1 COLOUR INTRODUCTION 1

1. Introduction.
COLOUR
Colour System Library
John Walker
This program is in the public domain.
This program provides tools for representing colours, interconverting colour spaces, and transforming
physical denitions of colour (for example, spectra or black body emission) into perceptual colour metrics
such as the CIE tristimulus values, and thence to computer approximations such as RGB values for various
phosphors.
This program is not presently used by the analysis suite; it is only exercised by its own
built-in test program. It is provided as part of the eventual goal of supporting internal
plotting without the need to invoke GNUPLOT, and also facilitate visual presentation of
data in the form of colour (for example, one might wish to express a z score as a colour
representing how hot it was, expressing z as a black body temperature).
References
Hunt, R.W.G. Measuring Colour. West Sussex England: Ellis Horwood Ltd., 1987. (Distributed in the U.S.
by John Wiley Sons). ISBN 0-470-20986-0.
Adobe Systems, Inc. PostScript Language Reference Manual, 3rd ed. Reading Massachusetts: Addison-
Wesley, 1999. ISBN 0-201-37922-8.
Rossotti, Hazel. Colour: Why the World Isnt Grey. Princeton: Princeton University Press, 1983. ISBN 0-
691-02386-7.
Judd, Deane B. and G unter Wyszecki. Color in Business, Science, and Industry. New York: John Wiley
Sons, 1975.
Arvo, James ed. Graphics Gems II. San Diego: Academic Press, Inc., 1991, section III.6, Television Color
Encoding. ISBN 0-12-064480-0.
Foley, J.D., A. van Dam, S.K. Feiner, and J.F. Hughes. Computer Graphics: Principles and Practice, 2nd
ed. in C. Reading Massachusetts: Addison-Wesley, 1996. ISBN 0-201-84840-6.
Pantone, Inc. PANTONE Process Color Imaging Guide. Moonachie NJ: Pantone, Inc., 1990.
colour_test.c 1 )
#dene REVDATE "1stFebruary2002"
See also section 40.
2 PROGRAM GLOBAL CONTEXT COLOUR 2
2. Program global context.
#include "config.h" / System-dependent conguration /
Preprocessor denitions )
Application include les 4 )
Colour system data tables 37 )
Class implementations 5 )
3. We export the class denitions for this package in the external le colour.h that programs which use
this library may include.
colour.h 3 )
#ifndef COLOUR_HEADER_DEFINES
#dene COLOUR_HEADER_DEFINES
#include <math.h> / Make sure math.h is available /
#include <iostream>
#include <exception>
#include <stdexcept>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;
#include "bitmap.h"
#include <stdio.h> / Needed to dene FILE for gifout.h /
#include "gifout.h"
#include "graphics.h"
#include "pstampr.h"
#include "psrtext.h"
Class denitions 6 )
#endif
4. The following include les provide access to external components of the program not dened herein.
Application include les 4 )
#include "colour.h" / Class denitions for this package /
This code is used in section 2.
5. The following classes are dened and their implementations provided.
Class implementations 5 )
Colour systems 17 )
This code is used in section 2.
6 COLOUR COLOUR SYSTEM PARENT CLASS: CSCOLOUR 3
6. Colour system parent class: csColour.
This is the parent class of all colour classes.
Class denitions 6 )
class csColour
public:
virtual string colourSystemName(void) = 0; / Return colour system name /
virtual void writeParameters (ostream &of )
/ Write description of colour system to output stream /
of "Coloursystem:" colourSystemName( ) "\n";

;
See also sections 7, 8, 9, 10, 11, 12, and 33.
This code is used in section 3.
4 SPECTRAL COLOUR SYSTEMS PARENT CLASS: CSSPECTRALCOLOUR COLOUR 7
7. Spectral colour systems parent class: csSpectralColour.
The most general of all our notions of colour is that of an function that maps wavelengths (given in metres)
onto intensities. This form allows specication of any radiation in the electromagnetic spectrum. Intensities
are normalised to the range zero to one by dividing the intensity for a given frequency by the integrated
intensity over the entire electromagnetic spectrum.
Class denitions 6 ) +
class csSpectralColour : public csColour
public: / Return normalised intensity for a given wavelength in metres /
virtual double getIntensity(double waveLength) = 0;
/ Return true if this is a pure (monochromatic) radiator, false / / otherwise. /
virtual bool isMonochromatic(void) = 0;
;
8 COLOUR MONOCHROMATIC SPECTRAL COLOUR SYSTEMS: CSMONOCHROMATICCOLOUR 5
8. Monochromatic spectral colour systems: csMonochromaticColour.
A monochromatic colour is a abstract notion of a source which radiates all its intensity at a single
wavelength. These dont really exist in the real world, since fundamental quantum processes will always
spread the spectrum of any real radiator.
Class denitions 6 ) +
class csMonochromaticColour : public csSpectralColour
private:
double wavelength;
public:
virtual string colourSystemName(void)

return "monochromaticspectral";

double getIntensity(double waveLength)

return (waveLength wavelength) ? 1.0 : 0.0;

bool isMonochromatic(void)

return true;
/ Constructors and destructors /
csMonochromaticColour(void)

wavelength = 0.0;

csMonochromaticColour(double waveLength)

wavelength = waveLength;
/ Class-specic methods /
void setWavelength(double waveLength)

wavelength = waveLength;

double getWavelength(void)

return wavelength;

void writeParameters (ostream &of )

csSpectralColour :: writeParameters (of );

of "Wavelength=" getWavelength( ) "\n";

;
6 BLACK: CSSPECTRALBLACK COLOUR 9
9. Black: csSpectralBlack. Black is the absence of colour. We dene it as a spectral colour with zero
intensity at any wavelength.
Class denitions 6 ) +
class csSpectralBlack : public csSpectralColour
public:
virtual string colourSystemName(void)

return "blackspectral";

double getIntensity(double waveLength)

return 0.0;

bool isMonochromatic(void)

return false;

