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https://github.com/nbehrnd/moreland-gnuplot-palettes

A reformat of Kenneth Moreland's color palettes to work with them in gnuplot.
https://github.com/nbehrnd/moreland-gnuplot-palettes

gnuplot moreland palette palette-colors perception visualization

Last synced: about 15 hours ago
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A reformat of Kenneth Moreland's color palettes to work with them in gnuplot.

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README 

          

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# date   2019-12-03 (YYYY-MM-DD)

# edit:  2019-12-10 (YYYY-MM-DD)



* Background



  On his web page, Kenneth Moreland suggests a number of continuous

  and diverge color palettes to improve scientific

  visualization.[fn:1] Contrasting to other approaches, they aim for a

  smooth variation of the hue between the extremes of a scale

  displayed.  While this reduces the brightness of the colors to

  choose from, their continuous transient hue offers a better visual

  inspection already when print in color.  Contrasting to classical

  "jet" or "rainbow" palettes (/vide infra/), they retain their

  information if the output is constrained to gray scale (e.g., if

  xeroxed).

  

  #+NAME:        appetizer

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./doc/appetizer.png]]



  Where possible, this project renders Kenneth Moreland's set of

  =.cvs= palette information accessible to gnuplot as =.plt= files.



* How to use the .plt palettes



  The color palettes are provided with a varying number of explicitly

  defined colors.  This range spans from eight up to 1024.  For

  smaller color palettes, a copy-paste of their content into an

  already existing gnuplot script file may be an option.  More

  convenient however, especially while working with larger color

  palettes, is to access them from gnuplot by adding the command

  #+BEGIN_SRC shell

    load "example_palette.plt"

  #+END_SRC

  at any point prior to the =[s]plot= instruction.



  Each sub-folder contains the corresponding =.plt= files.  The number

  in the file name indicates the number of explicitly defined colors

  in the file.



* Palettes at disposition



  For the display of continuous data, conversions of eight color

  palettes are provided: =black-body=, =extended-black-body=,

  =inferno=, =kindlmann=, =extended-kindlmann=, =magma=, =plasma=, and

  =viridis=.



  On the other hand, palette =bent-cool-warm= is designed with diverge

  data sets in mind where highlighting the transition across a

  critical value is important.  This may be useful to indicate

  relative velocities, or pressures below / above a threshold, for

  example.  It is complemented by =smooth-cool-warm=.  While again

  designed as diverging palette, the transition around the mid point

  now is gradual.  Thus, for data close at this transition, expect

  less detail displayed there with with palette =smooth-cool-warm= ,

  than with palette =bent-cool-warm=. \\ 



  The display of the palette's action is based on synthetic data

  computed for the Bessel function $f(x,y) = x^2 + y^2$ with a grid of

  500 \times 500 points in the (/x,y/)-plane.  1024 levels in the

  orthogonal /z/-direction accommodate the highest number of

  explicitly defined colors per palette file available ($n = 1024$).

  Next to it, a diagram depicts how the =R=, =G=, and =B= channel sum

  up to yield the =RGB= color displayed.  In addition, the NTSC

  luminance value is traced.  This is indicative about how the

  calculated result would look like for an output constrained to

  gray-scale.  Thirdly you see the Bessel plot a twice, actually

  simulating the gray-scale output.



  #+NAME:       Moreland_black_body_1024

  #+CAPTION:    Kenneth Moreland's continuous palette =black-body= used to display the Bessel function $f(x,y) = x^2 + y^2$.  This and the plots following are based on the explicit gnuplot instructions =set sample 500= and =set isosample 1024= to accommodate up to 1024 colors explicitly defined in the palettes.

  #+ATTR_LATEX: :width 15cm   

  #+ATTR_HTML:  :width 75%

  [[./black-body/black-body-table-float-1024_test.png]]



  #+NAME:       Moreland_extended_black_body_1024

  #+CAPTION:    Application of Kenneth Moreland's continuous palette =extended-black-body=.

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./extended-black-body/extended-black-body-table-float-1024_test.png]]



  #+NAME:       Moreland_inferno_1024

  #+CAPTION:    Application of Kenneth Moreland's continuous palette =inferno=.

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./inferno/inferno-table-float-1024_test.png]]



  #+NAME:       Moreland_kindlmann_1024

  #+CAPTION:    Application of Kenneth Moreland's continuous palette =kindlmann=.

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./kindlmann/kindlmann-table-float-1024_test.png]]



  #+NAME:       Moreland_extended_kindlmann_1024

  #+CAPTION:    Application of Kenneth Moreland's continuous palette =extended-kindlmann=.

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./extended-kindlmann/extended-kindlmann-table-float-1024_test.png]]

  

  #+NAME:       Moreland_magma_1024

  #+CAPTION:    Application of Kenneth Moreland's continuous palette =magma=.

