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Palette or color gradient[1]

Palette is a color storage for use by:

  • `pm3d`
  • filled color contours or polygons
  • color histograms
  • color gradient background
  • and whatever it is or it will be implemented...

Here it stands for a palette of smooth "continuous" colors or grays, but let's call it just a palette. Color palettes require terminal entries for filled color polygons and palettes of smooth colors, are currently available for terminals listed in help for `set pm3d`.

The range of color values are adjustable independently by:

  • `set cbrange`
  • `set log cb`.

The whole color palette is visualized in the `colorbox`.


show palette

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Syntax: 

 show palette
 show palette palette <n> {{float | int}}
 show palette gradient
 show palette fit2rgbformulae
 show palette rgbformulae


Command:

  • `show palette` shows the current palette properties.
  • `show palette gradient` displays the gradient defining the palette (if appropriate)
  • `show palette rgbformulae` prints the available fixed gray --> color transformation formulae.
  • `show palette palette <n>` prints to the screen or to the file given by `set print` a table of RGB triplets calculated for the current palette settings and a palette having <n> discrete colors. The default wide table can be limited to 3 columns of r,g,b float values [0..1] or integer values [0..255] by options float or int, respectively. This way, the current gnuplot color palette can be loaded into other imaging applications, for example Octave. Alternatively, the `test palette` command will plot the R,G,B profiles for the current palette and leave the profile values in a datablock $PALETTE.

Check the standard color gradient (traditional pm3d is black-blue-red-yellow): 

show palette

Output: 

palette is COLOR
rgb color mapping by rgbformulae are 7,5,15
figure is POSITIVE
all color formulae ARE NOT written into output postscript file
allocating ALL remaining color positions for discrete palette terminals
Color-Model: RGB
gamma is 1.5

Help: 

 help show palette

test palette

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Command `test palette` plots profiles of R(z),G(z),B(z), where 0<=z<=1. These are the RGB components of the current color `palette`. It also plots the apparent net intensity as calculated using NTSC coefficients to map RGB onto a grayscale. The profile values are also loaded into a datablock named $PALETTE. 


test palette[2]
Standard Gnuplot palette

It can be saved to the graphic file : 

set terminal png
set output 'p.png'
test palette


where

  • NTSC
    • gray value : calculated using NTSC coefficients to map RGB onto a grayscale[3]
    • the NTSC luminance, which corresponds to the Y channel in the YIQ model. It indicates the result if the color were displayed on a black-and-white TV screen[4]
    • the weighted sum of RGB color components [5] 
//from function test_palette_subcommand from command.c
ntsc = 0.299 * rgb.r + 0.587 * rgb.g + 0.114 * rgb.b;

Code : 

// command.c
/*
 * process the 'test palette' command
 * 1) Write a sequence of plot commands + set commands into a temp file
 * 2) Create a datablock with palette values
 * 3) Load the temp file to plot from the datablock
 *    The set commands then act to restore the initial state
 */
static void
test_palette_subcommand()
{
    enum {test_palette_colors = 256};
    struct udvt_entry *datablock;
    char *save_replot_line;
    TBOOLEAN save_is_3d_plot;
    int i;

    static const char pre1[] = "\
reset;\
uns border; se tics scale 0;\
se cbtic 0,0.1,1 mirr format '' scale 1;\
se xr[0:1];se yr[0:1];se zr[0:1];se cbr[0:1];\
set colorbox hor user orig 0.05,0.02 size 0.925,0.12;";

    static const char pre2[] = "\
se lmarg scre 0.05;se rmarg scre 0.975; se bmarg scre 0.22; se tmarg scre 0.86;\
se grid; se xtics 0,0.1;se ytics 0,0.1;\
se key top right at scre 0.975,0.975 horizontal \
title 'R,G,B profiles of the current color palette';";

    static const char pre3[] = "\
p NaN lc palette notit,\
$PALETTE u 1:2 t 'red' w l lt 1 lc rgb 'red',\
'' u 1:3 t 'green' w l lt 1 lc rgb 'green',\
'' u 1:4 t 'blue' w l lt 1 lc rgb 'blue',\
'' u 1:5 t 'NTSC' w l lt 1 lc rgb 'black'\
\n";

    FILE *f = tmpfile();

#if defined(_MSC_VER) || defined(__MINGW32__)
    /* On Vista/Windows 7 tmpfile() fails. */
    if (!f) {
	char buf[PATH_MAX];
	/* We really want the "ANSI" version */
	GetTempPathA(sizeof(buf), buf);
	strcat(buf, "gnuplot-pal.tmp");
	f = fopen(buf, "w+");
    }
#endif

    while (!END_OF_COMMAND)
	c_token++;
    if (!f)
	int_error(NO_CARET, "cannot write temporary file");

