Add blackbody color temperature function

src/game/astronomy/blackbody.cpp

@@ -0,0 +1,56 @@
+/*
+ * Copyright (C) 2020  Christopher J. Howard
+ *
+ * This file is part of Antkeeper source code.
+ *
+ * Antkeeper source code is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * Antkeeper source code is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#include "blackbody.hpp"
+#include <cmath>
+
+namespace ast
+{
+
+/// Transforms colors from CIE XYZ to linear RGB
+static constexpr double3x3 xyz_to_rgb =
+{
+	3.2404542, -0.9692660, 0.0556434,
+	-1.5371385, 1.8760108, -0.2040259,
+	-0.4985314, 0.0415560, 1.0572252
+};
+
+double3 blackbody(double t, double l)
+{
+	// Approximate the Planckian locus in CIE 1960 color space
+	double tt = t * t;
+    double u = (0.860117757 + 1.54118254e-4 * t + 1.28641212e-7 * tt) / (1.0 + 8.42420235e-4 * t + 7.08145163e-7 * tt);
+    double v = (0.317398726 + 4.22806245e-5 * t + 4.20481691e-8 * tt) / (1.0 - 2.89741816e-5 * t + 1.61456053e-7 * tt);
+	
+	// (u, v) -> (x, y)
+	double denom = (u * 2.0 - v * 8.0 + 4.0);
+	double x = u * 3.0 / denom;
+	double y = v * 2.0 / denom;
+	
+	// (x, y) -> CIE XYZ
+	double3 xyz;
+	xyz.y = l;
+	xyz.x = (xyz.y / y) * x;
+	xyz.z = (xyz.y / y) * (1.0 - x - y);
+	
+	/// CIE XYZ -> linear RGB
+	return xyz_to_rgb * xyz;
+}
+
+} // namespace ast

src/game/astronomy/blackbody.hpp

@@ -0,0 +1,42 @@
+/*
+ * Copyright (C) 2020  Christopher J. Howard
+ *
+ * This file is part of Antkeeper source code.
+ *
+ * Antkeeper source code is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * Antkeeper source code is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifndef ANTKEEPER_BLACKBODY_HPP
+#define ANTKEEPER_BLACKBODY_HPP
+
+#include "utility/fundamental-types.hpp"
+
+namespace ast
+{
+
+/**
+ * Calculates the color of an incandescent black-body.
+ *
+ * @param t Temperature, in Kelvin.
+ * @param l Luminance value.
+ * @return Linear RGB color.
+ *
+ * @see https://en.wikipedia.org/wiki/Planckian_locus
+ * @see https://en.wikipedia.org/wiki/CIE_1960_color_space
+ */
+double3 blackbody(double t, double l);
+
+} // namespace ast
+
+#endif // ANTKEEPER_BLACKBODY_HPP