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./magma/magma-table-float-1024_test.png]]

  

  #+NAME:       Moreland_plasma_1024

  #+CAPTION:    Application of Kenneth Moreland's continuous palette =plasma=.

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./plasma/plasma-table-float-1024_test.png]]



  #+NAME:       Moreland_viridis_1024

  #+CAPTION:    Application of Kenneth Moreland's continuous palette =viridis=.

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./viridis/viridis-table-float-1024_test.png]]



  #+NAME:        Moreland_bent_cool_warm_1024

  #+CAPTION:     Application of Kenneth Moreland's diverging palette =bent-cool-warm=, which accentuates the mid-point.

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./bent-cool-warm/bent-cool-warm-table-float-1024_test.png]]



  #+NAME:        Moreland_smooth_cool_warm_1024

  #+CAPTION:     Application of Kenneth Moreland's diverging palette =smooth-cool-warm=.

  #+ATTR_LATEX:  :width 15cm

  #+ATTR_HTML:   :width 75%

  [[./smooth-cool-warm/smooth-cool-warm-table-float-1024_test.png]]



  #+LATEX:  \clearpage{}



* Comparison with other palettes

  

  A few palettes are compared to those provided by Moreland.  They

  again rely on the high level of isosamples (=set iso 1024=) in /z/-,

  and samples (=set samples 500=) in /x/- and /y/-direction.



  Repositories like gnuplot-colorbrewer,[fn:2] and

  gnuplot-palettes[fn:3] host alternative palettes, too.



  + For the display of continuous data, either one of the following

    instructions prior to the =[s]plot= instruction may initiate

    palettes already included in gnuplot:

    #+BEGIN_SRC shell

      set palette gray   # gnuplot's gray palette

      set pm3d map       # access to gnuplot's default rainbow palette

      set palette cubehelix start 0 cycles -1. saturation 1

    #+END_SRC

    Note that palette =cubehelix= equally counters some cases of color

    blindness, too.

    

    #+NAME:     manual_gray_1024

    #+CAPTION:  Gnuplot's gray palette (=set palette gray=) displaying the Bessel function $f(x,y) = x^2 + y^2$.

    #+ATTR_LATEX:  :width 15cm

    #+ATTR_HTML:   :width 75%

    [[./extra_palette_tests/manual_gray_1024_test.png]]



    #+NAME:     manual_palette_1024

    #+CAPTION:  Gnuplot's default rainbow palette (=set palette; set pm3d=).

    #+ATTR_LATEX:  :width 15cm

    #+ATTR_HTML:   :width 75%

    [[./extra_palette_tests/manual_palette_1024_test.png]]



    #+NAME:     manual_cubehelix_1024

    #+CAPTION:  Gnuplot's =cubehelix= palette (=set palette cubehelix start 0 cycles -1. saturation 1=)

    #+ATTR_LATEX:  :width 15cm

    #+ATTR_HTML:   :width 75%

    [[./extra_palette_tests/manual_cubehelix_1024_test.png]]



    #+LATEX:  \clearpage{}



    As a contrasting example, =jet.pal= (provided by [[https://github.com/Gnuplotting/gnuplot-palettes][gnuplot-palettes]])

    mimics an elder matlab default palette with the perceptual

    problems meanwhile addressed by palettes by Moreland and others.

    address.  Its definitions relevant here are:

    #+BEGIN_SRC shell

    set palette defined (0  0.0 0.0 0.5, \

                     1  0.0 0.0 1.0, \

                     2  0.0 0.5 1.0, \

                     3  0.0 1.0 1.0, \

                     4  0.5 1.0 0.5, \

                     5  1.0 1.0 0.0, \

                     6  1.0 0.5 0.0, \

                     7  1.0 0.0 0.0, \

                     8  0.5 0.0 0.0 )

    #+END_SRC

    

    #+NAME:      manual_jet_1024

    #+CAPTION:  Display of the same Bessel function with defined with the external =jet.pal= palette from gnuplotting.org's repository.  Note how the ease to assign levels from the reference bar to the map is depends on the color-space accessed.

    #+ATTR_LATEX:   :width 15cm

    #+ATTR_HTML:    :width 75%

    [[./extra_palette_tests/manual_jet_1024_test.png]]



  + For diverge data, using a blue-white-red transient is a good

    choice /to begin with/.  For the RGB color space by the pngcairo

    terminal, these palettes may be defined by 'named colors' as with

    either of the example instructions below.  Similar as seen with

    Moreland's palettes, it is helpful to decrease the maximal

    luminosity, though (second example).

