Integrate blackbody lighting with atmospheric scattering

src/ecs/components/atmosphere-component.hpp

@@ -27,19 +27,19 @@ namespace ecs {
 /// Atmosphere
 struct atmosphere_component
 {
-	/// Radius of the outer atmosphere, in meters.
-	double exosphere_radius;
+	/// Altitude of the outer atmosphere, in meters.
+	double exosphere_altitude;
 	
-	/// Rayleigh scale height
+	/// Rayleigh scale height, in meters.
 	double rayleigh_scale_height;
 	
-	/// Mie scale height
+	/// Mie scale height, in meters.
 	double mie_scale_height;
 	
-	/// Rayleigh scattering coefficients
+	/// (Dependent) Rayleigh scattering coefficients
 	double3 rayleigh_scattering_coefficients;
 	
-	/// Mie scattering coefficients
+	/// (Dependent) Mie scattering coefficients
 	double3 mie_scattering_coefficients;
 };
 

src/ecs/components/blackbody-component.hpp

@@ -27,6 +27,21 @@ struct blackbody_component
 {
 	/// Effective temperature, in Kelvin.
 	double temperature;
+	
+	/// Blackbody radius, in meters.
+	double radius;
+	
+	/// (Dependent) Blackbody radiant flux, in watts.
+	double radiant_flux;
+	
+	/// (Dependent) Blackbody luminous flux, in lumens.
+	double luminous_flux;
+	
+	/// (Dependent) Blackbody luminous intensity, in lumens per steradian.
+	double luminous_intensity;
+	
+	/// (Dependent) ACEScg color
+	double3 color;
 };
 
 } // namespace ecs

src/ecs/systems/astronomy-system.cpp

@@ -36,47 +36,64 @@
 namespace ecs {
 
 /**
- * Calculates the optical depth between two points.
+ * Approximates the density of exponentially-distributed atmospheric particles between two points using the trapezoidal rule.
  *
- * @param start Start point.
- * @param end End point.
- * @param sample_count Number of samples to take between the start and end points.
- * @param scale_height Scale height of the atmospheric particles to measure.
+ * @param a Start point.
+ * @param b End point.
+ * @param r Radius of the planet.
+ * @param sh Scale height of the atmospheric particles.
+ * @param n Number of samples.
  */
 template <class T>
-T transmittance(math::vector3<T> start, math::vector3<T> end, std::size_t sample_count, T scale_height)
+T optical_depth(const math::vector3<T>& a, const math::vector3<T>& b, T r, T sh, std::size_t n)
 {
-	const T inverse_scale_height = T(1) / -scale_height;
+	T inverse_sh = T(-1) / sh;
 	
-	math::vector3<T> direction = end - start;
-	T distance = length(direction);
-	direction /= distance;
+	T h = math::length(b - a) / T(n);
 	
-	// Calculate the distance between each sample point
-	T step_distance = distance / T(sample_count);
+	math::vector3<T> dy = (b - a) / T(n);
+	math::vector3<T> y = a + dy;
 	
-	// Sum the atmospheric particle densities at each sample point
-	T total_density = 0.0;
-	math::vector3<T> sample_point = start;
-	for (std::size_t i = 0; i < sample_count; ++i)
+	T f_x = std::exp((length(a) - r) * inverse_sh);
+	T f_y = std::exp((length(y) - r) * inverse_sh);
+	T sum = (f_x + f_y);
+	
+	for (std::size_t i = 1; i < n; ++i)
 	{
-		// Determine altitude of sample point
-		T altitude = length(sample_point);
-		
-		// Calculate atmospheric particle density at sample altitude
-		T density = exp(altitude * inverse_scale_height);
-		
-		// Add density to the total density
-		total_density += density;
-		
-		// Advance to next sample point
-		sample_point += direction * step_distance;
+		f_x = f_y;
+		y += dy;
+		f_y = std::exp((length(y) - r) * inverse_sh);
+		sum += (f_x + f_y);
 	}
 	