;
10. White: csSpectralWhite. A theoretical source of white noise has equal power at all wavelengths.
Such a source is impossible in reality since the energy ux would be innite.
Class denitions 6 ) +
class csSpectralWhite : public csSpectralColour
public:
virtual string colourSystemName(void)

return "whitespectral";

double getIntensity(double waveLength)

return 1.0;

bool isMonochromatic(void)

return false;

;
11 COLOUR PLANCKIAN BLACK BODY: CSBLACKBODY 7
11. Planckian black body: csBlackBody. Dene the colour of a Planckian black body radiator with
a given colour temperature.
Class denitions 6 ) +
class csBlackBody : public csSpectralColour
private: / Change temperature to class with system conversions /
double temperature; / Temperature of radiator (

K) /
public:
double getIntensity(double waveLength)

return 0.0;

bool isMonochromatic(void)

return false;
/ Constructors and destructors /
csBlackBody(void)

temperature = 0.0;

csBlackBody(double temp)

temperature = temp;
/ Class-specic methods /
void setTemperature(double temp)

temperature = temp;

double getTemperature(void)

return temperature;

double totalFlux (void) / Total energy ux in W/m

2
/
/ Total energy ux in Watts per square metre of a black body with temperature T (degrees
Kelvin) is given by:
C
s
T
4
where C
s
is the Stefan-Boltzman constant:
5.67051 10
8
W/(m
2
K
4
)
which, in fundamental terms is:
(
2
k
4
)/(60(h/(2))
3
c
2
)
/
return 5.67051 10
8
(temperature temperature temperature temperature);

double ux (double wl ) / Energy ux at a given wavelength /

/ Energy ux from a black body with temperature T (degrees Kelvin), in Watts per square
metre at wavelength (metres) is given by:
M
e
= C
1

5
(e
C
2
/(T)
1)
1
8 PLANCKIAN BLACK BODY: CSBLACKBODY COLOUR 11
where:
C
1
= 3.74183e 16Wm
2
C
2
= 1.4388e 2m

K
/
return 3.74183 10
16
/((wl wl wl wl wl ) (exp(1.4388 10
2
/(wl temperature)) 1));

void writeParameters (ostream &of )

csSpectralColour :: writeParameters (of );

of "Temperature=" getTemperature( ) "K\n";

;
12 COLOUR DEVICE COLOUR SYSTEMS PARENT CLASS: CSDEVICECOLOUR 9
12. Device colour systems parent class: csDeviceColour. This class is the parent of all classes
which specify colour in a device-specic way, assuming a particular set of illuminants which are summed to
form the colour.
Class denitions 6 ) +
class csDeviceColour : public csColour
public:
Device colour fundamental methods 13 )
Device colour derived methods 14 )
Device colour system conversion utilities 15 )
;
13. The following three must-implement methods allow retrieving the colour in any of the three fun-
damental device colour spaces: RGB (additive), CMYK (subtractive), or Greyscale. Typically, a specic
device colour class will store the colour in one of these forms and implement the other retrieval methods by
converting the colour representation to that form.
Device colour fundamental methods 13 )
virtual void asRGB(double &r, double &g, double &b) = 0;
virtual void asCMYK(double &c, double &m, double &y, double &k) = 0;
virtual void asGreyScale(double &g) = 0;
This code is used in section 12.
14. The following methods allow retrieval of a device colour in other colour mapping spaces. The
csDeviceColour class implements methods for these functions which provide default denitions which
use the subclass asRGB method to obtain RGB components which are the converted into the requested
colour space.
Device colour derived methods 14 )
virtual void asHSV (double &h, double &s, double &v);
virtual void asHLS (double &h, double &l, double &s);
virtual void asYIQ(double &y, double &i, double &q);
virtual void asYUV (double &y, double &u, double &v);
virtual void asSMPTE(double &y, double &Pb, double &Pr );
virtual void asCMY (double &c, double &m, double &y);
This code is used in section 12.
10 DEVICE COLOUR SYSTEMS PARENT CLASS: CSDEVICECOLOUR COLOUR 15
15. The following static methods of the csDeviceColour class provide interconversions of common
colour systems using the convention that colour components c are double values 0 c 1.
Device colour system conversion utilities 15 )
protected:
static double hlsval (double n1 , double n2 , double hue);
public:
static void hsv rgb(double h, double s, double v, double r, double g, double b);
/ HSV RGB /
static void rgb hsv (double r, double g, double b, double h, double s, double v);
/ RGB HSV /
static void rgb hls (double r, double g, double b, double h, double l, double s);
/ RGB HLS /
static void hls rgb(double h, double l, double s, double r, double g, double b);
/ HLS RGB /
static void rgb yiq (double r, double g, double b, double y, double i, double q);
/ RGB YIQ /
static void yiq rgb(double y, double i, double q, double r, double g, double b);
/ YIQ RGB /
static void rgb yuv (double r, double g, double b, double y, double u, double v);
/ RGB YUV /
static void yuv rgb(double y, double u, double v, double r, double g, double b);
/ YUV RGB /
static void rgb smpte 204M (double r, double g, double b, double y, double Pb, double Pr );
/ RGB SMPTE 204M /
static void smpte 204M rgb(double y, double Pb, double Pr , double r, double g, double b);
/ SMPTE 204M RGB /
static void rgb cmy(double r, double g, double b, double c, double m, double y);
/ RGB CMY /
static void cmy rgb(double c, double m, double y, double r, double g, double b);
/ CMY RGB /
static void cmy cmyk (double c, double m, double y, double oc, double om, double oy, double
ok ); / CMY CMYK /
static void cmyk cmy(double c, double m, double y, double k, double oc, double om, double
oy); / CMYK CMY /
This code is used in section 12.
16. Colour system conversion utilities. The following static methods of the csDeviceColour class
implement interconversions of common colour systems using the convention that colour components c are
double values 0 c 1.
17 COLOUR COLOUR SYSTEM CONVERSION UTILITIES 11
17. HSV_RGB: Convert HSV colour specication to RGB intensities. Hue (h) is specied as a double
value from 0 to 360

