.. _Color Space:

Color Systems and Artificial Illumination
=========================================

In this Chapter, we are going to try to explain the relationship
between the RGB, CMYK, and HSV color systems so as to (hopefully) make
them more intuitive. GMT allows users to specify colors in CPTs
in either of these three systems. Interpolation between colors is
performed in either RGB or HSV, depending on the specification in the
CPT. Below, we will explain why this all matters.

RGB color system
----------------

Remember your (parents') first color television set? Likely it had three
little bright colored squares on it: red, green, and blue. And that is
exactly what each color on the tube is made of: varying levels of red,
green and blue light. Switch all of them off, *r=g=b=0*, then you
have black. All of them at maximum, *r=g=b=255*, creates white.
Your computer screen works the same way.

A mix of levels of red, green, and blue creates basically any color
imaginable. In GMT each color can be represented by the triplet
*r/g/b*. For example, 127/255/0 (half red, full
green, and no blue) creates a color called chartreuse. The color sliders
in the graphics program GIMP are an excellent way to experiment
with colors, since they show you in advance how moving one of the color
sliders will change the color. As Figure *(a)* of :ref:`Chartreuse in GIMP <GIMP>`
shows: increase
the red and you will get a more yellow color, while lowering the blue
level will turn it into brown.

.. _GIMP:

.. figure:: /_images/gimp-sliders+panel.png
   :height: 230 px
   :width: 775 px
   :align: center
   :scale: 75 %

   Chartreuse in GIMP. *(a)* Sliders indicate how the color is altered
   when changing the H, S, V, R, G, or B levels. *(b)* For a constant hue (here 90)
   value increases to the right and saturation increases up, so the pure
   color is on the top right.

Is chocolate your favorite color, but you do not know the RGB equivalent
values? Then look them up in :doc:`/gmtcolors` for a full list.
It's 210/105/30. But GMT makes it easy
on you: you can specify pen, fill, and palette colors by any of the
unique colors found in that file.

Are you very web-savvy and work best with hexadecimal color codes as
they are used in HTML? Even that is allowed in GMT. Just start with a
hash mark (``#``) and follow with the 2 hexadecimal characters for red,
green, and blue. For example, you can use ``#79ff00`` for chartreuse,
``#D2691E`` for chocolate.

HSV color system
----------------

If you have played around with RGB color sliders, you will have noticed
that it is not intuitive to make a chosen color lighter or darker, more
saturated or more gray. It would involve changing three sliders. To make
it easier to manipulate colors in terms of lightness and saturation,
another coordinate system was invented: HSV (hue, saturation, value).
Those terms can be made clear best by looking at the color sliders in
Figure :ref:`Chartreuse in GIMP <GIMP>`\ *a*. Hue (running from 0 to 360) gives you the full
spectrum of saturated colors. Saturation (from 0 to 1, or 100%) tells
you how ‘full' your color is: reduce it to zero and you only have gray
scales. Value (from 0 to 1, or 100%) will bring you from black to a
fully saturated color. Note that "value" is not the same as "intensity",
or "lightness", used in other color geometries. "Brilliance" may be the
best alternative word to describe "value". Apple calls it as
"brightness", and hence refers to HSB for this color space.

Want more chartreuse or chocolate? You can specify them in GMT as
90-1-1 and 25-0.86-0.82, respectively.

The color cube
--------------

We are going to try to give you a geometric picture of color mixing in
RGB and HSV by means of a tour of the RGB cube depicted in
Figure :ref:`fig_ex11`. The geometric picture is most
helpful, we think, since HSV are not orthogonal coordinates and not
found from RGB by a simple algebraic transformation. So here goes: Look
at the cube face with black, red, magenta, and blue corners. This is the
*g* = 0 face. Orient the cube so that you are looking at this face
with black in the lower left corner. Now imagine a right-handed
cartesian (*rgb*) coordinate system with
origin at the black point; you are looking at the *g = 0* plane
with *r* increasing to your right, *g* increasing away from
you, and *b* increasing up. Keep this sense of (*rgb*) as you look at the cube.

Now tip the cube such that the black corner faces down and the white
corner up. When looking from the top, you can see the hue, contoured in
gray solid lines, running around in 360° counter-clockwise. It starts
with shades of red (0), then goes through green (120) and blue (240),
back to red.

