From: wft@math.canterbury.ac.nz (Bill Taylor)
Newsgroups: sci.math
Subject: Re: Sorting Colors - How?
Date: 23 Nov 1994 01:25:05 GMT

|> >What I want to do is take a palette of colors,(0-255 say), in RGB format
|> >and re-arrange them in such a way that they _appear_ sorted/grouped
|> >by their _appearance_.  ie Blue-ish/Green-ish/Red-ish groups etc.
|> 
|> Color is a 3-dimensional property.  

Right.  I responded to this on sci.physics a little while ago; but again...

|> The Munsel color sphere is a nice way to  display them.  

Yep, it's good. It has re-appeared in many different guises and under other
names. My version of it is appended below.

|> If you can get by with implying a lightness/darkness axis not 
|> being displayed, a good 2-d representation is to use the a*, b* values 
|> (produces a fin shaped display if all of color space is spanned). 

You can take any appropriate 2-d slice of the double cone below.

|> Color is 
|> much more complicated (and non-linear) than most people suspect.

And how! Here we go then...

--------

Nice post on colors by Matt McIrvin!

mcirvin@scws37.harvard.edu (Matt McIrvin) writes:

|>   Though the retina has
|> receptors which correspond to broad ranges sort of centered around
|> red, green, and blue, there's a lot of processing in the visual cortex
|> that divides color space in rather different ways,

Yes indeed; and there's also a *lot* of pre-processing that goes on in the
optic nerve itself, at the retina end! This is well-known for shape/pattern
detection problems, and I think applies to color vision as well, especially
when boundary regions are involved. (Hence those simple optical illusions
whereby the same color looks quite different when surrounded by one border
or by a differently-colored border. Theres's no way we can "get them" to look
the same, no matter how certainly we know they are!)

|> (The science and art of color only begins with physics; a lot of it is
|> neurophysiology and psychology!

How very true.  And easily forgotten.

|> A better way to do this would be to transform the colors into a
|> coordinate system that is closer to the way we normally think about
|> colors, such as HLS, in which the coordinates are hue, luminance
|> (brightness, more or less), and saturation (which measures how vivid
|> or gray the color is) ...
|>                 ... pink is a lighter, less-saturated red, brown is a
|> range of darker, less-saturated yellows, oranges and reds, and so on.

All very nicely put.  And the grays are totally desaturated any-hues, of
varying luminance; black being totally dark gray, and white totally light gray.


I've always been intrigued by the two standard painters' ways of ordering
colors, and their "mathematical" relationship. (And actually, insofar as
colors are physical, I think the math is genuine, not pseudo.)

Both ways have one dimension being hue; arranged naturally in a circle from
red through orange, yellow, green, blue, purple, & back to red. The other two
dimensions are then Cartesian and Polar versions of the same colors!

The HLS mentioned above, is the polar, with the origin as the pure color,
the radius as the saturation (actually its complement), and the angle as
the luminance. The angle is one quadrant only, and the radius is in [0,1].

Then there is the cartesian style, HWB, Hue-%White-%Black, (more natural for
commercial paint mixers!) The pure hue is at the origin again, and the amounts
of black and white mixed in are along the two co-ordinates.

To get it just right, we must flatten the quarter-circle arc of total
de-saturation (100% black & white in various proportions) into a straight
line, and turn the diagram on its side. Here it is all pictured for hue yellow;
(and if you disagree with some of my color words just insert your own; and
this same slice could probably also take beige, sandy, khaki...)


           <--- de-saturation ---

       black
          |\        ___
          |  \     |\
          |    \   |  \  % of black added
    |     |      \      \
    |     | brown  \      \
    |     |          \
    |     dark         \
luminance gray         tan
    |     |                \
    |     |                  \
    |     mid         blonde   \
    |     gray              yellOw    <---(O is the origin as usual!)
    V     |      buff          /
          |                  /
          |                /
          |   fawn       /       /
          pale         /       /
          gray    cream      / % of white added
          |        /     | /
          |      /       |__
          |    /
          |  /
          |/
        white


This is the luminance/saturation ( = black/white)  slice for hue = yellow.

To make the polar/cartesian correspondence stand out, the left-hand line
of grays should really be a left-bulging arc, of course.   But
(i) this would be terrible in ascii, and
(ii) all the other hues can now be neatly added in by joining them all along
the gray-line, so as to get a nice little bi-conical booklet of colors, with
pages from yellow through orange, red etc and back to yellow, (with as many hue
gradations as suits you).

So color is thus naturally presented in 3-dimensional cylindrical co-ordinates!

Either as HLS, (circular hue crossed polar shades),
    or as HBW, (circular hue crossed cartesian b/w mixes).

I've always thought this polar/cartesian correspondence was particularly cool!

-------------------------------------------------------------------------------
              Bill Taylor              wft@math.canterbury.ac.nz
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              "We're pushing back the frontiers of knowledge!"

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