, Saturation (s) and Intensity (v) as doubles from 0 to 1. The (r, g, b) components are
returned as doubles from 0 to 1.
Colour systems 17 )
void csDeviceColour :: hsv rgb(double h, double s, double v, double r, double g, double b)

int i;
double f, p, q, t;
if (s 0)
r = g = b = v;

else
if (h 360.0) h = 0;
h /= 60.0;
i = (int) h;
f = h i;
p = v (1.0 s);
q = v (1.0 (s f));
t = v (1.0 (s (1.0 f)));
assert (i 0 i 5);
switch (i)
case 0: r = v;
g = t;
b = p;
break;
case 1: r = q;
g = v;
b = p;
break;
case 2: r = p;
g = v;
b = t;
break;
case 3: r = p;
g = q;
b = v;
break;
case 4: r = t;
g = p;
b = v;
break;
case 5: r = v;
g = p;
b = q;
break;

See also sections 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, and 36.
This code is used in section 5.
12 COLOUR SYSTEM CONVERSION UTILITIES COLOUR 18
18. RGB_HSV: Map r, g, b intensities in the range from 0 to 1 into Hue (h), Saturation (s), and Value (v):
Hue from 0 to 360

, Saturation from 0 to 1, and Value from 0 to 1. Special case: if Saturation is 0 (its a

grey scale tone), Hue is undened and is returned as -1.
This follows Foley et al., section 13.3.4.
Colour systems 17 ) +
void csDeviceColour :: rgb hsv (double r, double g, double b, double h, double s, double v)

double imax = max (r, max (g, b)), imin = min(r, min(g, b)), rc, gc, bc;
v = imax ;
if (imax ,= 0) s = (imax imin)/imax ;
else s = 0;
if (s 0)
h = 1;

else
rc = (imax r)/(imax imin);
gc = (imax g)/(imax imin);
bc = (imax b)/(imax imin);
if (r imax ) h = bc gc;
else if (g imax ) h = 2.0 + rc bc;
else h = 4.0 + gc rc;
h = 60.0;
if (h < 0.0) h += 360.0;

19 COLOUR COLOUR SYSTEM CONVERSION UTILITIES 13

19. RGB_HLS: Map r, g, b intensities in the range from 0 to 1 into Hue (h), Lightness (l), and Saturation
(s): Hue from 0 to 360

, Lightness from 0 to 1, and Saturation from 0 to 1. Special case: if Saturation is 0

(its a grey scale tone), Hue is undened and is returned as -1.
This follows Foley et al., section 13.3.5.
Colour systems 17 ) +
void csDeviceColour :: rgb hls (double r, double g, double b, double h, double l, double s)

double imax = max (r, max (g, b)), imin = min(r, min(g, b)), rc, gc, bc;
l = (imax + imin)/2;
if (imax imin)
s = 0;
h = 1;

else
if (l 0.5) s = (imax imin)/(imax + imin);
else s = (imax imin)/(2.0 imax imin);
rc = (imax r)/(imax imin);
gc = (imax g)/(imax imin);
bc = (imax b)/(imax imin);
if (r imax ) h = bc gc;
else if (g imax ) h = 2.0 + rc bc;
else h = 4.0 + gc rc;
h = 60.0;
if (h < 0) h += 360.0;

14 COLOUR SYSTEM CONVERSION UTILITIES COLOUR 20

20. HLS_RGB: Convert HLS colour specication to r, g, b intensities. Hue (h) is specied as a double
value from 0 to 360

; Lightness (l) and Saturation (s) as doubles from 0 to 1. The RGB components are
returned as doubles from 0 to 1.
Colour systems 17 ) +
double csDeviceColour :: hlsval (double n1 , double n2 , double hue)

if (hue > 360.0) hue = 360.0;

else if (hue < 0.0) hue += 360.0;
if (hue < 60.0)
return n1 + ((n2 n1 ) hue)/60.0;

else if (hue < 180.0)

return n2 ;

else if (hue < 240.0)

return n1 + ((n2 n1 ) (240.0 hue))/60.0;

else
return n1 ;

void csDeviceColour :: hls rgb(double h, double l, double s, double r, double g, double b)

double m1 , m2 ;
if (l 0.5) m2 = l (1.0 +s);
else m2 = l +s (l s);
m1 = 2 l m2 ;
if (s 0)
r = g = b = l;

else
r = hlsval (m1 , m2 , h + 120.0);
g = hlsval (m1 , m2 , h);
b = hlsval (m1 , m2 , h 120.0);

21 COLOUR COLOUR SYSTEM CONVERSION UTILITIES 15

21. RGB_YIQ Convert RGB colour specication, r, g, b ranging from 0 to 1, to Y, I, Q colour specication.
YIQ is the encoding used in NTSC television.

Y
I
Q

0.2989 0.5866 0.1144

0.5959 0.2741 0.3218
0.2113 0.5227 0.3113

R
G
B

Colour systems 17 ) +
void csDeviceColour :: rgb yiq (double r, double g, double b, double y, double i, double q)

double ay = (r 0.2989 + g 0.5866 + b 0.1144), ai = (r 0.5959 + g 0.2741 + b 0.3218),

aq = (r 0.2113 +g 0.5227 +b 0.3113);
y = ay;
if (ay 1.0) / Prevent round-o on grey scale /
ai = aq = 0.0;

i = ai ;
q = aq ;

22. YIQ_RGB: Convert YIQ colour specication, Y, I, Q given as doubles: 0 Y 1, 0.6 I 0.6,
0.52 Q 0.52, to R, G, B intensities in the range from 0 to 1. The matrix below is the inverse of the
RGB_YIQ matrix above. YIQ is the encoding used in NTSC television.

R
G
B

1.0000 0.9562 0.6210

1.0000 0.2717 0.6485
1.0000 1.1053 1.7020

Y
I
Q

Colour systems 17 ) +
void csDeviceColour :: yiq rgb(double y, double i, double q, double r, double g, double b)

double ar = (y + i 0.9562 + q 0.6210), ag = (y + i 0.2717 + q 0.6485),

ab = (y +i 1.1053 +q 1.7020);
r = max (0.0, min(1.0, ar ));
g = max (0.0, min(1.0, ag ));
b = max (0.0, min(1.0, ab));

16 COLOUR SYSTEM CONVERSION UTILITIES COLOUR 23

23. RGB_YUV: Convert RGB colour specication, R, G, B ranging from 0 to 1, to Y, U, V colour specica-
tion. YUV is the encoding used by PAL television.

