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Making a 3-D RGB color cube

In this example we generate a series of 6 color images, arranged in the shape of a cross, that can be cut out and assembled into a 3-D color cube. The six faces of the cube represent the outside of the R-G-B color space. On each face one of the color components is fixed at either 0 or 255 and the other two components vary smoothly across the face from 0 to 255. The cube is configured as a right-handed coordinate system with x-y-z mapping R-G-B. Hence, the 8 corners of the cube represent the primaries red, green, and blue, plus the secondaries cyan, magenta and yellow, plus black and white.

The method for generating the 6 color faces utilizes $AWK in two steps. First, a z-grid is composed which is 256 by 256 with z-values increasing in a planar fashion from 0 to 65535. This z-grid is common to all six faces. The color variations are generated by creating a different color palette for each face using the supplied $AWK script rgb_cube.awk. This script generates a ``cpt'' file appropriate for each face using arguments for each of the three color components. The arguments specify if that component (r,g,b) is to be held fixed at 0 or 255, is to vary in x, or is to vary in y. If the color is to increase in x or y, a lower case x or y is specified; if the color is to decrease in x or y, an upper case X or Y is used. Here is the shell script and accompanying $AWK script to generate the RGB cube:

    #!/bin/csh
    #        GMT EXAMPLE 11
    #
    #        @(#)job11.csh    1.6  01/22/99
    #
    # Purpose:    Create a 3-D RGB Cube
    # GMT progs:    gmtset, grdimage, grdmath, pstext, psxy
    # Unix progs:    $AWK, rm
    #
    # First create a Plane from (0,0,0) to (255,255,255).
    # Only needs to be done once, and is used on each of the 6 faces of the cube.
    #

    grdmath -I1 -R0/255/0/255 Y 256 MUL X ADD = rgb_cube.grd

    #
    # For each of the 6 faces, create a color palette with one color (r,g,b) fixed
    # at either the min. of 0 or max. of 255, and the other two components
    # varying smoothly across the face from 0 to 255.
    #
    # This uses $AWK script "rgb_cube.awk", with arguments specifying which color
    # (r,g,b) is held constant at 0 or 255, which color varies in the x-direction
    # of the face, and which color varies in the y-direction.  If the color is to
    # increase in x (y), a lower case x (y) is indicated; if the color is to
    # decrease in the x (y) direction, an upper case X (Y) is used.
    #
    # Use grdimage to paint the faces and psxy to add "cut-along-the-dotted" lines.
    #

    gmtset TICK_LENGTH 0

    pstext -R0/8/0/11 -Jx1i < /dev/null -P -U"Example 11 in Cookbook" -K >! example_11.ps
    $AWK -f rgb_cube.awk r=x g=y b=255 < /dev/null >! rgb_cube.cpt
    grdimage rgb_cube.grd -Crgb_cube.cpt -JX2.5i/2.5i -R0/255/0/255 -K -O -X2i -Y4.5i -B256wesn \
       >> example_11.ps

    $AWK -f rgb_cube.awk r=255 g=y b=X < /dev/null >! rgb_cube.cpt
    grdimage rgb_cube.grd -Crgb_cube.cpt -JX -K -O -X2.5i -B256wesn >> example_11.ps

    $AWK -f rgb_cube.awk r=x g=255 b=Y < /dev/null >! rgb_cube.cpt
    grdimage rgb_cube.grd -Crgb_cube.cpt -JX -K -O -X-2.5i -Y2.5i -B256wesn >> example_11.ps

    psxy -W0.25pto -JX -R -K -O -X2.5i << END >> example_11.ps
    0 0
    20 20
    20 235
    0 255
    END

    psxy -W0.25pto -JX -R -K -O -X-2.5i -Y2.5i << END >> example_11.ps
    0 0
    20 20
    235 20
    255 0
    END

    psxy -W0.25pto -JX -R -K -O -X-2.5i -Y-2.5i << END >> example_11.ps
    255 0
    235 20
    235 235
    255 255
    END

