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+// SPDX-License-Identifier: GPL-2.0-or-later
+/*
+ * HSLuv-C: Human-friendly HSL
+ *
+ * Authors:
+ * 2015 Alexei Boronine (original idea, JavaScript implementation)
+ * 2015 Roger Tallada (Obj-C implementation)
+ * 2017 Martin Mitas (C implementation, based on Obj-C implementation)
+ * 2021 Massinissa Derriche (C++ implementation for Inkscape, based on C implementation)
+ *
+ * Copyright (C) 2021 Authors
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+ * IN THE SOFTWARE.
+ */
+
+#include "hsluv.h"
+
+#include <limits>
+#include <cmath>
+#include <algorithm>
+#include <2geom/line.h>
+#include <2geom/ray.h>
+
+namespace Hsluv {
+
+/* for RGB */
+static const Triplet m[3] = {
+ { 3.24096994190452134377, -1.53738317757009345794, -0.49861076029300328366 },
+ { -0.96924363628087982613, 1.87596750150772066772, 0.04155505740717561247 },
+ { 0.05563007969699360846, -0.20397695888897656435, 1.05697151424287856072 }
+};
+
+/* for XYZ */
+static const Triplet m_inv[3] = {
+ { 0.41239079926595948129, 0.35758433938387796373, 0.18048078840183428751 },
+ { 0.21263900587151035754, 0.71516867876775592746, 0.07219231536073371500 },
+ { 0.01933081871559185069, 0.11919477979462598791, 0.95053215224966058086 }
+};
+
+static const double REF_U = 0.19783000664283680764;
+static const double REF_V = 0.46831999493879100370;
+
+// CIE LUV constants
+static const double KAPPA = 903.29629629629629629630;
+static const double EPSILON = 0.00885645167903563082;
+
+/**
+ * Calculate the bounds of the Luv colors in RGB gamut.
+ *
+ * @param l Lightness. Between 0.0 and 100.0.
+ * @return Bounds of Luv colors in RGB gamut.
+ */
+std::array<Geom::Line, 6> get_bounds(double l)
+{
+ std::array<Geom::Line, 6> bounds;
+
+ double tl = l + 16.0;
+ double sub1 = (tl * tl * tl) / 1560896.0;
+ double sub2 = (sub1 > EPSILON ? sub1 : (l / KAPPA));
+ int channel;
+ int t;
+
+ for(channel = 0; channel < 3; channel++) {
+ double m1 = m[channel][0];
+ double m2 = m[channel][1];
+ double m3 = m[channel][2];
+
+ for (t = 0; t < 2; t++) {
+ double top1 = (284517.0 * m1 - 94839.0 * m3) * sub2;
+ double top2 = (838422.0 * m3 + 769860.0 * m2 + 731718.0 * m1) * l * sub2 - 769860.0 * t * l;
+ double bottom = (632260.0 * m3 - 126452.0 * m2) * sub2 + 126452.0 * t;
+
+ bounds[channel * 2 + t].setCoefficients(top1, -bottom, top2);
+ }
+ }
+
+ return bounds;
+}
+
+/**
+ * Calculate the maximum in gamut chromaticity for the given luminance and hue.
+ *
+ * @param l Luminance.
+ * @param h Hue.
+ * @return The maximum chromaticity.
+ */
+static double max_chroma_for_lh(double l, double h)
+{
+ double min_len = std::numeric_limits<double>::max();
+ auto const ray = Geom::Ray(Geom::Point(0, 0), Geom::rad_from_deg(h));
+
+ for (auto const &line : get_bounds(l)) {
+ auto intersections = line.intersect(ray);
+ if (intersections.empty()) {
+ continue;
+ }
+ double len = intersections[0].point().length();
+
+ if (len >= 0 && len < min_len) {
+ min_len = len;
+ }
+ }
+
+ return min_len;
+}
+
+/**
+ * Calculate the dot product of the given arrays.
+ *
+ * @param t1 The first array.
+ * @param t2 The second array.
+ * @return The resulting dot product.
+ */
+static double dot_product(const Triplet &t1, const Triplet &t2)
+{
+ return (t1[0] * t2[0] + t1[1] * t2[1] + t1[2] * t2[2]);
+}
+
+/**
+ * Convenience function used for RGB conversions.
+ *
+ * @param c Value.
+ * @return RGB color component.
+ */
+double from_linear(double c)
+{
+ if (c <= 0.0031308) {
+ return 12.92 * c;
+ } else {
+ return 1.055 * std::pow(c, 1.0 / 2.4) - 0.055;
+ }
+}
+
+/**
+ * Convenience function used for RGB conversions.
+ *
+ * @param c Value.
+ * @return XYZ color component.