Y
U
V

0.2989 0.5866 0.1144

0.1473 0.2717 0.4364
0.6149 0.5145 0.1004

R
G
B

Colour systems 17 ) +
void csDeviceColour :: rgb yuv (double r, double g, double b, double y, double u, double v)

double ay = (r 0.2989 + g 0.5866 + b 0.1144), au = (r 0.1473 + g 0.2891 + b 0.4364),

av = (r 0.6149 +g 0.5145 +b 0.1004);
y = ay;
if (ay 1.0) / Prevent round-o on grey scale /
au = av = 0.0;

u = au;
v = av ;

24. YUV_RGB: Convert YUV colour specication, Y, U, V given as doubles, to R, G, B intensities in the
range from 0 to 1. The matrix below is the inverse of the rgb yuv matrix above. YUV is the encoding used
by PAL television.

R
G
B

1.0000 0.0000 1.1402

1.0000 0.3959 0.5810
1.0000 2.0294 0.0000

Y
U
V

Colour systems 17 ) +
void csDeviceColour :: yuv rgb(double y, double u, double v, double r, double g, double b)

double ar = (y + u 0.0000 + v 1.1402), ag = (y + u 0.3959 + v 0.5810),

ab = (y +u 2.0294 +v 0.0000);
r = max (0.0, min(1.0, ar ));
g = max (0.0, min(1.0, ag ));
b = max (0.0, min(1.0, ab));

25 COLOUR COLOUR SYSTEM CONVERSION UTILITIES 17

25. RGB_SMPTE_204M: Convert RGB colour specication, R, G, B ranging from 0 to 1, to Y, P
b
, P
r
colour specication according to the SMPTE 204M (1988) specication for HDTV using the SMPTE set of
phosphors.

Y
P
b
P
r

0.2122 0.7013 0.0865

0.1162 0.3838 0.5000
0.6149 0.4451 0.0549

R
G
B

Colour systems 17 ) +
void csDeviceColour :: rgb smpte 204M (double r, double g, double b, double y, double
Pb, double Pr )

double ay = (r 0.2122 + g 0.7013 + b 0.0865), aPb = (r 0.1162 + g 0.3838 + b 0.5000),

aPr = (r 0.5000 +g 0.4451 +b 0.0549);
y = ay;
if (ay 1.0) / Prevent round-o on grey scale /
aPb = aPr = 0.0;

Pb = aPb;
Pr = aPr ;

26. SMPTE_204M_RGB: Convert a colour specied using the SMPTE reference phosphors as given in the
SMPTE 204M (1988) specication for HDTV to R, G, B intensities in the range from 0 to 1. The matrix
below is the inverse of the RGB_SMPTE_204M matrix above.

R
G
B

1.0000 0.0000 1.5755

1.0000 0.2254 0.4768
1.0000 1.8270 0.0000

Y
P
b
P
r

Colour systems 17 ) +
void csDeviceColour :: smpte 204M rgb(double y, double Pb, double Pr , double r, double
g, double b)

double ar = (y + Pb 0.0000 + Pr 1.5755), ag = (y + Pb 0.2254 + Pr 0.4768),

ab = (y + Pb 1.8270 + Pr 0.0000);
r = max (0.0, min(1.0, ar ));
g = max (0.0, min(1.0, ag ));
b = max (0.0, min(1.0, ab));

18 COLOUR SYSTEM CONVERSION UTILITIES COLOUR 27

27. RGB_CMY: Convert RGB colour specication, R, G, B ranging from 0 to 1, to C, M, Y colour speci-
cation, also ranging from 0 to 1.

C
M
Y

1
1
1

R
G
B

Colour systems 17 ) +
void csDeviceColour :: rgb cmy(double r, double g, double b, double c, double m, double y)

c = 1.0 r;
m = 1.0 g;
y = 1.0 b;

28. CMY_RGB: Convert CMY colour specication, C, M, Y ranging from 0 to 1, to R, G, B colour speci-
cation, also ranging from 0 to 1.

R
G
B

1
1
1

C
M
Y

Colour systems 17 ) +
void csDeviceColour :: cmy rgb(double c, double m, double y, double r, double g, double b)

r = 1.0 c;
g = 1.0 m;
b = 1.0 y;

29. cmy cmyk : Convert CMY colour specication, C, M, Y ranging from 0 to 1, to C, M, Y, K colour
specication, also ranging from 0 to 1. K is the black ink component in four colour printing processes. We
convert C, M, Y by computing K = min(C, M, Y ), then subtracting that value from each of the C, M, Y
components.
Colour systems 17 ) +
void csDeviceColour :: cmy cmyk (double c, double m, double y, double oc, double om, double
oy, double ok )

double k = min(c, min(m, y));

oc = c k;
om = mk;
oy = y k;
ok = k;

30 COLOUR COLOUR SYSTEM CONVERSION UTILITIES 19

30. cmyk cmy: Convert CMYK colour specication, C, M, Y, K ranging from 0 to 1, to C, M, Y colour
specication, also ranging from 0 to 1. K is the black ink component in four colour printing processes. We
simply add the K component to each of the C, M, Y components.
Colour systems 17 ) +
void csDeviceColour :: cmyk cmy(double c, double m, double y, double k, double oc, double
om, double oy)

oc = c +k;
om = m+k;
oy = y +k;

20 COLOUR SYSTEM CONVERSION METHODS COLOUR 31

31. Colour system conversion methods.
The following methods express a colour in a given colour system in a variety of others. The class must
implement the asRGB method required for each of these conversions.
Colour systems 17 ) +
void csDeviceColour :: asHSV (double &h, double &s, double &v) / To HSV /

double r, g, b;
asRGB(r, g, b);
rgb hsv (r, g, b, &h, &s, &v);

void csDeviceColour :: asHLS (double &h, double &l, double &s) / To HLS /

double r, g, b;
asRGB(r, g, b);
rgb hls (r, g, b, &h, &l, &s);

void csDeviceColour :: asYIQ(double &y, double &i, double &q) / To YIQ /

double r, g, b;
asRGB(r, g, b);
rgb yiq (r, g, b, &y, &i, &q);

void csDeviceColour :: asYUV (double &y, double &u, double &v) / To YUV /

double r, g, b;
asRGB(r, g, b);
rgb yuv (r, g, b, &y, &u, &v);

void csDeviceColour :: asSMPTE(double &y, double &Pb, double &Pr )

