/*
Colour Rendering of Spectra
by John Walker
http://www.fourmilab.ch/
Last updated: March 9, 2003
This program is in the public domain.
For complete information about the techniques employed in
this program, see the World-Wide Web document:
http://www.fourmilab.ch/documents/specrend/
The xyz_to_rgb() function, which was wrong in the original
version of this program, was corrected by:
Andrew J. S. Hamilton 21 May 1999
Andrew.Hamilton@Colorado.EDU
http://casa.colorado.edu/~ajsh/
who also added the gamma correction facilities and
modified constrain_rgb() to work by desaturating the
colour by adding white.
A program which uses these functions to plot CIE
"tongue" diagrams called "ppmcie" is included in
the Netpbm graphics toolkit:
http://netpbm.sourceforge.net/
(The program was called cietoppm in earlier
versions of Netpbm.)
*/
#include
#include
/* A colour system is defined by the CIE x and y coordinates of
its three primary illuminants and the x and y coordinates of
the white point. */
struct colourSystem {
char *name; /* Colour system name */
double xRed, yRed, /* Red x, y */
xGreen, yGreen, /* Green x, y */
xBlue, yBlue, /* Blue x, y */
xWhite, yWhite, /* White point x, y */
gamma; /* Gamma correction for system */
};
/* White point chromaticities. */
#define IlluminantC 0.3101, 0.3162 /* For NTSC television */
#define IlluminantD65 0.3127, 0.3291 /* For EBU and SMPTE */
#define IlluminantE 0.33333333, 0.33333333 /* CIE equal-energy illuminant */
/* Gamma of nonlinear correction.
See Charles Poynton's ColorFAQ Item 45 and GammaFAQ Item 6 at:
http://www.poynton.com/ColorFAQ.html
http://www.poynton.com/GammaFAQ.html
*/
#define GAMMA_REC709 0 /* Rec. 709 */
static struct colourSystem
/* Name xRed yRed xGreen yGreen xBlue yBlue White point Gamma */
NTSCsystem = { "NTSC", 0.67, 0.33, 0.21, 0.71, 0.14, 0.08, IlluminantC, GAMMA_REC709 },
EBUsystem = { "EBU (PAL/SECAM)", 0.64, 0.33, 0.29, 0.60, 0.15, 0.06, IlluminantD65, GAMMA_REC709 },
SMPTEsystem = { "SMPTE", 0.630, 0.340, 0.310, 0.595, 0.155, 0.070, IlluminantD65, GAMMA_REC709 },
HDTVsystem = { "HDTV", 0.670, 0.330, 0.210, 0.710, 0.150, 0.060, IlluminantD65, GAMMA_REC709 },
CIEsystem = { "CIE", 0.7355, 0.2645, 0.2658, 0.7243, 0.1669, 0.0085, IlluminantE, GAMMA_REC709 },
Rec709system = { "CIE REC 709", 0.64, 0.33, 0.30, 0.60, 0.15, 0.06, IlluminantD65, GAMMA_REC709 };
/* UPVP_TO_XY
Given 1976 coordinates u', v', determine 1931 chromaticities x, y
*/
void upvp_to_xy(double up, double vp, double *xc, double *yc)
{
*xc = (9 * up) / ((6 * up) - (16 * vp) + 12);
*yc = (4 * vp) / ((6 * up) - (16 * vp) + 12);
}
/* XY_TO_UPVP
Given 1931 chromaticities x, y, determine 1976 coordinates u', v'
*/
void xy_to_upvp(double xc, double yc, double *up, double *vp)
{
*up = (4 * xc) / ((-2 * xc) + (12 * yc) + 3);
*vp = (9 * yc) / ((-2 * xc) + (12 * yc) + 3);
}
/* XYZ_TO_RGB
Given an additive tricolour system CS, defined by the CIE x
and y chromaticities of its three primaries (z is derived
trivially as 1-(x+y)), and a desired chromaticity (XC, YC,
ZC) 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.
Caller can use constrain_rgb() to desaturate an
outside-gamut colour to the closest representation within
the available gamut and/or norm_rgb to normalise the RGB
components so the largest nonzero component has value 1.