    /* Store R/G/B/Int curves in a datablock */
    datablock = add_udv_by_name("$PALETTE");
    if (datablock->udv_value.type != NOTDEFINED)
	gpfree_datablock(&datablock->udv_value);
    datablock->udv_value.type = DATABLOCK;
    datablock->udv_value.v.data_array = NULL;

    /* Part of the purpose for writing these values into a datablock */
    /* is so that the user can read them back if desired.  But data  */
    /* will be read back using the current numeric locale, so for    */
    /* consistency we must also use the locale when creating it.     */
    set_numeric_locale();
    for (i = 0; i < test_palette_colors; i++) {
	char dataline[64];
	rgb_color rgb;
	double ntsc;
	double z = (double)i / (test_palette_colors - 1);
	double gray = (sm_palette.positive == SMPAL_NEGATIVE) ? 1. - z : z;
	rgb1_from_gray(gray, &rgb);
	ntsc = 0.299 * rgb.r + 0.587 * rgb.g + 0.114 * rgb.b;
	sprintf(dataline, "%0.4f %0.4f %0.4f %0.4f %0.4f %c",
		z, rgb.r, rgb.g, rgb.b, ntsc, '\0');
	append_to_datablock(&datablock->udv_value, strdup(dataline));
    }
    reset_numeric_locale();

    /* commands to setup the test palette plot */
    enable_reset_palette = 0;
    save_replot_line = gp_strdup(replot_line);
    save_is_3d_plot = is_3d_plot;
    fputs(pre1, f);
    fputs(pre2, f);
    fputs(pre3, f);

    /* save current gnuplot 'set' status because of the tricky sets
     * for our temporary testing plot.
     */
    save_set(f);

    /* execute all commands from the temporary file */
    rewind(f);
    load_file(f, NULL, 1); /* note: it does fclose(f) */

    /* enable reset_palette() and restore replot line */
    enable_reset_palette = 1;
    free(replot_line);
    replot_line = save_replot_line;
    is_3d_plot = save_is_3d_plot;
}

set palette

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Command `set palette` without options 

 set palette

sets up the default values

Code: 

// color.c
void
init_color()
{
  /* initialize global palette */
  sm_palette.colorFormulae = 37;  /* const */
  sm_palette.formulaR = 7;
  sm_palette.formulaG = 5;
  sm_palette.formulaB = 15;
  sm_palette.positive = SMPAL_POSITIVE;
  sm_palette.use_maxcolors = 0;
  sm_palette.colors = 0;
  sm_palette.color = NULL;
  sm_palette.ps_allcF = FALSE;
  sm_palette.gradient_num = 0;
  sm_palette.gradient = NULL;
  sm_palette.cmodel = C_MODEL_RGB;
  sm_palette.Afunc.at = sm_palette.Bfunc.at = sm_palette.Cfunc.at = NULL;
  sm_palette.colorMode = SMPAL_COLOR_MODE_RGB;
  sm_palette.gamma = 1.5;
}

file

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Syntax: 

  set palette file '<filename>' {datafile-modifiers}

Where:

  • filename jest to nazwa pliku palety zawierającego kolumny z danymi. Nie jest to plik z rozszerzeniem pal zawierajacy polecenia gnuplota
  • data-modifiers jest to opcjonalny składnik służacy do wybierania elementów z palety( tabeli). Przykład: 'using ($1/255):($2/255):($3/255)'

Polecenie `set palette file` odpowiada poleceniu set palette defined a dane są wczytywane z pliku filename.

Sprawdzamy zawartość pomocy: 

 help set palette file

Przypadki użycia

  • plik tekstowy ( gpf nie pal, który wczytujemy za pomocą polecenia load)
  • plik binarny
  • dane wczytywane z linii poleceń

Text file

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Syntax: 

 set palette file 'palette.txt' using ($1/255):($2/255):($3/255) # Read in a palette of RGB triples each in range [0,255]

W pliku mogą być:

  • 4 kolumny: gray, R, G, B
  • trzy kolumny: R, G, B



# http://soliton.vm.bytemark.co.uk/pub/cpt-city/arendal/arctic.gpf
set palette file "arctic.gpf"
set terminal png
set output "arctic.png"
test palette


Zbiory plików tekstowych gpf 

 set palette file "Skydye07.map" using ($1/255):($2/255):($3/255) # Read in a palette of RGB triples each in range [0,255]