/ To SMPTE 204M /

double r, g, b;
asRGB(r, g, b);
rgb smpte 204M (r, g, b, &y, &Pb, &Pr );

void csDeviceColour :: asCMY (double &c, double &m, double &y) / To CMY /

double r, g, b;
asRGB(r, g, b);
rgb cmy(r, g, b, &c, &m, &y);

32 COLOUR PERCEPTUAL COLOUR SYSTEMS 21

32. Perceptual colour systems.
The following sections dene data used in manipulating colour systems.
22 CIE COLOUR SYSTEMS COLOUR 33
33. CIE colour systems.
A colour system is dened by the CIE x and y coordinates of its three primary illuminants and the x and
y coordinates of the white point.
Class denitions 6 ) +
class CIEColourSystem
private:
string name; / Colour system name /
double xRed , yRed , / Red primary illuminant /
xGreen, yGreen, / Green primary illuminant /
xBlue, yBlue, / Blue primary illuminant /
xWhite, yWhite; / White point /
public:
CIEColourSystem(string c name, double c xRed , double x yRed , double c xGreen, double
c yGreen, double c xBlue, double c yBlue, double c xWhite, double c yWhite)

name = c name;
xRed = c xRed ;
yRed = x yRed ;
xGreen = c xGreen;
yGreen = c yGreen;
xBlue = c xBlue;
yBlue = c yBlue;
xWhite = c xWhite;
yWhite = c yWhite;

void xyz to rgb(double xc, double yc, double zc, double r, double g, double b);
static bool inside gamut (double r, double g, double b);
bool constrain rgb(double x, double y, double z, double r, double g, double b, bool
interpwp = false);
protected:
static double clamp(double v, double l, double h)

return (v < l) ? l : ((v > h) ? h : v); / Constrain l v h /

;
extern CIEColourSystem NTSCsystem, EBUsystem, SMPTEsystem, HDTVsystem, CIEsystem;
/ Predened standard colour systems /
34 COLOUR CIE COLOUR SYSTEMS 23
34. xyz to rgb: Given an additive tricolour system dened by the CIE x and y chromaticities of its
three primaries (z is derived trivially as 1 (x + y)), and a desired chromaticity (x
c
, y
c
, z
c
) in CIE space,
determine the contribution of each primary in a linear combination which sums to the desired chromaticity.
If the requested chromaticity falls outside the Maxwell triangle (colour gamut) formed by the three primaries,
one of the r, g, or b weights will be negative. Use inside gamut to test for a valid colour and constrain rgb
to desaturate an outside-gamut colour to the closest representation within the available gamut.
Colour systems 17 ) +
void CIEColourSystem:: xyz to rgb(double xc, double yc, double zc, double r, double g, double
b)

double xr , yr , zr , xg , yg , zg , xb, yb, zb;

xr = xRed ;
yr = yRed ;
zr = 1 (xr + yr );
xg = xGreen;
yg = yGreen;
zg = 1 (xg + yg );
xb = xBlue;
yb = yBlue;
zb = 1 (xb + yb);
r = (xg yc zb + xc yg zb + xg yb zc xb yg zc xc yb zg + xb yc zg )/(xr yg
zb xg yr zb xr yb zg + xb yr zg + xg yb zr xb yg zr );
g = (xr yc zb xc yr zb xr yb zc +xb yr zc +xc yb zr xb yc zr )/(xr yg zb
xg yr zb xr yb zg + xb yr zg + xg yb zr xb yg zr );
b = (xr yg zc xg yr zc xr yc zg +xc yr zg +xg yc zr xc yg zr )/(xr yg zb
xg yr zb xr yb zg + xb yr zg + xg yb zr xb yg zr );

35. inside gamut : Test whether a requested colour is within the gamut achievable with the primaries of
the current colour system. This amounts simply to testing whether all the primary weights are non-negative.
Colour systems 17 ) +
bool CIEColourSystem:: inside gamut (double r, double g, double b)

return (r 0) (g 0) (b 0);

24 CIE COLOUR SYSTEMS COLOUR 36

36. constrain rgb: If the requested RGB shade contains a negative weight for one of the primaries, it
lies outside the colour gamut accessible from the given triple of primaries. Desaturate it by mixing with
the white point of the colour system so as to reduce the primary with the negative weight to zero. This
is equivalent to nding the intersection on the CIE diagram of a line drawn between the white point and
and the requested color and the edge of the Maxwell triangle formed by the three primaries. If interpwp is
nonzero, the white point dened by the sum of the three primary illuminants is used instead of the colour
systems actual white point. While indefensible from the standpoint of colour theory, this produces much
better looking charts on computer monitors, since the white points of most colour systems are well to the
blue of the white dened by the R = G = B = 1.
Colour systems 17 ) +
bool CIEColourSystem:: constrain rgb(double x, double y, double z, double r, double
g, double b, bool interpwp)
/ Is the contribution of one of the primaries negative ? /
if (inside gamut (r, g, b))
double par , wr , wg , wb, xw, yw;
/ Determine the white point used in interpolating out of gamut colours. If interpwp is set, the
colour systems white point is used. Otherwise, the white dened by an equal mix of the three
illuminants is taken as the origin of the interpolation line drawn to the out of gamut colour. /
if (interpwp)
xw = xWhite;
yw = yWhite;

else
xw = (xRed + xGreen + xBlue)/3;
yw = (yRed + yGreen + yBlue)/3;
/ Yes. Find the RGB mixing weights of the white point (we assume the white point is in the
gamut!). /
xyz to rgb(xw, yw, 1 (xw + yw), &wr , &wg , &wb);
/ Find the primary with negative weight and calculate the parameter of the point on the vector
from the white point to the original requested colour in RGB space. /
if (r < g r < b)
par = wr /(wr r);