*/
void xyz_to_rgb(struct colourSystem *cs,
double xc, double yc, double zc,
double *r, double *g, double *b)
{
double xr, yr, zr, xg, yg, zg, xb, yb, zb;
double xw, yw, zw;
double rx, ry, rz, gx, gy, gz, bx, by, bz;
double rw, gw, bw;
xr = cs->xRed; yr = cs->yRed; zr = 1 - (xr + yr);
xg = cs->xGreen; yg = cs->yGreen; zg = 1 - (xg + yg);
xb = cs->xBlue; yb = cs->yBlue; zb = 1 - (xb + yb);
xw = cs->xWhite; yw = cs->yWhite; zw = 1 - (xw + yw);
/* xyz -> rgb matrix, before scaling to white. */
rx = (yg * zb) - (yb * zg); ry = (xb * zg) - (xg * zb); rz = (xg * yb) - (xb * yg);
gx = (yb * zr) - (yr * zb); gy = (xr * zb) - (xb * zr); gz = (xb * yr) - (xr * yb);
bx = (yr * zg) - (yg * zr); by = (xg * zr) - (xr * zg); bz = (xr * yg) - (xg * yr);
/* White scaling factors.
Dividing by yw scales the white luminance to unity, as conventional. */
rw = ((rx * xw) + (ry * yw) + (rz * zw)) / yw;
gw = ((gx * xw) + (gy * yw) + (gz * zw)) / yw;
bw = ((bx * xw) + (by * yw) + (bz * zw)) / yw;
/* xyz -> rgb matrix, correctly scaled to white. */
rx = rx / rw; ry = ry / rw; rz = rz / rw;
gx = gx / gw; gy = gy / gw; gz = gz / gw;
bx = bx / bw; by = by / bw; bz = bz / bw;
/* rgb of the desired point */
*r = (rx * xc) + (ry * yc) + (rz * zc);
*g = (gx * xc) + (gy * yc) + (gz * zc);
*b = (bx * xc) + (by * yc) + (bz * zc);
}
/* 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. */
int inside_gamut(double r, double g, double b)
{
return (r >= 0) && (g >= 0) && (b >= 0);
}
/* 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 adding white, equal quantities of R, G, and B, enough
to make RGB all positive. The function returns 1 if the
components were modified, zero otherwise.
*/
int constrain_rgb(double *r, double *g, double *b)
{
double w;
/* Amount of white needed is w = - min(0, *r, *g, *b) */
w = (0 < *r) ? 0 : *r;
w = (w < *g) ? w : *g;
w = (w < *b) ? w : *b;
w = -w;
/* Add just enough white to make r, g, b all positive. */
if (w > 0) {
*r += w; *g += w; *b += w;
return 1; /* Colour modified to fit RGB gamut */
}
return 0; /* Colour within RGB gamut */
}
/* GAMMA_CORRECT_RGB
Transform linear RGB values to nonlinear RGB values. Rec.
709 is ITU-R Recommendation BT. 709 (1990) ``Basic
Parameter Values for the HDTV Standard for the Studio and
for International Programme Exchange'', formerly CCIR Rec.
709. For details see
http://www.poynton.com/ColorFAQ.html
http://www.poynton.com/GammaFAQ.html
*/
void gamma_correct(const struct colourSystem *cs, double *c)
{
double gamma;
gamma = cs->gamma;
if (gamma == GAMMA_REC709) {
/* Rec. 709 gamma correction. */
double cc = 0.018;
if (*c < cc) {
*c *= ((1.099 * pow(cc, 0.45)) - 0.099) / cc;
} else {
*c = (1.099 * pow(*c, 0.45)) - 0.099;
}
} else {
/* Nonlinear colour = (Linear colour)^(1/gamma) */
*c = pow(*c, 1.0 / gamma);
}
}
void gamma_correct_rgb(const struct colourSystem *cs, double *r, double *g, double *b)
{
gamma_correct(cs, r);
gamma_correct(cs, g);
gamma_correct(cs, b);
}
/* NORM_RGB
Normalise RGB components so the most intense (unless all
are zero) has a value of 1.
*/
void norm_rgb(double *r, double *g, double *b)
{
#define Max(a, b) (((a) > (b)) ? (a) : (b))
double greatest = Max(*r, Max(*g, *b));
if (greatest > 0) {
*r /= greatest;
*g /= greatest;
*b /= greatest;
}
#undef Max
}
/* SPECTRUM_TO_XYZ
Calculate the CIE X, Y, and Z coordinates corresponding to
a light source with spectral distribution given by the
function SPEC_INTENS, which is called with a series of
wavelengths between 380 and 780 nm (the argument is
expressed in meters), which returns emittance at that
wavelength in arbitrary units. The chromaticity
coordinates of the spectrum are returned in the x, y, and z
arguments which respect the identity:
x + y + z = 1.
