## 2021-03-30

### Notes on Color #6: Creating a Zorn Palette

Update: the palette for Krita is available here.

For beginners, limited palette is a useful tool for learning to use colors. Among many of those, the Zorn palette, used by Anders Zorn, seems popular in some ateliers.

There are a few variations of the Zorn palette. The version that I'm learning consists of the following base colors:

• Ivory Black
• Permanent White or Titanium White
• Yellow Ochre
When painting, you are only allowed to obtain colors by mixing these base cases. Depsite of its simplicity, the palette is surprisingly powerful, especially for portrait painting.

Since I'm learning both painting and color theories, I find it interesting to make a digital version.

## Mixing Paints

The process of mixing paints is rather complicated. It is somewhere between additive-average and subtractive. However the situation is simple because the Black and White has very few chroma, and the Red and Yellow are very close in the color space.

In this case we could get quite good estimation of the mixed color by taking (weighted) geoemtric means of the spectral reflectance curves. More details can be found here. A more realistic result can be obtained with ColorMixingTools. Here is a comparison, they look close enough.
 Spectral Reflection Curves of Cadmium Red, Yellow Orche and their 1:1 geometric mean.

 Mixing Cadmium Red and Yellow Orche using drop2color.

Then I plotted mixes of pairs of base colors in XYZ and CAM16UCS.

 Mix of pairs of base colors in XYZ

 Mix of pairs of base colors in CAM16UCS

Interestingly, the edges look quite straight. This means we could even simply use linear combination as a good estimate. Note that linear combinations does make sense in term of mixing lights, and it is much easier to compute.

## Computing the Zorn Color Space

Now the task is to compute all linear combinations of the colors. More accurately, we want all weighted arithmetic means of these colors. This is naturally the volume enclosed by the convex hull of the 4 colors.

The convex hull may be computed in XYZ or a linear RGB space. Note that since XYZ and linear RGB are just linear tranformation of each other, the result color space are essentially the same.

To me it was not trivial how to arrange the color space into a palette. Note that the Zorn color space is a 3d volume, but a palette is ususally 1d or 2d. After some research I decided to put the volume in CAM16UCS, then take slices of the volume at different luma's, which fit the way I intend to use it in painting.

At last, just for fun, I also computed the convext hull in CAM16UCS for comparison, which may or may not make any sense.

Here's the result:

While both versions look simliar, the XYZ version seems better.

## Producing the Palette

Now the palette can be obtained by taking samples of the volume at grid points. Here are two slices.

 The Zorn Palette at J=35
 The Zorn Palette at J=65

I was also able to export the palette for Krita.

 Zorn Palette for Krita.

## Final Thoughts

While it is merely a quick hack with random decisions here and there. I reckon this palette would serve well in my learning of the palette.

The Zorn palette may be viewed as a simple specific version of color gamut masks, which I plan to study further. In fact I do have questions and complaints about popular implementations of gamut masks. For example, common implementations involve:
• The HSV/HSL/HSY color wheel
• A regular, fixed shape on the color wheel, regardless of the value.
However I don't find good color/math theories supporting these choices. As shown above, I expect the shape of the mask to be irregular and changing at different values.

On the other hand, probably it doesn't matter at all. After all this is merely a guide for artists. It is up to the artists to make decisions based on their knowledge and styles.