else if (g < r g < b)

par = wg /(wg g);

else
par = wb/(wb b);
/ Since XYZ space is a linear transformation of RGB space, we can nd the XYZ space
coordinates of the point where the edge of the gamut intersects the vector from the white
point to the original colour by multiplying the parameter in RGB space by the dierence
vector in XYZ space. /
x = clamp(xw + par (x xw), 0, 1);
y = clamp(yw + par (y yw), 0, 1);
z = clamp(1 (x +y), 0, 1); / Now nally calculate the gamut-constrained RGB weights. /
r = clamp(wr + par (r wr ), 0, 1);
g = clamp(wg + par (g wg ), 0, 1);
b = clamp(wb + par (b wb), 0, 1);
return true; / Colour modied to t RGB gamut /

return false; / Colour within RGB gamut /

37 COLOUR CIE COLOUR SYSTEMS 25

37. CIE colour matching functions.
The following table gives the CIE colour matching functions x(), y(), and z(), for wavelengths at 5
nanometre increments from 380 nm through 780 nm. This table is used in conjunction with Plancks law for
the energy spectrum of a black body at a given temperature to plot the black body curve on the CIE chart.
Colour system data tables 37 )
static double cie colour match[ ][3] = 0.0014, 0.0000, 0.0065, / 380 nm /
0.0022, 0.0001, 0.0105, 0.0042, 0.0001, 0.0201, 0.0076, 0.0002, 0.0362, 0.0143, 0.0004, 0.0679,
0.0232, 0.0006, 0.1102, 0.0435, 0.0012, 0.2074, 0.0776, 0.0022, 0.3713, 0.1344, 0.0040, 0.6456,
0.2148, 0.0073, 1.0391, 0.2839, 0.0116, 1.3856, 0.3285, 0.0168, 1.6230, 0.3483, 0.0230, 1.7471,
0.3481, 0.0298, 1.7826, 0.3362, 0.0380, 1.7721, 0.3187, 0.0480, 1.7441, 0.2908, 0.0600, 1.6692,
0.2511, 0.0739, 1.5281, 0.1954, 0.0910, 1.2876, 0.1421, 0.1126, 1.0419, 0.0956, 0.1390, 0.8130,
0.0580, 0.1693, 0.6162, 0.0320, 0.2080, 0.4652, 0.0147, 0.2586, 0.3533, 0.0049, 0.3230, 0.2720,
0.0024, 0.4073, 0.2123, 0.0093, 0.5030, 0.1582, 0.0291, 0.6082, 0.1117, 0.0633, 0.7100, 0.0782,
0.1096, 0.7932, 0.0573, 0.1655, 0.8620, 0.0422, 0.2257, 0.9149, 0.0298, 0.2904, 0.9540, 0.0203,
0.3597, 0.9803, 0.0134, 0.4334, 0.9950, 0.0087, 0.5121, 1.0000, 0.0057, 0.5945, 0.9950, 0.0039,
0.6784, 0.9786, 0.0027, 0.7621, 0.9520, 0.0021, 0.8425, 0.9154, 0.0018, 0.9163, 0.8700, 0.0017,
0.9786, 0.8163, 0.0014, 1.0263, 0.7570, 0.0011, 1.0567, 0.6949, 0.0010, 1.0622, 0.6310, 0.0008,
1.0456, 0.5668, 0.0006, 1.0026, 0.5030, 0.0003, 0.9384, 0.4412, 0.0002, 0.8544, 0.3810, 0.0002,
0.7514, 0.3210, 0.0001, 0.6424, 0.2650, 0.0000, 0.5419, 0.2170, 0.0000, 0.4479, 0.1750, 0.0000,
0.3608, 0.1382, 0.0000, 0.2835, 0.1070, 0.0000, 0.2187, 0.0816, 0.0000, 0.1649, 0.0610, 0.0000,
0.1212, 0.0446, 0.0000, 0.0874, 0.0320, 0.0000, 0.0636, 0.0232, 0.0000, 0.0468, 0.0170, 0.0000,
0.0329, 0.0119, 0.0000, 0.0227, 0.0082, 0.0000, 0.0158, 0.0057, 0.0000, 0.0114, 0.0041, 0.0000,
0.0081, 0.0029, 0.0000, 0.0058, 0.0021, 0.0000, 0.0041, 0.0015, 0.0000, 0.0029, 0.0010, 0.0000,
0.0020, 0.0007, 0.0000, 0.0014, 0.0005, 0.0000, 0.0010, 0.0004, 0.0000, 0.0007, 0.0002, 0.0000,
0.0005, 0.0002, 0.0000, 0.0003, 0.0001, 0.0000, 0.0002, 0.0001, 0.0000, 0.0002, 0.0001, 0.0000,
0.0001, 0.0000, 0.0000, 0.0001, 0.0000, 0.0000, 0.0001, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000
/ 780 nm /
;
See also sections 38 and 39.
This code is used in section 2.
26 CIE COLOUR SYSTEMS COLOUR 38
38. Spectral chromaticity co-ordinates.
The following table gives the spectral chromaticity co-ordinates x() and y() for wavelengths in 5
nanometre increments from 380 nm through 780 nm. These co-ordinates represent the position in the
CIE xy space of pure spectral colours of the given wavelength, and thus dene the outline of the CIE
tongue diagram.
Colour system data tables 37 ) +
static double spectral chromaticity[81][3] = 0.1741, 0.0050, / 380 nm /
0.1740, 0.0050, 0.1738, 0.0049, 0.1736, 0.0049, 0.1733, 0.0048, 0.1730, 0.0048, 0.1726, 0.0048,
0.1721, 0.0048, 0.1714, 0.0051, 0.1703, 0.0058, 0.1689, 0.0069, 0.1669, 0.0086, 0.1644,
0.0109, 0.1611, 0.0138, 0.1566, 0.0177, 0.1510, 0.0227, 0.1440, 0.0297, 0.1355, 0.0399,
0.1241, 0.0578, 0.1096, 0.0868, 0.0913, 0.1327, 0.0687, 0.2007, 0.0454, 0.2950, 0.0235,
0.4127, 0.0082, 0.5384, 0.0039, 0.6548, 0.0139, 0.7502, 0.0389, 0.8120, 0.0743, 0.8338,
0.1142, 0.8262, 0.1547, 0.8059, 0.1929, 0.7816, 0.2296, 0.7543, 0.2658, 0.7243, 0.3016,
0.6923, 0.3373, 0.6589, 0.3731, 0.6245, 0.4087, 0.5896, 0.4441, 0.5547, 0.4788, 0.5202,
0.5125, 0.4866, 0.5448, 0.4544, 0.5752, 0.4242, 0.6029, 0.3965, 0.6270, 0.3725, 0.6482,
0.3514, 0.6658, 0.3340, 0.6801, 0.3197, 0.6915, 0.3083, 0.7006, 0.2993, 0.7079, 0.2920,
0.7140, 0.2859, 0.7190, 0.2809, 0.7230, 0.2770, 0.7260, 0.2740, 0.7283, 0.2717, 0.7300, 0.2700,
0.7311, 0.2689, 0.7320, 0.2680, 0.7327, 0.2673, 0.7334, 0.2666, 0.7340, 0.2660, 0.7344, 0.2656,
0.7346, 0.2654, 0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653,
0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653,
0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653, 0.7347, 0.2653
/ 780 nm /
;
39. Standard colour system denitions.
The following dene the white point chromaticities for the NTSC, EBU, and SMPTE colour systems.
#dene IlluminantC 0.3101, 0.3162 / For NTSC television /
#dene IlluminantD65 0.3127, 0.3291 / For EBU and SMPTE /
Colour system data tables 37 ) +
CIEColourSystem NTSCsystem("NTSC", 0.67, 0.33, 0.21, 0.71, 0.14, 0.08, IlluminantC),
EBUsystem("EBU(PAL/SECAM)", 0.64, 0.33, 0.29, 0.60, 0.15, 0.06, IlluminantD65 ),
SMPTEsystem("SMPTE", 0.630, 0.340, 0.310, 0.595, 0.155, 0.070,
IlluminantD65 ), HDTVsystem("HDTV", 0.670, 0.330, 0.210, 0.710, 0.150, 0.060, IlluminantD65 ),
CIEsystem("CIE", 0.7355, 0.2645, 0.2658, 0.7243, 0.1669, 0.0085, 0.3894, 0.3324);
40 COLOUR TEST PROGRAM 27
40. Test program.
colour_test.c 1 ) +
Test program include les 43 );
Show how to call test program 42 );
int main(int argc, char argv [ ])