Binary file

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Syntax 

  set palette file "palette.bin" binary record=64 using 1:2:3 # put 64 triplets of R,G,B doubles into file palette.bin and load

CLI

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Możemy użyć tego polecenia do wprowadzenie tabeli kolorów w linii komend:

  • zamiast nazwy pliku podajemy "-"[6]
  • wprowadzmy tabelę
  • kończymy literą e
# Equidistant rainbow (blue-green-yellow-red) palette 
     set palette model RGB file "-"
     0 0 1
     0 1 0
     1 1 0
     1 0 0
     e

# cpt-city/ma/gray/grayscale01a 0 … 100, continuous, RGB, 3 segments
set palette file "-"
0.00000 0.00000 0.00000 0.00000
0.35010 0.93333 0.93333 0.93333
0.75000 0.80000 0.80000 0.80000
1.00000 0.66667 0.66667 0.66667 
e

cubehelix

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  • Cubehelix gradient
  • 2D RGB profile
    2D RGB profile
  • 3D RGB profile
    3D RGB profile

Rodzina palet kolorów opracowana przez D A Green (2011)[7] w której kolor (odcień) zmienia się wzdłuż standardowego koła kolorów, a jednocześnie intensywność rośnie monotonicznie, gdy wartość szarości zmienia się od 0 do 1.

Zalety:

  • drukuje równie dobrze w kolorze i czerni/bieli[8]


gnuplot> set palette cubehelix
gnuplot> show palette
	palette is COLOR
	Cubehelix color palette: start 0.5 cycles -1.5 saturation 1
	figure is POSITIVE
	all color formulae ARE NOT written into output postscript file
	allocating ALL remaining color positions for discrete palette terminals
	Color-Model: RGB
	gamma is 1.5



W kodzie: 

  
  // color.h: t_sm_palette typedef struct (Declaration of smooth palette, i.e. palette for smooth colours)
  /* control parameters for the cubehelix palette scheme */
  double cubehelix_start;	/* offset (radians) from colorwheel 0 */
  double cubehelix_cycles;	/* number of times round the colorwheel */
  double cubehelix_saturation;	/* color saturation */


the cubehelix palette can be modified by gamma. E.g. 

    set palette cubehelix gamma 2.0


C function using gnuplot code : 

/* 
 GNUPLOT - stdfn.h 
 Copyright 1986 - 1993, 1998, 2004   Thomas Williams, Colin Kelley 
*/
#ifndef clip_to_01
#define clip_to_01(val)	\
    ((val) < 0 ? 0 : (val) > 1 ? 1 : (val))
#endif

/*
 input : position
 output : c array ( rgb color)
 
the colour scheme spirals (as a squashed helix) around the diagonal of the RGB colour cube 

https://arxiv.org/abs/1108.5083
A colour scheme for the display of astronomical intensity images by D. A. Green 
*/
void GiveCubehelixColor(double position, unsigned char c[]){



	/* GNUPLOT - color.h 
	 * Petr Mikulik, December 1998 -- June 1999
	 * Copyright: open source as much as possible
	*/

	// t_sm_palette 
  	/* gamma for gray scale and cubehelix palettes only */
  	double gamma = 1.5;

  	/* control parameters for the cubehelix palette scheme */
  	//set palette cubehelix start 0.5 cycles -1.5 saturation 1
	//set palette gamma 1.5
  	double cubehelix_start = 0.5;	/* offset (radians) from colorwheel 0 */
  	double cubehelix_cycles = -1.5;	/* number of times round the colorwheel */
  	double cubehelix_saturation = 1.0;	/* color saturation */
	double r,g,b;
	double gray = position; 
 


	
	/*
 	 Petr Mikulik, December 1998 -- June 1999
 	* Copyright: open source as much as possible
 	*/
	// /* Map gray in [0,1] to color components according to colorMode */
	// function color_components_from_gray
	// from gnuplot/src/getcolor.c
	double phi, a;
	
	phi = 2. * M_PI * (cubehelix_start/3. +  gray * cubehelix_cycles);
	
	// gamma correction
	if (gamma != 1.0)    gray = pow(gray, 1./gamma);
	
	
	a = cubehelix_saturation * gray * (1.-gray) / 2.;
	
	// compute
	r = gray + a * (-0.14861 * cos(phi) + 1.78277 * sin(phi));
	g = gray + a * (-0.29227 * cos(phi) - 0.90649 * sin(phi));
	b = gray + a * ( 1.97294 * cos(phi));
	
	// normalize to [9,1] range
	r = clip_to_01(r);
	g = clip_to_01(g);
	b = clip_to_01(b);
	
