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

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

Answer 2

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);

Answer 3

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 4

A little late, but I was trying to do the same and found I can modify HSV to RGB to get a similar result. It's similar to the wavelength approach but by passes the need to convert to wavelength first. Just substitute H with your value (assuming a value between 0 and 1), and fix S and V to 1. I found the HSVtoRGB example here to be very helpful:

http://www.cs.rit.edu/~ncs/color/t_convert.html

However, I had to change the lines

h /= 60;
i = floor ( h );

to

h *= 5;
i = (int) h;

to get an output that goes through the whole spectrum.

Additional resource: http://www.easyrgb.com/index.php?X=MATH&H=21#text21