-	// Scale the total density by the step distance
-	return total_density * step_distance;
+	return sum / T(2) * h;
+}
+
+template <class T>
+math::vector3<T> transmittance(T depth_r, T depth_m, T depth_o, const math::vector3<T>& beta_r, const math::vector3<T>& beta_m)
+{
+	math::vector3<T> transmittance_r = beta_r * depth_r;
+	math::vector3<T> transmittance_m = beta_m * depth_m;
+	math::vector3<T> transmittance_o = {0, 0, 0};
+	
+	math::vector3<T> t = transmittance_r + transmittance_m + transmittance_o;
+	t.x = std::exp(-t.x);
+	t.y = std::exp(-t.y);
+	t.z = std::exp(-t.z);
+	
+	return t;
+}
+
+double calc_beta_r(double wavelength, double ior, double density)
+{
+	double wavelength2 = wavelength * wavelength;
+	double ior2m1 = ior * ior - 1.0;
+	double num = 8.0 * (math::pi<double> * math::pi<double> * math::pi<double>) * ior2m1 * ior2m1;
+	double den = 3.0 * density * (wavelength2 * wavelength2);
+	return num / den;
 }
 
+
 astronomy_system::astronomy_system(ecs::registry& registry):
 	entity_system(registry),
 	universal_time(0.0),
@@ -86,7 +103,13 @@ astronomy_system::astronomy_system(ecs::registry& registry):
 	reference_body_axial_rotation(0.0),
 	sun_light(nullptr),
 	sky_pass(nullptr)
-{}
+{
+	registry.on_construct<ecs::blackbody_component>().connect<&astronomy_system::on_blackbody_construct>(this);
+	registry.on_replace<ecs::blackbody_component>().connect<&astronomy_system::on_blackbody_replace>(this);
+	
+	registry.on_construct<ecs::atmosphere_component>().connect<&astronomy_system::on_atmosphere_construct>(this);
+	registry.on_replace<ecs::atmosphere_component>().connect<&astronomy_system::on_atmosphere_replace>(this);
+}
 
 void astronomy_system::update(double t, double dt)
 {
@@ -130,59 +153,45 @@ void astronomy_system::update(double t, double dt)
 		transform.local.translation = math::type_cast<float>(r_topocentric);
 	});
 	
-	// Get atmosphere component of reference body, if any
-	if (registry.has<ecs::atmosphere_component>(reference_body))
-	{
-		const ecs::atmosphere_component& atmosphere = registry.get<ecs::atmosphere_component>(reference_body);
-	}
-	
-	if (sun_light != nullptr)
-	{
-		const math::vector3<double> sun_position_inertial = {0, 0, 0};
-		const math::vector3<double> sun_forward_inertial = math::normalize(reference_orbit.state.r - sun_position_inertial);
-		const math::vector3<double> sun_up_inertial = {0, 0, 1};
+	// Update blackbody lighting
+	registry.view<blackbody_component, orbit_component>().each(
+	[&](ecs::entity entity, auto& blackbody, auto& orbit)
+	{		
+		// Calculate blackbody inertial basis
+		double3 blackbody_forward_inertial = math::normalize(reference_orbit.state.r - orbit.state.r);
+		double3 blackbody_up_inertial = {0, 0, 1};
 		
-		// Transform sun position, forward, and up vectors into topocentric space
-		const math::vector3<double> sun_position_topocentric = inertial_to_topocentric * sun_position_inertial;
-		const math::vector3<double> sun_forward_topocentric = inertial_to_topocentric.rotation * sun_forward_inertial;
-		const math::vector3<double> sun_up_topocentric = inertial_to_topocentric.rotation * sun_up_inertial;
+		// Transform blackbody inertial position and basis into topocentric space
+		double3 blackbody_position_topocentric = inertial_to_topocentric * orbit.state.r;
+		double3 blackbody_forward_topocentric = inertial_to_topocentric.rotation * blackbody_forward_inertial;
+		double3 blackbody_up_topocentric = inertial_to_topocentric.rotation * blackbody_up_inertial;
 		
-		// Update sun light transform
-		sun_light->set_translation(math::type_cast<float>(sun_position_topocentric));
-		sun_light->set_rotation
-		(
-			math::look_rotation
-			(
-				math::type_cast<float>(sun_forward_topocentric),
-				math::type_cast<float>(sun_up_topocentric)
-			)
-		);
+		// Calculate distance from observer to blackbody
+		const double meters_per_au = 1.496e+11;
+		double blackbody_distance = math::length(blackbody_position_topocentric) * meters_per_au;
 		
