Copyright © 1993, Dr. Dobb's Journal

Copyright © 1993, Dr. Dobb's Journal

Copyright © 1993, Dr. Dobb's Journal

Copyright © 1993, Dr. Dobb's Journal

Copyright © 1993, Dr. Dobb's Journal

Copyright © 1993, Dr. Dobb's Journal

Copyright © 1993, Dr. Dobb's Journal

Bruce Schneier

What's so great about red, green, and blue? Why not orange, yellow, and violet? Or, for that matter, why not turquoise, ochre, and periwinkle? Why not two colors? Or four?

The answers to these questions involve the human eye. Our perception of color begins when light passes through visual pigments in the retinal cones. There are three pigments-red, green, and blue-that are optimally perceived at wavelengths of approximately 580, 545, and 440 nanometers, respectively.

In 1931, the Comission Internationale de l'Eclairage, or CIE (also known as the International Commission on Illumination) established a color standard, deciding that all colors should be defined in terms of three principal colors: red, green, and blue (RGB). The standard was first used in color television, and eventually in computers. Not every color can be reproduced with this red/green/blue color model (or any other color model for that matter) but it suffices. More colors could be added, but the payoff would not be worth the extra bits. RGB is here to stay.

Still, RGB isn't the only game in town. There are several other color models, each with its strengths and weaknesses. Among those discussed in this article are CMY, HSV, HLS, and YIQ. Additionally, there's the HVC model, described in the text box "Putting Colors in Order." But let's start by reviewing RGB.

Computer monitors are additive, but color printers are generally subtractive. Instead of combining light from phosphors, printers coat paper with colored pigments. The eye sees colors by reflected light, which is a subtractive process.

Cyan, magenta, and yellow (CMY) are the complements of red, green, and blue. For example, cyan is everything that isn't red. When white light is reflected off cyan-colored ink, the red light is absorbed, or subtracted, and the reflected light has no red component. To get the color red, you have to deposit magenta (which absorbs green) and yellow (which absorbs blue), leaving only red light to be reflected into the human eyeball.

The CMY cube is the opposite of the RGB cube. White is (0,0,0) and black is (1,1,1). Cyan is (1,0,0), magenta is (0,1,0), green is (1,0,1), and so on.

Converting from RGB to CMY is easy:

C=1-R

M=1-G

Y=1-B

Many printers use a four-color process by adding black because in real life the combination of CMY pigments produces something more akin to gray than black. The CMYK color model, for cyan-magenta-yellow-black, is defined as:

K=minimum (C,M,Y)

C=C-K

M=M-K

Y=Y-K

Red, green, and blue may be how the human eye perceives light, but it isn't the way the human mind perceives color. Instead, we see the color, or hue, which is the frequency of the light. We see the luminance, or brightness, which is a measure of the intensity of the light. The higher the intensity of the light, the brighter it appears. We also see the saturation, or purity, of the light. Bold primaries are very pure. Pastels are not.

YIQ is the color model used for U.S. commercial television. It was designed to be backwards-compatible with black-and-white TV sets, and thus may seem a bit odd. Y stands for luminance, or brightness-the only variable that black-and-white television sets display. (Note that this Y is slightly different from the V in the HSV color model and the L in the HLS model.) I and Q contain color information, and are called the "chromaticity." You can convert from RGB to YIQ using the following formulas:

Y=030*R+0.59*G+0.11*B

I=060*R-0.28*G-0.32*B

Q=021*R-0.53*G+0.31*B

These equations assume the standard RGB NTSC phosphor, whose CIE numbers are exactly defined. If you're finicky enough about the particular characteristics of your monitor for this to make a difference, consult Computer Graphics: Principles and Practice, second edition by Foley, van Dam, et al. (Addison-Wesley, 1992) or another good graphics text.

It is interesting to note that according to the first equation of the RGB-to-YIQ set, green is much more important in determining luminosity than blue. In fact, the human eye is far less sensitive to blue light than it is to red or green light. That's why in 8-bit color RGB models, three bits each are used to store the red and green values, while only two bits are used to store the blue value.

Harry is an engineer specializing in satellite-telemetry data processing. He can be reached at 19628 Via Monte Drive, Saratoga, CA 95070.

In any software or hardware interface to a color display, there must be a way of specifying the various colors that can be displayed. However, specifying many colors (say 64, 256, or 256,000) in an orderly, understandable fashion can become a significant problem. This article discusses a method of converting an RGB (red, green, and blue) specification to another color specification-HVC (hue, value, and chroma). HVC has an advantage over RGB, in that colors can be ordered by dominant frequency (hue), luminance (value), and the amount of color (chroma).

