Algorithm to convert any positive integer to an RGB value

Question

We have a heatmap we want to display. The numbers that will make up the values being displayed are unknown (except that they will be positive integers). The range of numbers is also unknown (again, except that they will be posiitive integars). The range could be between 0 and 200 or 578 and 1M or whatever. It depends on the data, which is unknown.

We want to take an unknown range of positive integers and turn it into a scaled (compressed) range to be displayed with RGB values in a heatmap. I hope this makes sense. Thanks!

I want to clarify that the min/max values need to be "plugged" into the forumla.

Answer 1

You need to first find the range of those values to get the min and max. Then you need to create a colour scale like the bar below this image. You can experiment with different functions to map an integer to an RGB. You need 3 functions R(X), G(X), B(X). Looking at the image below it loks like B(X) peaks in the middle, R(X) peaks at the end and green is somewhere else. As long as you make sure that you never get two (RGBs) for some value of X then you've got your conversion.

EDIT: Come to think of it you could sample some unit circle around YUV space.

Or even just download a high-res colour bar and sample that.

Answer 2

Without knowing the range of values, there isn't much you can do to come up with a meaningful function mapping an arbitrary range of positive integers to a heat-map type range of colors.

I think you're going to have to run through your data at least once to get the min/max or know them ahead of time. Once you have that you can normalize appropriately and use any number of color schemes. The simplest solution would be to specify something like "hue" and convert from HSV to RGB.

Answer 3

Simple algorithm

// given a max and min value
float red,green,blue;
float range=max-min;
float mid=(max+min)/2.0;

//foreach value
    red = (value[ii]-mid)/range;            
    if (red>0.0) {
        //above mid = red-green
        blue=0.0;
        green = 1.0-red;
    } else {
        // lower half green-blue
        blue=-red;
        green = 1.0-blue;
        red=0.0;
    }

}

More complex:
If your range is a few million but most are around 0 you want to scale it so that 'red' in the above example is the log of the distance from the midpoint. The cod eis a little more complicated if the values are +/-

// assume equally distributed around 0 so max is the largest (or most negative number)
float range = log(fabs(max));
float mid=0.0

// foreach value
if (value[ii] > 0.0 ) {
    // above mid = red-green
    red = log(value[ii])/range;
    blue=0.0;
    green = 1.0 - red;
} else {
    // below mid = green-blue
    blue=-log(value[ii])/range;
    green = 1.0 - blue;
   red = 0.0;
}

note - I haven't tested this code, just spinning ideas!

Answer 4

man, you could probably use YUV color space and only for demonstration purposes convert it to RGB.

Answer 5

You want to convert your data values to a frequency of light:

• lower wavelength = cooler colors = blueish
• higher wavelength = warmer colors = redder

The frequencies of visible light go from about 350nm (violet) to 650nm (red):

The following function converts numbers in your specified range to the the range of visible light, then gets the rgb:

function DataPointToColor(Value, MinValue, MaxValue: Real): TColor;
var
   r, g, b: Byte;
   WaveLength: Real;
begin
   WaveLength := GetWaveLengthFromDataPoint(Value, MinValue, MaxValue);
   WavelengthToRGB(Wavelength, r, g, b);
   Result := RGB(r, g, b);
end;

With the function i wrote off the top of my head:

function GetWaveLengthFromDataPoint(Value: Real; MinValues, MaxValues: Real): Real;
const
   MinVisibleWaveLength = 350.0;
   MaxVisibleWaveLength = 650.0;
begin
   //Convert data value in the range of MinValues..MaxValues to the 
   //range 350..650

   Result := (Value - MinValue) / (MaxValues-MinValues) *
         (MaxVisibleWavelength - MinVisibleWavelength) +
         MinVisibleWaveLength;
end;

And a function i found on the internets, that converts a wavelength into RGB:

PROCEDURE WavelengthToRGB(CONST Wavelength:  Nanometers;
                          VAR R,G,B:  BYTE);
  CONST
    Gamma        =   0.80;
    IntensityMax = 255;
  VAR
    Blue   :  DOUBLE;
    factor :  DOUBLE;
    Green  :  DOUBLE;
    Red    :  DOUBLE;
  FUNCTION Adjust(CONST Color, Factor:  DOUBLE):  INTEGER;
  BEGIN
    IF   Color = 0.0
    THEN RESULT := 0     // Don't want 0^x = 1 for x <> 0
    ELSE RESULT := ROUND(IntensityMax * Power(Color * Factor, Gamma))
  END {Adjust};
BEGIN
  CASE TRUNC(Wavelength) OF
    380..439:
      BEGIN
        Red   := -(Wavelength - 440) / (440 - 380);
        Green := 0.0;
        Blue  := 1.0
      END;
    440..489:
      BEGIN
        Red   := 0.0;
        Green := (Wavelength - 440) / (490 - 440);
        Blue  := 1.0
      END;
    490..509:
      BEGIN
        Red   := 0.0;
        Green := 1.0;
        Blue  := -(Wavelength - 510) / (510 - 490)
      END;
    510..579:
      BEGIN
        Red   := (Wavelength - 510) / (580 - 510);
        Green := 1.0;
        Blue  := 0.0
      END;
    580..644:
      BEGIN
        Red   := 1.0;
        Green := -(Wavelength - 645) / (645 - 580);
        Blue  := 0.0
      END;
    645..780:
      BEGIN
        Red   := 1.0;
        Green := 0.0;
        Blue  := 0.0
      END;
    ELSE
      Red   := 0.0;
      Green := 0.0;
      Blue  := 0.0
  END;
  // Let the intensity fall off near the vision limits
  CASE TRUNC(Wavelength) OF
    380..419:  factor := 0.3 + 0.7*(Wavelength - 380) / (420 - 380);
    420..700:  factor := 1.0;
    701..780:  factor := 0.3 + 0.7*(780 - Wavelength) / (780 - 700)
    ELSE       factor := 0.0
  END;
  R := Adjust(Red,   Factor);
  G := Adjust(Green, Factor);
  B := Adjust(Blue,  Factor)
END {WavelengthToRGB}; 

Sample use:

Data set in the range of 10..65,000,000. And this particular data point has a value of 638,328:

color = DataPointToColor(638328, 10, 65000000);