*/
void spectrum_to_xyz(double (*spec_intens)(double wavelength),
double *x, double *y, double *z)
{
int i;
double lambda, X = 0, Y = 0, Z = 0, XYZ;
/* CIE colour matching functions xBar, yBar, and zBar for
wavelengths from 380 through 780 nanometers, every 5
nanometers. For a wavelength lambda in this range:
cie_colour_match[(lambda - 380) / 5][0] = xBar
cie_colour_match[(lambda - 380) / 5][1] = yBar
cie_colour_match[(lambda - 380) / 5][2] = zBar
To save memory, this table can be declared as floats
rather than doubles; (IEEE) float has enough
significant bits to represent the values. It's declared
as a double here to avoid warnings about "conversion
between floating-point types" from certain persnickety
compilers. */
static double cie_colour_match[81][3] = {
{0.0014,0.0000,0.0065}, {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}
};
for (i = 0, lambda = 380; lambda < 780.1; i++, lambda += 5) {
double Me;
Me = (*spec_intens)(lambda);
X += Me * cie_colour_match[i][0];
Y += Me * cie_colour_match[i][1];
Z += Me * cie_colour_match[i][2];
}
XYZ = (X + Y + Z);
*x = X / XYZ;
*y = Y / XYZ;
*z = Z / XYZ;
}
/* BB_SPECTRUM
Calculate, by Planck's radiation law, the emittance of a black body
of temperature bbTemp at the given wavelength (in metres). */
double bbTemp = 5000; /* Hidden temperature argument
to BB_SPECTRUM. */
double bb_spectrum(double wavelength)
{
double wlm = wavelength * 1e-9; /* Wavelength in meters */
return (3.74183e-16 * pow(wlm, -5.0)) /
(exp(1.4388e-2 / (wlm * bbTemp)) - 1.0);
}
/* Built-in test program which displays the x, y, and Z and RGB
values for black body spectra from 1000 to 10000 degrees kelvin.
When run, this program should produce the following output:
Temperature x y z R G B
----------- ------ ------ ------ ----- ----- -----
1000 K 0.6528 0.3444 0.0028 1.000 0.007 0.000 (Approximation)
1500 K 0.5857 0.3931 0.0212 1.000 0.126 0.000 (Approximation)
2000 K 0.5267 0.4133 0.0600 1.000 0.234 0.010
2500 K 0.4770 0.4137 0.1093 1.000 0.349 0.067
3000 K 0.4369 0.4041 0.1590 1.000 0.454 0.151
3500 K 0.4053 0.3907 0.2040 1.000 0.549 0.254
4000 K 0.3805 0.3768 0.2428 1.000 0.635 0.370
4500 K 0.3608 0.3636 0.2756 1.000 0.710 0.493
5000 K 0.3451 0.3516 0.3032 1.000 0.778 0.620
5500 K 0.3325 0.3411 0.3265 1.000 0.837 0.746
6000 K 0.3221 0.3318 0.3461 1.000 0.890 0.869
6500 K 0.3135 0.3237 0.3628 1.000 0.937 0.988
7000 K 0.3064 0.3166 0.3770 0.907 0.888 1.000
7500 K 0.3004 0.3103 0.3893 0.827 0.839 1.000
8000 K 0.2952 0.3048 0.4000 0.762 0.800 1.000
8500 K 0.2908 0.3000 0.4093 0.711 0.766 1.000
9000 K 0.2869 0.2956 0.4174 0.668 0.738 1.000
9500 K 0.2836 0.2918 0.4246 0.632 0.714 1.000
10000 K 0.2807 0.2884 0.4310 0.602 0.693 1.000
*/
int main()
{
double t, x, y, z, r, g, b;
struct colourSystem *cs = &SMPTEsystem;
printf("Temperature x y z R G B\n");
printf("----------- ------ ------ ------ ----- ----- -----\n");
for (t = 1000; t <= 10000; t+= 500) {
bbTemp = t;
spectrum_to_xyz(bb_spectrum, &x, &y, &z);
xyz_to_rgb(cs, x, y, z, &r, &g, &b);
printf(" %5.0f K %.4f %.4f %.4f ", t, x, y, z);
if (constrain_rgb(&r, &g, &b)) {
norm_rgb(&r, &g, &b);
printf("%.3f %.3f %.3f (Approximation)\n", r, g, b);
} else {
norm_rgb(&r, &g, &b);
printf("%.3f %.3f %.3f\n", r, g, b);
}
}
return 0;
}