On the three faces that are now on the lower side (with the white print)
one of (*rgb*) is equal to 0. These three
faces meet at the black corner, where *r = g = b = 0*. On these
three faces the colors are fully saturated: *s = 1*. The dashed
white lines indicate different levels of *v*, ranging from 0 to 1
with contours every 0.1.

On the upper three faces (with the black print), one of
(*rgb*) is equal to the maximum value. These
three faces meet at the white corner, where *r = g = b = 255*. On
these three faces value is at its maximum: *v = 1* (or 100%). The
dashed black lines indicate varying levels of saturation: *s*
ranges from 0 to 1 with contours every 0.1.

Now turn the cube around on its vertical axis (running from the black to
the white corner). Along the six edges that zigzag around the "equator",
both saturation and value are maximum, so *s = v = 1*. Twirling
the cube around and tracing the zigzag, you will visit six of the eight
corners of the cube, with changing hue (*h*): red (0), yellow
(60), green (120), cyan (180), blue (240), and magenta (300). Three of
these are the RGB colors; the other three are the CMY colors which are
the complement of RGB and are used in many color hardcopy devices (see
below). The only cube corners you did not visit on this path are the
black and white corners. They lie on the vertical axis where hue is
undefined and *r = g = b*. Any point on this axis is a shade of gray.

Let us call the points where *s = v = 1* (points along the RYGCBM
path described above) the "pure" colors. If we start at a pure color and
we want to whiten it, we can keep *h* constant and *v = 1*
while decreasing *s*; this will move us along one of the cube
faces toward the white point. If we start at a pure color and we want to
blacken it, we can keep *h* constant and *s = 1* while
decreasing *v*; this will move us along one of the cube faces
toward the black point. Any point in (*rgb*)
space which can be thought of as a mixture of pure color + white, or
pure color + black, is on a face of the cube.

The points in the interior of the cube are a little harder to describe.
The definition for *h* above works at all points in (non-gray)
(*rgb*) space, but so far we have only
looked at (*s*, *v*) on the cube faces, not inside it. At
interior points, none of (*rgb*) is equal to
either 0 or 255. Choose such a point, not on the gray axis. Now draw a
line through your point so that the line intersects the gray axis and
also intersects the RYGCBM path of edges somewhere. It is always
possible to construct this line, and all points on this line have the
same hue. This construction shows that any point in RGB space can be
thought of as a mixture of a pure color plus a shade of gray. If we move
along this line away from the gray axis toward the pure color, we are
"purifying" the color by "removing gray"; this move increases the
color's saturation. When we get to the point where we cannot remove any
more gray, at least one of (*rgb*) will have
become zero and the color is now fully saturated; *s = 1*.
Conversely, any point on the gray axis is completely undersaturated, so
that *s = 0* there. Now we see that the black point is special,
*s* is both 0 and 1 at the same time. In other words, at the black
point saturation in undefined (and so is hue). The convention is to use
*h = s = v = 0* at this point.

It remains to define value. To do so, try this: Take your point in RGB
space and construct a line through it so that this line goes through the
black point; produce this line from black past your point until it hits
a face on which *v = 1*. All points on this line have the same
hue. Note that this line and the line we made in the previous paragraph
are both contained in the plane whose hue is constant. These two lines
meet at some arbitrary angle which varies depending on which point you
chose. Thus HSV is not an orthogonal coordinate system. If the line you
made in the previous paragraph happened to touch the gray axis at the
black point, then these two lines are the same line, which is why the
black point is special. Now, the line we made in this paragraph
illustrates the following: If your chosen point is not already at the
end of the line, where *v = 1*, then it is possible to move along
the line in that direction so as to increase
(*rgb*) while keeping the same hue. The
effect this has on a color monitor is to make the color more
"brilliant", your hue will become "stronger"; if you are already on a
plane where at least one of (*rgb*) = 255,
then you cannot get a stronger version of the same hue. Thus, *v*
measures brilliance or strength. Note that it is not quite true to say
that *v* measures distance away from the black point, because
*v* is not equal to :math:`\sqrt{r^2 + g^2 + b^2}/255`.

Another representation of the HSV space is the color cone illustrated in
Figure :ref:`hsv_cone`.