extern char optarg ; / Imported from getopt /

extern int optind ;
int opt ;
Process command-line options 41 );
return 0;

41. We use getopt to process command line options. This permits aggregation of options without
arguments and both darg and d arg syntax.
Process command-line options 41 )
while ((opt = getopt (argc, argv , "nu:")) ,= 1)
switch (opt )
case u: / u Print how-to-call information /
case ?: usage( );
return 0;
case : / Extended options /
switch (optarg [0])
case c: / copyright /
cout "Thisprogramisinthepublicdomain.\n";
return 0;
case h: / help /
usage( );
return 0;
case v: / version /
cout PRODUCT "" VERSION "\n";
cout "Lastrevised:" REVDATE "\n";
cout "Thelatestversionisalwaysavailable\n";
cout "athttp://www.fourmilab.ch/eggtools/eggshell\n";
return 0;

This code is used in section 40.

28 TEST PROGRAM COLOUR 42
42. Procedure usage prints how-to-call information.
Show how to call test program 42 )
static void usage(void)

cout PRODUCT "Analyseeggsummaryfiles.Call:\n";

cout "" PRODUCT "[options][infile][outfile]\n";
cout "\n";
cout "Options:\n";
cout "copyrightPrintcopyrightinformation\n";
cout "u,helpPrintthismessage\n";
cout "versionPrintversionnumber\n";
cout "\n";
cout "byJohnWalker\n";
cout "http://www.fourmilab.ch/\n";

This code is used in section 40.