    $AWK -f rgb_cube.awk r=0 g=y b=x < /dev/null >! rgb_cube.cpt
    grdimage rgb_cube.grd -Crgb_cube.cpt -JX -K -O -Y-2.5i -B256wesn >> example_11.ps

    $AWK -f rgb_cube.awk r=x g=0 b=y < /dev/null >! rgb_cube.cpt
    grdimage rgb_cube.grd -Crgb_cube.cpt -JX -K -O -X2.5i -Y-2.5i -B256wesn >> example_11.ps

    pstext -JX -R -G255 -K -O << END >> example_11.ps
    10 10 14 0 -Times-BoldItalic 1 GMT 3
    END

    psxy -W0.25pto -JX -R -K -O -X2.5i << END >> example_11.ps
    0 0
    20 20
    20 235
    0 255
    END

    psxy -W0.25pto -JX -R -K -O -X-5i << END >> example_11.ps
    255 0
    235 20
    235 235
    255 255
    END

    $AWK -f rgb_cube.awk r=x g=Y b=0 < /dev/null >! rgb_cube.cpt
    grdimage rgb_cube.grd -Crgb_cube.cpt -JX -K -O -X2.5i -Y-2.5i -B256wesn >> example_11.ps

    psxy -W0.25pto -JX -R -K -O -X2.5i << END >> example_11.ps
    0 0
    20 20
    20 235
    0 255
    END

    psxy -W0.25pto -JX -R -O -X-5i << END >> example_11.ps
    255 0
    235 20
    235 235
    255 255
    END

    \rm -f rgb_cube.cpt rgb_cube.grd .gmtcommands

The $AWK script rgb_cube.awk is as follows:

    #    @(#)rgb_cube.awk    1.1  09/21/98
    END{
      z=-.5;

      if(r=="X" || g=="X" || b=="X"){
        xl=255; xr=0; xd=-255;
      }else{
        xl=0; xr=255; xd=255;
      }

      if(r=="Y" || g=="Y" || b=="Y"){
        yb=255; yt=-1; yd=-1;
      }else{
        yb=0; yt=256; yd=1;
      }

      for(y=yb; y!=yt; y+=yd){

        x=xl;

        if(r=="x" || r=="X"){
          if(g=="y" || g=="Y"){
        printf("%7.1f %3d %3d %3d " ,z,x,y,b);
        x+=xd; z+=256;
        printf("%7.1f %3d %3d %3d\n",z,x,y,b);
          }else{
        printf("%7.1f %3d %3d %3d " ,z,x,g,y);
        x+=xd; z+=256;
        printf("%7.1f %3d %3d %3d\n",z,x,g,y);
          }

        }else if(g=="x" || g=="X"){
          if(r=="y" || r=="Y"){
        printf("%7.1f %3d %3d %3d " ,z,y,x,b);
        x+=xd; z+=256;
        printf("%7.1f %3d %3d %3d\n",z,y,x,b);
          }else{
        printf("%7.1f %3d %3d %3d " ,z,r,x,y);
        x+=xd; z+=256;
        printf("%7.1f %3d %3d %3d\n",z,r,x,y);
          }

        }else{
          if(r=="y" || r=="Y"){
        printf("%7.1f %3d %3d %3d " ,z,y,g,x);
        x+=xd; z+=256;
        printf("%7.1f %3d %3d %3d\n",z,y,g,x);
          }else{
        printf("%7.1f %3d %3d %3d " ,z,r,y,x);
        x+=xd; z+=256;
        printf("%7.1f %3d %3d %3d\n",z,r,y,x);
          }
        }
      }
      exit;
    }

The cube can be viewed in Figure 6.11

Figure 6.11: The color cube

Next: Optimal triangulation of data Up: Cook-book Previous: A geographical bar graph