-		// Convert sun topocentric Cartesian coordinates to spherical coordinates
-		math::vector3<double> sun_az_el = geom::cartesian::to_spherical(ezs_to_sez * sun_position_topocentric);
-		sun_az_el.z = math::pi<double> - sun_az_el.z;
+		// Calculate blackbody illuminance according to distance
+		double blackbody_illuminance = blackbody.luminous_intensity / (blackbody_distance * blackbody_distance);
 		
-		//std::cout << "el: " << math::degrees(sun_az_el.y) << "; az: " << math::degrees(sun_az_el.z) << std::endl;
+		// Get blackbody color
+		double3 blackbody_color = blackbody.color;
 		
-		// If the reference body has an atmosphere
-		if (registry.has<ecs::atmosphere_component>(reference_body))
+		// Get atmosphere component of reference body, if any
+		if (this->registry.has<ecs::atmosphere_component>(reference_body))
 		{
-			// Get the atmosphere component of the reference body
-			const auto& atmosphere = registry.get<ecs::atmosphere_component>(reference_body);
+			const ecs::atmosphere_component& atmosphere = this->registry.get<ecs::atmosphere_component>(reference_body);
 			
-			const double meters_per_au = 1.496e+11;
 			const double earth_radius_au = 4.26352e-5;
 			const double earth_radius_m = earth_radius_au * meters_per_au;
-			const double observer_altitude_m = (observer_location[0] - earth_radius_au) * meters_per_au;
 			
-			// Altitude of observer in meters			
+			// Altitude of observer in meters	
 			geom::ray<double> sample_ray;
-			sample_ray.origin = {0, observer_altitude_m, 0};
-			sample_ray.direction = math::normalize(sun_position_topocentric);
+			sample_ray.origin = {0, observer_location[0] * meters_per_au, 0};
+			sample_ray.direction = math::normalize(blackbody_position_topocentric);
 			
 			geom::sphere<double> exosphere;
-			exosphere.center = {0, -earth_radius_m, 0};
-			exosphere.radius = atmosphere.exosphere_radius;
+			exosphere.center = {0, 0, 0};
+			exosphere.radius = earth_radius_m + atmosphere.exosphere_altitude;
 			
 			auto intersection_result = geom::ray_sphere_intersection(sample_ray, exosphere);
 			
@@ -191,50 +200,44 @@ void astronomy_system::update(double t, double dt)
 				double3 sample_start = sample_ray.origin;
 				double3 sample_end = sample_ray.extrapolate(std::get<2>(intersection_result));
 				
-				double transmittance_rayleigh = transmittance(sample_start, sample_end, 16, atmosphere.rayleigh_scale_height);
-				double transmittance_mie = transmittance(sample_start, sample_end, 16, atmosphere.mie_scale_height);
-				
-				// Calculate attenuation due to atmospheric scattering
-				double3 scattering_attenuation =
-					atmosphere.rayleigh_scattering_coefficients * transmittance_rayleigh +
-					atmosphere.mie_scattering_coefficients * transmittance_mie;
-				scattering_attenuation.x = std::exp(-scattering_attenuation.x);
-				scattering_attenuation.y = std::exp(-scattering_attenuation.y);
-				scattering_attenuation.z = std::exp(-scattering_attenuation.z);
-				
-				double scattering_mean = (scattering_attenuation.x + scattering_attenuation.y + scattering_attenuation.z) / 3.0;
-				
-				const double sun_temperature = 5777.0;
-				const double sun_radius = 6.957e+8;
-				const double sun_surface_area = 4.0 * math::pi<double> * sun_radius * sun_radius;
-				
-				// Calculate distance attenuation
-				double sun_distance_m = math::length(sun_position_topocentric) * meters_per_au;
-				double distance_attenuation = 1.0 / (sun_distance_m * sun_distance_m);
-				
-				double sun_luminous_flux = blackbody_luminous_flux(sun_temperature, sun_radius);
-				double sun_luminous_intensity = sun_luminous_flux / (4.0 * math::pi<double>);
-				double sun_illuminance = sun_luminous_intensity / (sun_distance_m * sun_distance_m);
-				
-				std::cout << "distance atten: " << distance_attenuation << std::endl;
-				std::cout << "scatter atten: " << scattering_attenuation << std::endl;
-				
-				std::cout << "luminous flux: " << sun_luminous_flux << std::endl;
-				std::cout << "luminous intensity: " << sun_luminous_intensity << std::endl;
-				std::cout << "illuminance: " << sun_illuminance * scattering_mean << std::endl;
-				
+				double optical_depth_r = optical_depth(sample_start, sample_end, earth_radius_m, atmosphere.rayleigh_scale_height, 32);
+				double optical_depth_k = optical_depth(sample_start, sample_end, earth_radius_m, atmosphere.mie_scale_height, 32);
+				double optical_depth_o = 0.0;
 				
