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1 files changed, 152 insertions, 0 deletions

diff --git a/color.c b/color.c
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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;
+}