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

Answer 1

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):

_{(source: gamonline.com)}

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);