-				// Calculate sun color
-				double3 color_xyz = color::cct::to_xyz(sun_temperature);
-				double3 color_acescg = color::xyz::to_acescg(color_xyz);
+				double3 attenuation = transmittance(optical_depth_r, optical_depth_k, optical_depth_o, atmosphere.rayleigh_scattering_coefficients, atmosphere.mie_scattering_coefficients);
 				
-				sun_light->set_color(math::type_cast<float>(color_acescg * scattering_attenuation));
-				
-				sun_light->set_intensity(sun_illuminance);
+				// Attenuate blackbody color
+				blackbody_color *= attenuation;
 			}
 		}
-	}
+		
+		if (sun_light != nullptr)
+		{
+			// Update blackbody light transform
+			sun_light->set_translation(math::type_cast<float>(blackbody_position_topocentric));
+			sun_light->set_rotation
+			(
+				math::look_rotation
+				(
+					math::type_cast<float>(blackbody_forward_topocentric),
+					math::type_cast<float>(blackbody_up_topocentric)
+				)
+			);
+			
+			// Update blackbody light color and intensity
+			sun_light->set_color(math::type_cast<float>(blackbody_color));	
+			sun_light->set_intensity(static_cast<float>(blackbody_illuminance));
+			
+			// Pass blackbody params to sky pas
+			if (this->sky_pass)
+			{
+				this->sky_pass->set_sun_object(sun_light);
+				this->sky_pass->set_sun_color(math::type_cast<float>(blackbody.color * blackbody_illuminance));
+			}
+		}
+	});
 	
+	// Update sky pass topocentric frame
 	if (sky_pass != nullptr)
 	{
 		sky_pass->set_topocentric_frame
@@ -245,8 +248,6 @@ void astronomy_system::update(double t, double dt)
 				math::type_cast<float>(inertial_to_topocentric.rotation)
 			}
 		);
-		
-		sky_pass->set_sun_object(sun_light);
 	}
 }
 
@@ -307,15 +308,26 @@ void astronomy_system::set_sky_pass(::sky_pass* pass)
 	this->sky_pass = pass;
 }
 
-double astronomy_system::blackbody_luminous_flux(double t, double r)
+void astronomy_system::on_blackbody_construct(ecs::registry& registry, ecs::entity entity, ecs::blackbody_component& blackbody)
 {
+	on_blackbody_replace(registry, entity, blackbody);
+}
+
+void astronomy_system::on_blackbody_replace(ecs::registry& registry, ecs::entity entity, ecs::blackbody_component& blackbody)
+{
+	// Calculate surface area of spherical blackbody
+	const double surface_area = double(4) * math::pi<double> * blackbody.radius * blackbody.radius;
+	
+	// Calculate radiant flux
+	blackbody.radiant_flux = physics::light::blackbody::radiant_flux(blackbody.temperature, surface_area);
+	
 	// Blackbody spectral power distribution function
-	auto spd = [t](double x) -> double
+	auto spd = [blackbody](double x) -> double
 	{
 		// Convert nanometers to meters
 		x *= double(1e-9);
 		
-		return physics::light::blackbody::spectral_radiance<double>(t, x, physics::constants::speed_of_light<double>);
+		return physics::light::blackbody::spectral_radiance<double>(blackbody.temperature, x, physics::constants::speed_of_light<double>);
 	};
 	
 	// Luminous efficiency function (photopic)
@@ -331,16 +343,41 @@ double astronomy_system::blackbody_luminous_flux(double t, double r)
 	// Calculate luminous efficiency
 	const double efficiency = physics::light::luminous_efficiency<double>(spd, lef, samples.begin(), samples.end());
 	
-	// Calculate surface area of spherical blackbody
-	const double a = double(4) * math::pi<double> * r * r;
+	// Convert radiant flux to luminous flux
+	blackbody.luminous_flux = physics::light::watts_to_lumens<double>(blackbody.radiant_flux, efficiency);
 	