43. We need the following denitions to compile the test program.
Test program include les 43 )
#include "config.h" / Our conguration / / C++ include les /
#include <iostream>
#include <exception>
#include <stdexcept>
#include <string>
using namespace std;
#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
#ifdef HAVE_GETOPT
#ifdef HAVE_UNISTD_H
#include <unistd.h>
#endif
#else
#include "getopt.h" / No system getoptuse our own /
#endif
#include "colour.h" / Class denitions for this package /
This code is used in section 40.
44 COLOUR INDEX 29
44. Index. The following is a cross-reference table for colour. Single-character identiers are not
indexed, nor are reserved words. Underlined entries indicate where an identier was declared.
ab: 22, 24, 26.
ag : 22, 24, 26.
ai : 21.
aPb: 25.
aPr : 25.
aq : 21.
ar : 22, 24, 26.
argc: 40, 41.
argv : 40, 41.
asCMY : 14, 31.
asCMYK: 13.
asGreyScale: 13.
asHLS : 14, 31.
asHSV : 14, 31.
asRGB: 13, 14, 31.
assert : 17.
asSMPTE: 14, 31.
asYIQ: 14, 31.
asYUV : 14, 31.
au: 23.
av : 23.
ay: 21, 23, 25.
b: 13, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
27, 28, 31, 33, 34, 35, 36.
bc: 18, 19.
c: 13, 14, 15, 27, 28, 29, 30, 31.
c name: 33.
c xBlue: 33.
c xGreen: 33.
c xRed : 33.
c xWhite: 33.
c yBlue: 33.
c yGreen: 33.
c yWhite: 33.
cie colour match: 37.
CIEColourSystem: 33, 34, 35, 36, 39.
CIEsystem: 33, 39.
clamp: 33, 36.
cmy cmyk : 15, 29.
cmy rgb: 15, 28.
CMY_RGB: 28.
cmyk cmy: 15, 30.
COLOUR_HEADER_DEFINES: 3.
colourSystemName: 6, 8, 9, 10.
constrain: 36.
constrain rgb: 33, 34, 36.
cout : 41, 42.
csBlackBody: 11.
csColour: 6, 7, 12.
csDeviceColour: 12, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31.
csMonochromaticColour: 8.
csSpectralBlack: 9.
csSpectralColour: 7, 8, 9, 10, 11.
csSpectralWhite: 10.
EBUsystem: 33, 39.
exp: 11.
f: 17.
false: 7, 9, 10, 11, 33, 36.
ux : 11.
g: 13, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
27, 28, 31, 33, 34, 35, 36.
gc: 18, 19.
getIntensity: 7, 8, 9, 10, 11.
getopt : 40, 41.
getTemperature: 11.
getWavelength: 8.
h: 14, 15, 17, 18, 19, 20, 31, 33.
HAVE_GETOPT: 43.
HAVE_UNISTD_H: 43.
HDTVsystem: 33, 39.
hls rgb: 15, 20.
HLS_RGB: 20.
hlsval : 15, 20.
HSV_RGB: 17.
hsv rgb: 15, 17.
hue: 15, 20.
i: 14, 15, 17, 21, 22, 31.
IlluminantC: 39.
IlluminantD65 : 39.
imax : 18, 19.
imin: 18, 19.
inside gamut : 33, 34, 35, 36.
interpwp: 33, 36.
isMonochromatic: 7, 8, 9, 10, 11.
k: 13, 15, 29, 30.
l: 14, 15, 19, 20, 31, 33.
m: 13, 14, 15, 27, 28, 29, 30, 31.
main: 40.
max : 18, 19, 22, 24, 26.
min: 18, 19, 22, 24, 26, 29.
m1 : 20.
m2 : 20.
name: 33.
NTSCsystem: 33, 39.
n1 : 15, 20.
n2 : 15, 20.
oc: 15, 29, 30.
of : 6, 8, 11.
30 INDEX COLOUR 44
ok : 15, 29.
om: 15, 29, 30.
opt : 40, 41.
optarg : 40, 41.
optind : 40.
ostream: 6, 8, 11.
oy: 15, 29, 30.
p: 17.
par : 36.
Pb: 14, 15, 25, 26, 31.
Pr : 14, 15, 25, 26, 31.
PRODUCT: 41, 42.
q: 14, 15, 17, 21, 22, 31.
r: 13, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
27, 28, 31, 33, 34, 35, 36.
rc: 18, 19.
REVDATE: 1, 41.
rgb: 36.
rgb cmy: 15, 27, 31.
RGB_CMY: 27.
rgb hls : 15, 19, 31.
RGB_HLS: 19.
rgb hsv : 15, 18, 31.
RGB_HSV: 18.
RGB_SMPTE_204M: 25, 26.
rgb smpte 204M : 15, 25, 31.
RGB_YIQ: 21, 22.
rgb yiq : 15, 21, 31.
RGB_YUV: 23.
rgb yuv : 15, 23, 24, 31.
s: 14, 15, 17, 18, 19, 20, 31.
setTemperature: 11.
setWavelength: 8.
smpte 204M rgb: 15, 26.
SMPTE_204M_RGB: 26.
SMPTEsystem: 33, 39.
spectral chromaticity: 38.
std: 3, 43.
string: 6, 8, 9, 10, 33.
t: 17.
temp: 11.
temperature: 11.
totalFlux : 11.
true: 7, 8, 36.
u: 14, 15, 23, 24, 31.
usage: 41, 42.
v: 14, 15, 17, 18, 23, 24, 31, 33.
VERSION: 41.
waveLength: 7, 8, 9, 10, 11.
wavelength: 8.
wb: 36.
wg : 36.
wl : 11.
wr : 36.
writeParameters : 6, 8, 11.
x: 33, 36.
x yRed : 33.
xb: 34.
xBlue: 33, 34, 36.
xc: 33, 34.
xg : 34.
xGreen: 33, 34, 36.
xr : 34.
xRed : 33, 34, 36.
xw: 36.
xWhite: 33, 36.
xyz to rgb: 33, 34, 36.
y: 13, 14, 15, 21, 22, 23, 24, 25, 26, 27, 28,
29, 30, 31, 33, 36.
yb: 34.
yBlue: 33, 34, 36.
yc: 33, 34.
yg : 34.
yGreen: 33, 34, 36.
YIQ_RGB: 22.
yiq rgb: 15, 22.
yr : 34.
yRed : 33, 34, 36.
yuv rgb: 15, 24.
YUV_RGB: 24.
yw: 36.
yWhite: 33, 36.
z: 33, 36.
zb: 34.
zc: 33, 34.
zg : 34.
zr : 34.
COLOUR NAMES OF THE SECTIONS 31
Application include les 4 ) Used in section 2.
Class denitions 6, 7, 8, 9, 10, 11, 12, 33 ) Used in section 3.
Class implementations 5 ) Used in section 2.
Colour system data tables 37, 38, 39 ) Used in section 2.
Colour systems 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36 ) Used in section 5.
Device colour derived methods 14 ) Used in section 12.
Device colour fundamental methods 13 ) Used in section 12.
Device colour system conversion utilities 15 ) Used in section 12.
Process command-line options 41 ) Used in section 40.
Show how to call test program 42 ) Used in section 40.
Test program include les 43 ) Used in section 40.
colour.h 3 )
colour_test.c 1, 40 )
COLOUR
Section Page
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1
Program global context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2
Colour system parent class: csColour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3
Spectral colour systems parent class: csSpectralColour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4
Monochromatic spectral colour systems: csMonochromaticColour . . . . . . . . . . . . . . . . . . . . 8 5
Black: csSpectralBlack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6
White: csSpectralWhite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 6
Planckian black body: csBlackBody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 7
Device colour systems parent class: csDeviceColour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 9
Colour system conversion utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 10
Colour system conversion methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 20
Perceptual colour systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 21
CIE colour systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 22
Standard colour system denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 26
Test program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 27
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 29