmulling-ga List Price: \$100.00 Posted: 04 Jan 2006 15:27 PST Expires: 03 Feb 2006 15:27 PST Question ID: 429179
 ```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.``` 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?``` 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?``` 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.``` 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?``` 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?``` 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```
 There is no answer at this time.

 Subject: Re: paint drop color calculation From: myoarin-ga on 05 Jan 2006 05:25 PST
 ```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```
 Subject: Re: paint drop color calculation From: hmulling-ga on 05 Jan 2006 09:33 PST
 ```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?```
 Subject: Re: paint drop color calculation From: myoarin-ga on 05 Jan 2006 15:25 PST
 ```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```
 Subject: Re: paint drop color calculation From: hedgie-ga on 07 Jan 2006 03:14 PST
 ```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.```
 Subject: Re: paint drop color calculation From: myoarin-ga on 08 Jan 2006 21:13 PST
 ```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```
 Subject: Re: paint drop color calculation From: hammer-ga on 09 Jan 2006 14:34 PST
 ```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```
 Subject: Re: paint drop color calculation From: myoarin-ga on 09 Jan 2006 18:08 PST
 ```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```