    #+BEGIN_SRC shell

      set palette defined (-1 "blue", 0 "white", 1 "red")

      set palette defined (-1 "blue", 0 "light-gray", 1 "red")

    #+END_SRC

    

    #+NAME:    manual_rainbow_blue_white_red_1024

    #+CAPTION: Manually set up diverging blue--white-red color palette displaying the Bessel function.

    #+ATTR_LATEX:  :width 15cm

    #+ATTR_HTML:   :width 75%

    [[./extra_palette_tests/manual_blue_white_red_1024_test.png]]



    #+NAME:    manual_rainbow_blue_light-gray_red_1024

    #+CAPTION: Slightly improved version of the earlier diverging three-level color palette by exchange of "white" by "light-gray" as central transition.

    #+ATTR_LATEX:  :width 15cm

    #+ATTR_HTML:   :width 75%

    [[./extra_palette_tests/manual_blue_light-gray_red_1024_test.png]]

  

* Generation of the data



  Departing from Moreland's RGB palettes defined as /floating

  numbers/, script =csv2plt.py= (sub-folder =tools=) reformatted the

  entries to five decimals.  Script =RGB_check.py= provided a control

  if the RGB tuples converted stay within the permitted interval of

  $[0,1]$.



  Script =palette_decomposition.py= provided a quick channel-wise

  decomposition of the RGB color space, complemented by the NTSC

  luminosity.  Each synopsis per =.plt= file displays this result in

  between the test plots in color and gray-scale.



  Script =bessel_test_center.py= computed the synthetic data of the

  Bessel function $f(x,y) = x^2 + y^2$ eventually displayed as color

  plot.  It called ImageMagick to convert this result into gray-scale,

  and concatenated the two plots with the diagram by

  =palette_decomposition.py=.



* Comparison of similar palettes



  Gnuplot's rapid scrutiny about the contribution of =R=, =G=, and =B=

  channel of a palette, reported as =.png=, allows a programmatic

  visual comparison of palettes with each other.  This task addressed

  by script =vignette_comparison.py=, to be run right after

  =palette_decomposition.py=, without provision of parameters from the

  CLI by

  #+BEGIN_SRC shell

    python3 vignette_comparison.py

  #+END_SRC

  

  Each pairwise comparison yields a new file named in the pattern of

  =diff_fileA_fileB.png=.  Differences identified by ImageMagick will

  be indicated with bright red pixels.  This reveals, for example,

  palette =magma.pal= provided by gnuplotting.org[fn:4] /

  [[https://github.com/Gnuplotting/gnuplot-palettes][gnuplot-palettes]] differs from all =magma.plt= definitions derived

  from Kenneth Moreland's palettes based on floating numbers in this

  repository as illustrated below, or with animation =magma_diff.gif=

  (in sub-folder =extra_palette_tests=).



  #+NAME:       magma_testing

  #+CAPTION:    Comparison of two =magma= palettes: Kenneth Moreland's =magma= palette (256 colors, floating RGB definition, left hand side).  Gnuplotting's definition of =magma= (256 colors, floating RGB definition, center).  Difference plot by ImageMagick's =compare= of the two former (right hand).

  #+ATTR_LATEX: :width 15cm

  #+ATTR_HTML:  :width 75%

  [[./extra_palette_tests/magma_testing/synopsis_magma_palettes.png]]



  Sub-folder =extra_palette_tests/magma_testing/= includes further

  details about this analysis and an animated =.gif= about all tests

  performed relevant here.  This and all other data processing was

  run under Linux (Xubuntu 18.04.3 LTS) with CPython (3.6.8,

  October 7, 2019), gnuplot (5.2.7beta, last modified 2019-05-14), and

  ImageMagick (6.9.7-4 Q16).



* Vector-based export



  It is possible to engage gnuplot's =set terminal pdfcairo=

  instruction to provide a native export of the results as the

  resolution independent =.pdf= format.  This was tested for the

  palette maps of 512 explicitly defined colors with now 256 iso

  samples computed by gnuplot for the same Bessel function.  While

  this document contains only the example for the continuously smooth

  viridis palette, tests with this and the other palettes are stored

  in sub-folder =pdf-tests=.



  #+NAME:    viridis_pdf_test

  #+CAPTION: Test of Kenneth Moreland's RGB definition of palette =viridis-table-float-0512= with gnuplot's =set terminal pdfcairo= instruction and 256 isosamples.

  #+ATTR_LATEX: :width 15cm

  #+ATTR_HTML:  :width 75%

  [[./pdf_tests/viridis-table-float-0512_test.pdf]]



  #+LATEX:  \begin{center} $\diamond{}$ \end{center}



* Footnotes

[fn:1] http://www.kennethmoreland.com/color-advice/

[fn:2] https://github.com/aschn/gnuplot-colorbrewer

[fn:3] https://github.com/Gnuplotting/gnuplot-palettes

[fn:4] http://www.gnuplotting.org/