wlsunset/color_math.c

#define _USE_MATH_DEFINES
#define _XOPEN_SOURCE 700
#define _POSIX_C_SOURCE 200809L
#include <math.h>
#include <errno.h>
#include <time.h>
#include "color_math.h"

static double SOLAR_START_TWILIGHT = RADIANS(90.833 + 6.0);
static double SOLAR_END_TWILIGHT   = RADIANS(90.833 - 3.0);

static int days_in_year(int year) {
	int leap = (year % 4 == 0 && year % 100 != 0) || year % 400 == 0;
	return leap ? 366 : 365;
}

static double date_orbit_angle(struct tm *tm) {
	return 2 * M_PI / (double)days_in_year(tm->tm_year + 1900) * tm->tm_yday;
}

static double equation_of_time(double orbit_angle) {
	// https://www.esrl.noaa.gov/gmd/grad/solcalc/solareqns.PDF
	return 4 * (0.000075 +
		0.001868 * cos(orbit_angle) -
		0.032077 * sin(orbit_angle) -
		0.014615 * cos(2*orbit_angle) -
		0.040849 * sin(2*orbit_angle));
}

static double sun_declination(double orbit_angle) {
	// https://www.esrl.noaa.gov/gmd/grad/solcalc/solareqns.PDF
	return 0.006918 -
		0.399912 * cos(orbit_angle) +
		0.070257 * sin(orbit_angle) -
		0.006758 * cos(2*orbit_angle) +
		0.000907 * sin(2*orbit_angle) -
		0.002697 * cos(3*orbit_angle) +
		0.00148 * sin(3*orbit_angle);
}

static double sun_hour_angle(double latitude, double declination, double target_sun) {
	// https://www.esrl.noaa.gov/gmd/grad/solcalc/solareqns.PDF
	return acos(cos(target_sun) /
		cos(latitude) * cos(declination) -
		tan(latitude) * tan(declination));
}

static time_t hour_angle_to_time(double hour_angle, double eqtime) {
	// https://www.esrl.noaa.gov/gmd/grad/solcalc/solareqns.PDF
	return DEGREES((4.0 * M_PI - 4 * hour_angle - eqtime) * 60);
}

static enum sun_condition condition(double latitude_rad, double sun_declination) {
	int sign_lat = signbit(latitude_rad) == 0;
	int sign_decl = signbit(sun_declination) == 0;
	return sign_lat == sign_decl ? MIDNIGHT_SUN : POLAR_NIGHT;
}

enum sun_condition calc_sun(struct tm *tm, double latitude, struct sun *sun) {
	double orbit_angle = date_orbit_angle(tm);
	double decl = sun_declination(orbit_angle);
	double eqtime = equation_of_time(orbit_angle);

	double ha_twilight = sun_hour_angle(latitude, decl, SOLAR_START_TWILIGHT);
	double ha_daylight = sun_hour_angle(latitude, decl, SOLAR_END_TWILIGHT);

	sun->dawn = hour_angle_to_time(fabs(ha_twilight), eqtime);
	sun->dusk = hour_angle_to_time(-fabs(ha_twilight), eqtime);
	sun->sunrise = hour_angle_to_time(fabs(ha_daylight), eqtime);
	sun->sunset = hour_angle_to_time(-fabs(ha_daylight), eqtime);

	return isnan(ha_twilight) || isnan(ha_daylight) ?
		condition(latitude, decl) : NORMAL;
}

/*
 * 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 srgb_gamma(double value, double gamma) {
	// https://en.wikipedia.org/wiki/SRGB
	if (value <= 0.0031308) {
		return 12.92 * value;
	} else {
		return pow(1.055 * value, 1.0/gamma) - 0.055;
	}
}

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_srgb(const struct xyz *xyz) {
	// http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html
	return (struct rgb) {
		.r = srgb_gamma(clamp(3.2404542 * xyz->x - 1.5371385 * xyz->y - 0.4985314 * xyz->z), 2.2),
		.g = srgb_gamma(clamp(-0.9692660 * xyz->x + 1.8760108 * xyz->y + 0.0415560 * xyz->z), 2.2),
		.b = srgb_gamma(clamp(0.0556434 * xyz->x - 0.2040259 * xyz->y + 1.0572252 * xyz->z), 2.2)
	};
}

static void srgb_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_srgb(&wp);
	srgb_normalize(&wp_rgb);

	return wp_rgb;
}