+ */
+double to_linear(double c)
+{
+ if (c > 0.04045) {
+ return std::pow((c + 0.055) / 1.055, 2.4);
+ } else {
+ return c / 12.92;
+ }
+}
+
+/**
+ * @overload
+ * @param t RGB color components.
+ * @return XYZ color components.
+ */
+static Triplet to_linear(const Triplet &t)
+{
+ return {
+ to_linear(t[0]),
+ to_linear(t[1]),
+ to_linear(t[2])
+ };
+}
+
+/**
+ * Convert a color from the the XYZ colorspace to the RGB colorspace.
+ *
+ * @param in_out[in,out] The XYZ color converted to a RGB color.
+ */
+static void xyz2rgb(Triplet &in_out)
+{
+ Triplet result;
+ for (size_t i : {0, 1, 2}) {
+ result[i] = from_linear(dot_product(m[i], in_out));
+ }
+ in_out = result;
+}
+
+/**
+ * Convert a color from the the RGB colorspace to the XYZ colorspace.
+ *
+ * @param in_out[in,out] The RGB color converted to a XYZ color.
+ */
+static void rgb2xyz(Triplet &in_out)
+{
+ Triplet rgbl = to_linear(in_out);
+ for (size_t i : {0, 1, 2}) {
+ in_out[i] = dot_product(m_inv[i], rgbl);
+ }
+}
+
+/**
+ * Utility function used to convert from the XYZ colorspace to CIELuv.
+ * https://en.wikipedia.org/wiki/CIELUV
+ *
+ * @param y Y component of the XYZ color.
+ * @return Luminance component of Luv color.
+ */
+static double y2l(double y)
+{
+ if (y <= EPSILON)
+ return y * KAPPA;
+ else
+ return 116.0 * std::cbrt(y) - 16.0;
+}
+
+/**
+ * Utility function used to convert from CIELuv colorspace to XYZ.
+ *
+ * @param l Luminance component of Luv color.
+ * @return Y component of the XYZ color.
+ */
+static double l2y(double l)
+{
+ if (l <= 8.0) {
+ return l / KAPPA;
+ } else {
+ double x = (l + 16.0) / 116.0;
+ return (x * x * x);
+ }
+}
+
+/**
+ * Convert a color from the the XYZ colorspace to the Luv colorspace.
+ *
+ * @param in_out[in,out] The XYZ color converted to a Luv color.
+ */
+static void xyz2luv(Triplet &in_out)
+{
+ double const denominator = in_out[0] + (15.0 * in_out[1]) + (3.0 * in_out[2]);
+ double var_u = 4.0 * in_out[0] / denominator;
+ double var_v = 9.0 * in_out[1] / denominator;
+ double l = y2l(in_out[1]);
+ double u = 13.0 * l * (var_u - REF_U);
+ double v = 13.0 * l * (var_v - REF_V);
+
+ in_out[0] = l;
+ if (l < 0.00000001) {
+ in_out[1] = 0.0;
+ in_out[2] = 0.0;
+ } else {
+ in_out[1] = u;
+ in_out[2] = v;
+ }
+}
+
+/**
+ * Convert a color from the the Luv colorspace to the XYZ colorspace.
+ *
+ * @param in_out[in,out] The Luv color converted to a XYZ color.
+ */
+static void luv2xyz(Triplet &in_out)
+{
+ if (in_out[0] <= 0.00000001) {
+ /* Black would create a divide-by-zero error. */
+ in_out[0] = 0.0;
+ in_out[1] = 0.0;
+ in_out[2] = 0.0;
+ return;
+ }
+
+ double var_u = in_out[1] / (13.0 * in_out[0]) + REF_U;
+ double var_v = in_out[2] / (13.0 * in_out[0]) + REF_V;
+ double y = l2y(in_out[0]);
+ double x = -(9.0 * y * var_u) / ((var_u - 4.0) * var_v - var_u * var_v);
+ double z = (9.0 * y - (15.0 * var_v * y) - (var_v * x)) / (3.0 * var_v);
+
+ in_out[0] = x;
+ in_out[1] = y;
+ in_out[2] = z;
+}
+
+/**
+ * Convert a color from the the Luv colorspace to the LCH colorspace.
+ *
+ * @param in_out[in,out] The Luv color converted to a LCH color.
+ */
+static void luv2lch(Triplet &in_out)
+{
+ double l = in_out[0];
+ auto uv = Geom::Point(in_out[1], in_out[2]);
+ double h;
+ double const c = uv.length();
+
+ /* Grays: disambiguate hue */
+ if (c < 0.00000001) {
+ h = 0;
+ } else {
+ h = Geom::deg_from_rad(Geom::atan2(uv));
+ if (h < 0.0) {
+ h += 360.0;
+ }
+ }
+
+ in_out[0] = l;
+ in_out[1] = c;
+ in_out[2] = h;
+}
+
+/**
+ * Convert a color from the the LCH colorspace to the Luv colorspace.
