# How do you find an inverse colour?

In printing, CMY are the inverse colours of RGB (possibly not in the right order!) and in light a colour negative is made up of the inverse colours of what was projected onto it.

How exactly do you find the inverse of a colour, and why is it "inverse"?

For example, what is the inverse of (Cadbury's chocolate) Purple, and why?

Additional: I am not asking how I can find the inverse of a colour, I am asking how is an inverse colour actually calculated/found - I am fully aware there are tools that do this, but how?

• I'm not sure I exactly understand your question. Are you looking for the CMYK version of an RBG color? 'Purple' is not an RBG value so I'm not sure what exactly you expect me to give you. You can use the color inspector in ie Photoshop to inspect a color and find both RGB and CMYK values. – Summer Jul 17 '17 at 13:14
• What I am really asking in WHY is CMY the "inverse" of RGB - the purple bit is just an example, as in if i took a photo of a purple chocolate bar wrapper, what would it look like on the negative, and why. I used Cadburys purple as an example as it is a very specific colour. indeed, is "Negative" the same thing as "Inverse"? – Digital Lightcraft Jul 17 '17 at 13:17
• Rephrasing it to "How do you calculate the inverse of a colour" might aid in making your question more clear – Zach Saucier Jul 17 '17 at 13:28
• I see what you mean, but that's not where I'm going with this question, I want to know WHY a colour is an inverse, not just how to calculate it. – Digital Lightcraft Jul 17 '17 at 13:33

Interesting question.

First. Remember that colors can be arranged in a color wheel, but in reality that is not a circle, but a solid, that can come in different shapes, depending on what color model we want to choose.

# Some initial Color solids

For example, the RGB-CMY solid is a cube. Here is an HBS solid. As it is a 3D object we need to choose our parameters of "inverse". You can choose an inverse color on the same "slice" (A) or across the height of the solid (B) Depending on the model an inverse color of any of the top slice will be black in this case (C).

On this HSB figure (that can be either a cylinder or a cone) to find the opposite hue you need to add 180°, because it is using radial coordinates. If you want, you simply choose an opposite color adding 180° to the choosen color.

We also can choose opposite colors seeing the RGB components as graphs, in this case, the range is from 0 to 255.

We add colors modifying this values, adding more color, sliding the graph upwards (or simply adding a bigger number)

You can see that if you do not assign 255 to any RGB slider, you have a gap.

This gap is the value of the opposite color: Let us see how this reacts to some known opposite colors.

• Red is the opposite of cyan in our color wheel. Checked.

• Black is the opposite of white. Checked. This makes changes to the RGB solid in 3 dimensions.

So the inverse of a light color is a dark color: But if you want to stick to changes in the same plane, the graph itself provides the lower and the upper limit of the changes. Now the opposite of a light color is the opposite hue, but the same brightness: So, at the end, it is simply a matter of counting your RGB values and make a series of subtractions.

Here is a related explanation to modify the same color to a lighter and darker one using the same methodology: How to make a given color a bit darker or lighter?

P.S. This is actually how different blending modes on different programs work. Making some simple arithmetic operations on the values of the colors. Inverse, Multiply, difference, etc.

# Other color modes

There are some other color modes that actually have different HUE opposites, for example, the LAB model has Green as opposed to Red, instead of cyan, and Yellow as opposite to Blue.

Take pure white as combination of all colors. When this white light hits an object some colors are absorbed, and some colors are reflected. The color we humans perceive and generally identify the object as are the colors that were reflected NOT the colors that were absorbed.

The inverse of a color is most widely defined as the absorbed light.

Within color models this is approximated within each models mathematical constraints.

For more reading you should look into Goethe's Theory of Colors, 1810

There's many articles on the it too:

I also discussed it a bit in the first part of my answer here, What are the pros and cons of Lab

• Thanks - That's a very simple way to describe it without getting bogged down in the maths of emulating it. – Digital Lightcraft Jul 17 '17 at 14:01
• @DigitalLightcraft You can find the full text of Goethe's Theory of Colors online here. – BANG Jul 18 '17 at 1:34

For CMY to RGB, in a linear colorspace where the color components range linearly from 0 to 1, the conversion is

``````C = 1-R
M = 1-G
Y = 1-B
``````

See for example this online CMYK-RGB converter (assuming K=0).

However, when the range is nonlinear, such as in the sRGB colorspace, there is no exact conversion. See this Wikipedia article which says, among other things,

Since RGB and CMYK spaces are both device-dependent spaces, there is no simple or general conversion formula that converts between them. Conversions are generally done through color management systems, using color profiles that describe the spaces being converted. Nevertheless, the conversions cannot be exact, particularly where these spaces have different gamuts.

About "why is it inverse", the same article explains

Such a model [CMYK] is called subtractive because inks "subtract" brightness from white.

In additive color models, such as RGB, white is the "additive" combination of all primary colored lights, while black is the absence of light. In the CMYK model, it is the opposite: white is the natural color of the paper or other background, while black results from a full combination of colored inks.

See also this technical article from Adobe which demonstrates RGB versus CMY colorspaces. Unfortunately the animation is phoney; it contains actual green frames rather than letting your eye create the green color from the spinning wheel.

• Thank you - Can you also add (If you know) they physics behind WHY a colour is an inverse of another? – Digital Lightcraft Jul 17 '17 at 13:38
• Maybe the final link (the Adobe article) will help with WHY. – Glenn Randers-Pehrson Jul 17 '17 at 13:45