	// change range to [0,255]
  	c[0] = (unsigned char) 255*r; //R
  	c[1] = (unsigned char) 255*g; // G
  	c[2] = (unsigned char) 255*b; // B	

}


Examples:

gamma

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Składnia: 

set palette  gamma <gamma>

Ustawia współczynnik gamma na wartość <gamma>

Standardowa wartość współczynnika gamma = 1.5

Przykłady:[9] 

 set palette gamma 1.25


Gamma korekcja innymi metodami:[10] 

  set palette model RGB
  set palette functions gray**0.64, gray**0.67, gray**0.70


lub: 

gamma = 2.2
color(gray) = gray**(1./gamma)
set palette model RGB functions color(gray), color(gray), color(gray) # A gamma-corrected black and white palette


W stosunku do palet szarych zamiast 

 set palette defined ( 0 0 0 0, 1 1 1 1 )

możemy użyć : 

 set palette defined ( 0 0 0 0, 0.5 .73 .73 .73, 1 1 1 1 )


Zobacz w kodzie: 

// color.h
/* gamma for gray scale and cubehelix palettes only */
  double gamma;

gray/color

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Ustawienie szarej palety kolorów 

 set palette gray

przy standarowych ustawieniach odpowiada to : 

 set palette gray positive gamma 1.5 # nieliniowa

Jeśli chcemy otrzymać liniową palete to ustawiamy gamma na 1.0: 

 set palette gray gamma 1.0 # liniowa plaeta


Powrót do kolorowej palety: 

 set palette color


Zobacz też color modes: 

//color.h
/*
 *    color modes
 */
typedef enum {
    SMPAL_COLOR_MODE_NONE = '0',
    SMPAL_COLOR_MODE_GRAY = 'g',      /* grayscale only */
    SMPAL_COLOR_MODE_RGB = 'r',       /* one of several fixed transforms */
    SMPAL_COLOR_MODE_FUNCTIONS = 'f', /* user defined transforms */
    SMPAL_COLOR_MODE_GRADIENT = 'd',  /* interpolated table:
				       * explicitly defined or read from file */
    SMPAL_COLOR_MODE_CUBEHELIX = 'c'
} palette_color_mode;

model/functions

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Składnia: 

  set palette functions <R>,<G>,<B>
  set palette model { RGB | HSV | CMY | YIQ | XYZ }

może być łączone:[11] 

 set palette model HSV functions gray, 1, 1 # full color hsv = rainbow
 set palette model XYZ functions gray**0.35, gray**0.5, gray**0.8 # black to gold

gamma = 2.2
color(gray) = gray**(1./gamma)
set palette model RGB functions color(gray), color(gray), color(gray) # A gamma-corrected black and white palette


Definicje

  • gray jest zmienną przyjmującą wartości od 0 do 1

rgbformulae

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Składnia: 

 set palette rgbformulae <r>,<g>,<b>

skrócona postać : 

 set palette rgb r,g,b


r, g i b są to funkcje odpowiadające za obliczenie każdej ze składowej koloru. (mimo że nazwy składowych są R,G oraz B to ich znaczenie jest zależne od modelu koloru, tzn. w modelu HSV R będzie oznaczało H). Mamy do dyspozycji 37 wbudowanych funkcji ponumerowanych od 0 do 36 (liczby ujemne dają odwrócony gradient). Możemy je wyświetlić: 

show palette rgbformulae

Otrzymamy: 

* there are 37 available rgb color mapping formulae:
0: 0               1: 0.5             2: 1
3: x               4: x^2             5: x^3
6: x^4             7: sqrt(x)         8: sqrt(sqrt(x))
9: sin(90x)       10: cos(90x)       11: |x-0.5|
12: (2x-1)^2       13: sin(180x)      14: |cos(180x)|
15: sin(360x)      16: cos(360x)      17: |sin(360x)|
18: |cos(360x)|    19: |sin(720x)|    20: |cos(720x)|
21: 3x             22: 3x-1           23: 3x-2
24: |3x-1|         25: |3x-2|         26: (3x-1)/2
27: (3x-2)/2       28: |(3x-1)/2|     29: |(3x-2)/2|
30: x/0.32-0.78125 31: 2*x-0.84       32: 4x;1;-2x+1.84;x/0.08-11.5
33: |2*x - 0.5|    34: 2*x            35: 2*x - 0.5
36: 2*x - 1
* negative numbers mean inverted=negative colour component
* thus the ranges in `set pm3d rgbformulae' are -36..36