 (a)   R = V - C cos(H + 120 degrees)
       G = V - C cos(H)
       B = V - C cos(H - 120 degrees)

 (b)   H = atan2( R - B, (sqrt(3) / 3)(R - 2G + B))
       V = (R + G + B) / 3
       C = (R - 2G + B) / (3 cos(H)
       or
       C = (R - B) / (sqrt(3) sin(H))

 (c)   V = (R + G + B) / 3
       H = atan2(R - B, sqrt(3)(V - G))
       C = (V - G) / cos(H)               if |cos(H)| > 0.2
       C = (R - B) / (sqrt(3) sin(H))      if |cos(H)| <= 0.2

 (d)   V = (1.0 + 0.25 + 0.75) / 3 = 0.6667
       H = atan2(0.25, sqrt(3)(0.4167)) = 19.1066 degrees
       C = 0.4167 / cos(19.1066 degrees) = 0.4410

{---- RGB -> HLS by Bruce Schneier ----}
procedure RGB_to_HLS (r,g,b : real; var h,l,s, : real)
   var min, max, delta : real;
   begin
      max := maximum(r,g,b);
      min := minimum(r,g,b);
      l := (max + min)/2;
      if max = min
         then begin s:= 0; h := UNDEFINED end
         else
            begin
               if l <= 0.5
                  then s := (max - min)/(max + min)

                  else s := (max - min)/(2 - max - min);
               delta := max - min;
               if r = max then h := (g - b)/delta
               else if g = max then h := 2 + (b - r)/delta
               else if b = max then h := 4 + (r - g)/delta;
               h := h*60;
               if h<0 then h := h + 360
            end
   end;
procedure HLS_to_RGB (h,l,s : real; var r,g,b : real)
   var m,n : real;
   int function value (a,b,hue : real)
      begin
         if hue > 360 then hue := hue - 360
         else if hue < 0 then hue := hue + 360;
         if hue < 60 then value := a + (b-a) * hue/60
         else if hue < 180 then value := b
         else if hue < 240 then value := a + (b - a)*(240-hue)/60
         else value := a
      end
   begin
      if l <= 0.5
         then n := l * (l + s)
         else n := l + s + l * s;
      m := 2 * l - n;
      if s = 0
         then begin r := l; g := l; b := l end
         else
            begin
               r := value (m,n,h+120);
               g := value (m,n,h);
               b := value (m,n,h-120)
           end
   end;

{---- HVC -> RGB  by Harry Smith ----}

procedure Hvc2Rgb( H, V, C : Double; var R, G, B : Double);
  { Converts H-hue, V-value, C-chroma to R-red, G-green, B-blue }
const
  Pi    = 3.14159265358979324;
  Pi2o3 = 2.0 * Pi / 3.0;
  DpR   = 180.0 / Pi;          { Degrees per Radian }
var
  HRad : Double;
begin
  HRad:= H / DpR;
  R:= V - C * Cos( HRad + Pi2o3);
  G:= V - C * Cos( HRad);
  B:= V - C * Cos( HRad - Pi2o3);
end; { Hvc2Rgb }

{----  RGB -> HVC by Harry Smith ----}
function ATan2( Y, X : Double) : Double;
  { Arc Tangent of Y over X }
  { -Pi < ATan2 <= Pi }
const
  Pi   = 3.14159265358979324;
  Pio2 = Pi / 2.0;
var
  Temp : Double;
begin
  if X = 0 then begin
    if Y > 0 then  ATan2:= Pio2
    else if Y < 0 then  ATan2:= -Pio2
    else  ATan2:= 0;
  end
  else begin
    Temp:= ArcTan( Y / X);
    if X > 0 then  ATan2:= Temp
    else if Y >= 0 then  ATan2:= Temp + Pi
    else  ATan2:= Temp - Pi;
  end;
end; { ATan2 }
{--------------------------------------}
procedure Rgb2Hvc( R, G, B : Double; var H, V, C : Double);
  { Converts R-red, G-green B-blue, to H-hue, V-value, C-chroma }
const
  Pi    = 3.14159265358979324;
  Pi2   = 2.0 * Pi;
  DpR   = 180.0 / Pi;          { Degrees per Radian }
  SqRt3 = 1.73205080756887719; { Square root of 3.0 }
var
  CosHue : Double;
  HRad   : Double;
begin
  V:= (R + G + B) / 3.0;
  HRad:= ATan2( R - B, SqRt3 * (V - G));
  CosHue:= Cos( HRad);
  if abs( CosHue) > 0.2 then
    C:= (V - G) / CosHue
  else
    C:= (R - B) / (SqRt3 * Sin( HRad));
  H:= HRad * DpR;
  if H < 0.0 then  H:= H + 360.0;
end; { Rgb2Hvc }
End Listings

Copyright © 1993, Dr. Dobb's Journal