.. _hsv_cone:

.. figure:: /_images/hsv-cone.png
   :height: 508 px
   :width: 750 px
   :align: center
   :scale: 50 %

   The HSV color space

Color interpolation
-------------------

From studying the RGB cube, we hope you will have understood that there
are different routes to follow between two colors, depending whether you
are in the RGB or HSV system. Suppose you would make an interpolation
between blue and red. In the RGB system you would follow a path
diagonally across a face of the cube, from 0/0/255 (blue) via 127/0/127
(purple) to 255/0/0 (red). In the HSV system, you would trace two edges,
from 240-1-1 (blue) via 300-1-1 (magenta) to 360-1-1 (red). That is even
assuming software would be smart enough to go the shorter route. More
likely, red will be recorded as 0-1-1, so hue will be interpolated the
other way around, reducing hue from 240 to 0, via cyan, green, and yellow.

Depending on the design of your CPT, you may want to have it
either way. By default, GMT interpolates in RGB space, even when the
original CPT is in the HSV system. However, when you add the
line ``#COLOR_MODEL=hsv`` in the header of the CPT, GMT will not only read the color
representation as HSV values, but also interpolate colors in the HSV
system. That means that H, S, and V values are interpolated linearly
between two colors, instead of their respective R, G, and B values.

The top row in Figure :ref:`Interpolating colors <color_interpolate>`
illustrates two examples: a blue-white-red scale (the palette in
Chapter :ref:`Of Colors and Color Legends`) interpolated in RGB and the palette interpolated in
HSV. The bottom row of the Figure demonstrates how things can go
terribly wrong when you do the interpolation in the other system.

.. _color_interpolate:

.. figure:: /_images/GMT_color_interpolate.*
   :width: 500 px
   :align: center

   When interpolating colors, the color system matters. The polar palette on the left needs to
   be interpolated in RGB, otherwise hue will change between blue (240) and white (0). The rainbow
   palette should be interpolated in HSV, since only hue should change between magenta (300) and red (0).
   Diamonds indicate which colors are defined in the palettes; they are fixed, the rest is interpolated.

.. toggle::

   Here is the source script for the figure above:

   .. literalinclude:: /_verbatim/GMT_color_interpolate.txt

Artificial illumination
-----------------------

.. _slope2intensity:

.. figure:: /_images/GMT_slope2intensity.*
   :width: 500 px
   :align: center

   For digital elevation models (DEM) one can specify an illumination azimuth
   and elevation and compute the unit vector **s**. Then, at any point on the grid
   we can compute the normal vector **n**. Their dot products can be used to compute an
   *intensity* grid that will be positive if the surface faces the light, negative if facing
   away, and zero if the vectors are orthogonal.  In GMT, uses may wish to add artificial
   illumination on non-DEM data, such as geopotential data.  In those cases, while an
   illumination azimuth still makes sense, an elevation does not since the normal vectors
   no longer can easily be related to elevation. GMT thus only uses the directions of these
   vectors and normalizes the intensities to yield suitable shading; see :doc:`/grdgradient`
   for more details.

.. toggle::

   Here is the source script for the figure above:

   .. literalinclude:: /_verbatim/GMT_slope2intensity.txt

GMT uses the HSV system to achieve artificial illumination of colored
images (e.g., **-I** option in :doc:`/grdimage`) by changing the saturation
*s* and value *v* coordinates of the color. As explained above, when the *intensity* is zero
(flat illumination), the data are colored according to the CPT. If
the intensity is non-zero, the color is either lightened or darkened
depending on the illumination. The color is first converted to HSV (if
necessary) and then darkened by moving (*sv*) toward
(:term:`COLOR_HSV_MIN_S`, :term:`COLOR_HSV_MIN_V`)
if the intensity is negative, or lightened by sliding (*sv*) toward
(:term:`COLOR_HSV_MAX_S`, :term:`COLOR_HSV_MAX_V`)
if the illumination is positive. The extremes of the *s* and *v* are defined in the
:doc:`/gmt.conf` file and are usually chosen so the corresponding points are nearly black
(*s = 1*, *v = 0*) and white (*s = 0*, *v = 1*).
The reason this works is that the HSV system allows movements in color
space which correspond more closely to what we mean by "tint" and
"shade"; an instruction like "add white" is easy in HSV and not so
obvious in RGB.