+ *
+ * @param in_out[in,out] The LCH color converted to a Luv color.
+ */
+static void lch2luv(Triplet &in_out)
+{
+ double sinhrad, coshrad;
+ Geom::sincos(Geom::rad_from_deg(in_out[2]), sinhrad, coshrad);
+ double u = coshrad * in_out[1];
+ double v = sinhrad * in_out[1];
+
+ in_out[1] = u;
+ in_out[2] = v;
+}
+
+/**
+ * Convert a color from the the HSLuv colorspace to the LCH colorspace.
+ *
+ * @param in_out[in,out] The HSLuv color converted to a LCH color.
+ */
+static void hsluv2lch(Triplet &in_out)
+{
+ double h = in_out[0];
+ double s = in_out[1];
+ double l = in_out[2];
+ double c;
+
+ /* White and black: disambiguate chroma */
+ if(l > 99.9999999 || l < 0.00000001) {
+ c = 0.0;
+ } else {
+ c = max_chroma_for_lh(l, h) / 100.0 * s;
+ }
+
+ /* Grays: disambiguate hue */
+ if (s < 0.00000001) {
+ h = 0.0;
+ }
+
+ in_out[0] = l;
+ in_out[1] = c;
+ in_out[2] = h;
+}
+
+/**
+ * Convert a color from the the LCH colorspace to the HSLuv colorspace.
+ *
+ * @param in_out[in,out] The LCH color converted to a HSLuv color.
+ */
+static void lch2hsluv(Triplet &in_out)
+{
+ double l = in_out[0];
+ double c = in_out[1];
+ double h = in_out[2];
+ double s;
+
+ /* White and black: disambiguate saturation */
+ if (l > 99.9999999 || l < 0.00000001) {
+ s = 0.0;
+ } else {
+ s = c / max_chroma_for_lh(l, h) * 100.0;
+ }
+
+ /* Grays: disambiguate hue */
+ if (c < 0.00000001) {
+ h = 0.0;
+ }
+
+ in_out[0] = h;
+ in_out[1] = s;
+ in_out[2] = l;
+}
+
+// Interface functions
+Triplet luv_to_rgb(double l, double u, double v)
+{
+ Triplet result{l, u, v};
+ luv2xyz(result);
+ xyz2rgb(result);
+
+ for (size_t i : {0, 1, 2}) {
+ result[i] = std::clamp(result[i], 0.0, 1.0);
+ }
+ return result;
+}
+
+Triplet hsluv_to_luv(double h, double s, double l)
+{
+ Triplet result{h, s, l};
+ hsluv2lch(result);
+ lch2luv(result);
+ return result;
+}
+
+Triplet luv_to_hsluv(double l, double u, double v)
+{
+ Triplet result{l, u, v};
+ luv2lch(result);
+ lch2hsluv(result);
+ return result;
+}
+
+Triplet rgb_to_hsluv(double r, double g, double b)
+{
+ Triplet result{r, g, b};
+ rgb2xyz(result);
+ xyz2luv(result);
+ luv2lch(result);
+ lch2hsluv(result);
+ return result;
+}
+
+Triplet hsluv_to_rgb(double h, double s, double l)
+{
+ Triplet result{h, s, l};
+ hsluv2lch(result);
+ lch2luv(result);
+ luv2xyz(result);
+ xyz2rgb(result);
+
+ for (size_t i : {0, 1, 2}) {
+ result[i] = std::clamp(result[i], 0.0, 1.0);
+ }
+ return result;
+}
+
+Triplet hsluv_to_luv(double *hsl)
+{
+ return hsluv_to_luv(hsl[0], hsl[1], hsl[2]);
+}
+
+double perceptual_lightness(double l)
+{
+ return l <= 0.885645168 ? l * 0.09032962963 : std::cbrt(l) * 0.249914424 - 0.16;
+}
+
+double rgb_to_perceptual_lightness(Triplet const &rgb)
+{
+ return perceptual_lightness(rgb_to_hsluv(rgb[0], rgb[1], rgb[2])[2]);
+}
+
+std::pair<double, double> get_contrasting_color(double l)
+{
+ double constexpr l_threshold = 0.85;
+ if (l > l_threshold) { // Draw dark over light.
+ auto t = (l - l_threshold) / (1.0 - l_threshold);
+ return {0.0, 0.4 - 0.1 * t};
+ } else { // Draw light over dark.
+ auto t = (l_threshold - l) / l_threshold;
+ return {1.0, 0.6 + 0.1 * t};
+ }
+}
+
+} // namespace Hsluv
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