Kod znajdziemy w: gnuplot/src/getcolor.c/GetColorValueFromFormula

Hot gradient
Inverse hot gradient
Inverse linear gray gradient

Standardowo są wybrane funkcje nr 7 dla składowej czerwonej, 5 dla składowej zielonej i 15 dla niebieskiej. Możemy wybrać inny zestaw, na przykład proponowany w dokumentacji zestaw "gorący" ( ang. hot =black-red-yellow-white): 

set palette rgbformulae 21,22,23

albo odwrócony gorący gradient: 

set palette rgbformulae -21,-22,-23

lub odwrócony liniowy gradient szarości 

 set palette rgbformulae -3,-3,-3 # 1-x, 1-x, 1-x


Przykłady przestrzenie RGB:[12] 

       7,5,15   ... traditional pm3d (black-blue-red-yellow)
       3,11,6   ... green-red-violet
       23,28,3  ... ocean (green-blue-white); try also all other permutations
       30,31,32 ... color printable on gray (black-blue-violet-yellow-white)
       33,13,10 ... rainbow (blue-green-yellow-red)
       34,35,36 ... AFM hot (black-red-yellow-white)

Pełna paleta HSV 

       3,2,2    ... red-yellow-green-cyan-blue-magenta-red

defined

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Składnia: 

 set palette  defined { ( <gray1> <color1> {, <grayN> <colorN>}... ) }

gdzie 

   <color> := { <r> <g> <b> | ’<color-name>’ | ’#rrggbb’ }

Paleta jest zbudowana poprzez liniową interpolację między wartościami określonymi w definicji.

Przykłady: 

 set palette defined (0 "dark-green", 1 "green", 1 "yellow", 4 "red")
 test palette

Otrzymujemy nieciągły gradient.

Za pomocą 2 kolorów otrzymujemy ciągły gradient ( liniowy) pomiędzy bielą ( 1 1 1) a czernią ( 0 0 0 ) 

   set palette model RGB
   set output "gray.png"
   set palette defined (0 1 1 1, 1 0 0 0) # <r> <g> <b> 
   test palette

Inna równowazna składnie polecena set palette: 

   set palette defined ( 0 "white", 1 "black") # ’<color-name>’
   set palette defined ( 0 "#ffffff", 1 "#000000") # ’#rrggbb’
Gnuplot linear gray gradient


# Approximate the default palette used by MATLAB:
set pal defined (1 '#00008f', 8 '#0000ff', 24 '#00ffff', 40 '#ffff00', 56 '#ff0000', 64 '#800000')
Matlab gradient


Dane możemy wprowadzić z

  • linii poleceń
  • z pliku palety pal
 load 'a.pal'


Przykład pliku tekstowego pal: 

# jet.pal with 4 columns
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 )

#  ColorBrewer Accent
# https://github.com/Gnuplotting/gnuplot-palettes/blob/master/accent.pal
# for use with qualitative/categorical data
# provides 8 colors, 4 pale and 4 saturated
# compatible with gnuplot >=4.2
# author: Anna Schneider
# pale green - pale purple - pale orange - pale yellow - blue - magenta - brown - grey
# palette
set palette maxcolors 8
set palette defined (
0 '#7FC97F',\
1 '#BEAED4',\
2 '#FDC086',\
3 '#FFFF99',\
4 '#386CB0',\
5 '#F0027F',\
6 '#BF5B17',\
7 '#666666' )

Zbiory palet:


Sprawdzamy jaki gradient ma aktualna paleta: 

show palette gradient

Otrzymujemy: 


 0. gray=0.0000, (r,g,b)=(1.0000,1.0000,1.0000), #ffffff = 255 255 255
 1. gray=1.0000, (r,g,b)=(0.0000,0.0000,0.0000), #000000 =   0   0   0

References

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  1. ↑ Color_gradient in wikipedia
  2. ↑ /src/command.c
  3. ↑ Poynton's Color FAQ by Charles Poynton
  4. ↑ https://livebook gnuplot-in-action-second-edition by P K Janert
  5. ↑ Luma_(video) w ang wikipedii
  6. ↑ gnuplot 5.0.4 : Special-filenames
  7. ↑ A colour scheme for the display of astronomical intensity images by D. A. Green
  8. ↑ cubehelix-or-how-i-learned-to-love by James Davenport
  9. ↑ gnuplot 5.5 demo pm3dgamma
  10. ↑ gnuplot 5.0.4 : gamma
  11. ↑ gnuplot 4.2 docs: Palette/Functions
  12. ↑ gnuplot-doc : rgbformulae
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