.. _color_hsv:

.. figure:: /_images/GMT_color_hsv.*
   :width: 500 px
   :align: center

   The red circle represents the RGB color (217, 271, 54).  This color has a hue that
   is yellow, which is H = 60 degrees in the HSV system.  Here we show a slice through
   the color RGB cube at H = 60.  All the colors in this slice have a yellow hue but
   there saturation and values vary.  Our point has an S of 0.75 and a V of 0.85. In
   applications that take intensity values we use an intensity (in the range of ±1)
   to move the color towards the  black (B) or white (W) point for negative and positive
   intensities, respectively (an intensity of 0 leaves the color unchanged).  Because (a) printers
   are not good at yielding near-black or near-white colors, and (2) to avoid colors
   with saturating intensities being pushed into black and white, we do not use the
   B and W points as terminal points but instead end at the two white circles.  Their
   coordinates are given by (:term:`COLOR_HSV_MIN_S`, :term:`COLOR_HSV_MIN_V`) [1, 0.3]
   and (:term:`COLOR_HSV_MAX_S`, :term:`COLOR_HSV_MAX_V`) [0.1, 1].

.. toggle::

   Here is the source script for the figure above:

   .. literalinclude:: /_verbatim/GMT_color_hsv.txt

Thinking in RGB or HSV
----------------------

The RGB system is understandable because it is cartesian, and we all
learned cartesian coordinates in school. But it doesn't help us create a
tint or shade of a color; we cannot say, "We want orange, and a lighter
shade of orange, or a less vivid orange". With HSV we can do this, by
saying, "Orange must be between red and yellow, so its hue is about
*h = 30*; a less vivid orange has a lesser *s*, a darker
orange has a lesser *v*". On the other hand, the HSV system is a
peculiar geometric construction, more like a cone
(Figure :ref:`hsv_cone`). It is not an orthogonal coordinate system, and
it is not found by a matrix transformation of RGB; these make it
difficult in some cases too. Note that a move toward black or a move
toward white will change both *s* and *v*, in the general
case of an interior point in the cube. The HSV system also doesn't
behave well for very dark colors, where the gray point is near black and
the two lines we constructed above are almost parallel. If you are
trying to create nice colors for drawing chocolates, for example, you
may be better off guessing in RGB coordinates.

CMYK color system
-----------------

Finally, you can imagine that printers work in a different way: they mix
different paints to make a color. The more paint, the darker the color,
which is the reverse of adding more light. Also, mixing more colored
paints does not give you true black, so that means that you really need
four colors to do it right. Open up your color printer and you'll
probably find four cartridges: cyan, magenta, yellow (often these are
combined into one), and black. They form the CMYK system of colors, each
value running from 0 to 1 (or 100%). In GMT CMYK color coding can be
achieved using *c/m/y/k* quadruplets.

.. _color_cmyk:

.. figure:: /_images/GMT_cmyk.*
   :width: 500 px
   :align: center

   (left) Mixing of light on a computer screen shows that the mixing
   of primary colors red (R), green (G) and blue (B) yields the other
   primary colors of magenta (M), cyan (C) and yellow (Y), plus white.
   (right) Mixing of colors for printing uses C, M and Y and when these
   mix completely we get black (K).  To get a better representation of black
   the amount of black in any particular color is removed from the color
   and painted with a specific black ink instead, leading to under-color
   removal of the remaining three pigments.

.. toggle::

   Here is the source script for the figure above:

   .. literalinclude:: /_verbatim/GMT_cmyk.txt

Obviously, there is no unique way to go from the 3-dimensional RGB
system to the 4-dimensional CMYK system. So, again, there is a lot of
hand waving applied in the transformation. Strikingly, CMYK actually
covers a smaller color space than RGB. We will not try to explain you
the details behind it, just know that there is a transformation needed
to go from the colors on your screen to the colors on your printer. It
might explain why what you see is not necessarily what you get. If you
are really concerned about how your color plots will show up in your PhD
thesis, for example, it might be worth trying to save and print all your
color plots using the CMYK system. Letting GMT do the conversion to
CMYK may avoid some nasty surprises when it comes down to printing. To
specify the color space of your PostScript file, set
:term:`PS_COLOR_MODEL` in the :doc:`/gmt.conf` file to RGB, HSV, or CMYK.
