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#define _USE_MATH_DEFINES
#define _XOPEN_SOURCE 700
#define _POSIX_C_SOURCE 200809L
#include <errno.h>
#include <math.h>
#include "color.h"
/*
* Illuminant D, or daylight locus, is is a "standard illuminant" used to
* describe natural daylight as we perceive it, and as such is how we expect
* bright, cold white light sources to look. This is different from the
* planckian locus due to the effects of the atmosphere on sunlight travelling
* through it.
*
* It is on this locus that D65, the whitepoint used by most monitors and
* assumed by display servers, is defined.
*
* This approximation is strictly speaking only well-defined between 4000K and
* 25000K, but we stretch it a bit further down for transition purposes.
*/
static int illuminant_d(int temp, double *x, double *y) {
// https://en.wikipedia.org/wiki/Standard_illuminant#Illuminant_series_D
if (temp >= 2500 && temp <= 7000) {
*x = 0.244063 +
0.09911e3 / temp +
2.9678e6 / pow(temp, 2) -
4.6070e9 / pow(temp, 3);
} else if (temp > 7000 && temp <= 25000) {
*x = 0.237040 +
0.24748e3 / temp +
1.9018e6 / pow(temp, 2) -
2.0064e9 / pow(temp, 3);
} else {
errno = EINVAL;
return -1;
}
*y = (-3 * pow(*x, 2)) + (2.870 * (*x)) - 0.275;
return 0;
}
/*
* Planckian locus, or black body locus, describes the color of a black body at
* a certain temperatures directly at its source, rather than observed through
* a thick atmosphere.
*
* While we are used to bright light coming from afar and going through the
* atmosphere, we are used to seeing dim incandescent light sources from close
* enough for the atmosphere to not affect its perception, dictating how we
* expect dim, warm light sources to look.
*
* This approximation is only valid from 1667K to 25000K.
*/
static int planckian_locus(int temp, double *x, double *y) {
// https://en.wikipedia.org/wiki/Planckian_locus#Approximation
if (temp >= 1667 && temp <= 4000) {
*x = -0.2661239e9 / pow(temp, 3) -
0.2343589e6 / pow(temp, 2) +
0.8776956e3 / temp +
0.179910;
if (temp <= 2222) {
*y = -1.1064814 * pow(*x, 3) -
1.34811020 * pow(*x, 2) +
2.18555832 * (*x) -
0.20219683;
} else {
*y = -0.9549476 * pow(*x, 3) -
1.37418593 * pow(*x, 2) +
2.09137015 * (*x) -
0.16748867;
}
} else if (temp > 4000 && temp < 25000) {
*x = -3.0258469e9 / pow(temp, 3) +
2.1070379e6 / pow(temp, 2) +
0.2226347e3 / temp +
0.240390;
*y = 3.0817580 * pow(*x, 3) -
5.87338670 * pow(*x, 2) +
3.75112997 * (*x) -
0.37001483;
} else {
errno = EINVAL;
return -1;
}
return 0;
}
static double clamp(double value) {
if (value > 1.0) {
return 1.0;
} else if (value < 0.0) {
return 0.0;
} else {
return value;
}
}
static struct rgb xyz_to_rgb(const struct xyz *xyz) {
// http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html
return (struct rgb) {
.r = pow(clamp(3.2404542 * xyz->x - 1.5371385 * xyz->y - 0.4985314 * xyz->z), 1.0 / 2.2),
.g = pow(clamp(-0.9692660 * xyz->x + 1.8760108 * xyz->y + 0.0415560 * xyz->z), 1.0 / 2.2),
.b = pow(clamp(0.0556434 * xyz->x - 0.2040259 * xyz->y + 1.0572252 * xyz->z), 1.0 / 2.2)
};
}
static void rgb_normalize(struct rgb *rgb) {
double maxw = fmax(rgb->r, fmax(rgb->g, rgb->b));
rgb->r /= maxw;
rgb->g /= maxw;
rgb->b /= maxw;
}
struct rgb calc_whitepoint(int temp) {
if (temp == 6500) {
return (struct rgb) {.r = 1.0, .g = 1.0, .b = 1.0};
}
// We are not trying to calculate the accurate whitepoint, but rather
// an expected observed whitepoint. We generally expect dim and warm
// light sources to follow the planckian locus, while we expect bright
// and cold light sources to follow the daylight locus. There is no
// "correct" way to transition between these two curves, and so the
// goal is purely to be subjectively pleasant/non-jarring.
//
// A smooth transition between the two in the range between 2500K and
// 4000K seems to do the trick for now.
struct xyz wp;
if (temp >= 25000) {
illuminant_d(25000, &wp.x, &wp.y);
} else if (temp >= 4000) {
illuminant_d(temp, &wp.x, &wp.y);
} else if (temp >= 2500) {
double x1, y1, x2, y2;
illuminant_d(temp, &x1, &y1);
planckian_locus(temp, &x2, &y2);
double factor = (4000. - temp) / 1500.;
double sinefactor = (cos(M_PI*factor) + 1.0) / 2.0;
wp.x = x1 * sinefactor + x2 * (1.0 - sinefactor);
wp.y = y1 * sinefactor + y2 * (1.0 - sinefactor);
} else {
planckian_locus(temp >= 1667 ? temp : 1667, &wp.x, &wp.y);
}
wp.z = 1.0 - wp.x - wp.y;
struct rgb wp_rgb = xyz_to_rgb(&wp);
rgb_normalize(&wp_rgb);
return wp_rgb;
}
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