-	// Calculate radiant flux
-	const double radiant_flux = physics::light::blackbody::radiant_flux(t, a);
+	// Calculate luminous intensity from luminous flux
+	blackbody.luminous_intensity = blackbody.luminous_flux / (4.0 * math::pi<double>);
 	
-	// Convert radiant flux to luminous flux
-	const double luminous_flux = physics::light::watts_to_lumens<double>(radiant_flux, efficiency);
+	// Calculate blackbody color from temperature
+	double3 color_xyz = color::cct::to_xyz(blackbody.temperature);
+	blackbody.color = color::xyz::to_acescg(color_xyz);
+}
+
+void astronomy_system::on_atmosphere_construct(ecs::registry& registry, ecs::entity entity, ecs::atmosphere_component& atmosphere)
+{
+	on_atmosphere_replace(registry, entity, atmosphere);
+}
+
+void astronomy_system::on_atmosphere_replace(ecs::registry& registry, ecs::entity entity, ecs::atmosphere_component& atmosphere)
+{
+	// ACEScg wavelengths determined by matching wavelengths to XYZ, transforming XYZ to ACEScg, then selecting the max wavelengths for R, G, and B.
+	const double3 acescg_wavelengths_nm = {600.0, 540.0, 450.0};
+	const double3 acescg_wavelengths_m = acescg_wavelengths_nm * 1.0e-9;
+	
+	// Calculate Rayleigh scattering coefficients
+	const double air_ior = 1.0003;
+	const double molecular_density = 2.545e25;
+	double3 beta_r;
+	atmosphere.rayleigh_scattering_coefficients =
+	{
+		calc_beta_r(acescg_wavelengths_m.x, air_ior, molecular_density),
+		calc_beta_r(acescg_wavelengths_m.y, air_ior, molecular_density),
+		calc_beta_r(acescg_wavelengths_m.z, air_ior, molecular_density)
+	};
 	
-	return luminous_flux;
+	// Calculate Mie scattering coefficients
+	atmosphere.mie_scattering_coefficients = {2.0e-6, 2.0e-6, 2.0e-6};
 }
 
 } // namespace ecs

src/ecs/systems/astronomy-system.hpp

@@ -26,11 +26,13 @@
 #include "utility/fundamental-types.hpp"
 #include "physics/frame.hpp"
 #include "renderer/passes/sky-pass.hpp"
+#include "ecs/components/blackbody-component.hpp"
+#include "ecs/components/atmosphere-component.hpp"
 
 namespace ecs {
 
 /**
- * Calculates apparent properties of celestial bodies relative to an observer (magnitude, angular radius, horizontal coordinates) and modifies their model component and/or light component to render them accordingly.
+ * Calculates apparent properties of celestial bodies relative to an observer.
  */
 class astronomy_system:
 	public entity_system
@@ -86,14 +88,12 @@ public:
 	void set_sky_pass(sky_pass* pass);
 	
 private:
-	/**
-	 * Calculates the luminous flux of a spherical blackbody in vacuum using the CIE 1931 standard observer photopic luminosity function.
-	 *
-	 * @param t Temperature of the blackbody, in kelvin.
-	 * @param r Radius of the blackbody, in meters.
-	 * @return Luminous flux, in lumens.
-	 */
-	static double blackbody_luminous_flux(double t, double r);
+	void on_blackbody_construct(ecs::registry& registry, ecs::entity entity, ecs::blackbody_component& blackbody);
+	void on_blackbody_replace(ecs::registry& registry, ecs::entity entity, ecs::blackbody_component& blackbody);
+	
+	void on_atmosphere_construct(ecs::registry& registry, ecs::entity entity, ecs::atmosphere_component& atmosphere);
+	void on_atmosphere_replace(ecs::registry& registry, ecs::entity entity, ecs::atmosphere_component& atmosphere);
+
 	
 	double universal_time;
 	double time_scale;

src/game/states/play-state.cpp

@@ -114,7 +114,8 @@ void play_state_enter(game_context* ctx)
 		orbit.elements.ta = math::radians(0.0);
 		
 		ecs::blackbody_component blackbody;
-		blackbody.temperature = 5772.0;
+		blackbody.temperature = 5777.0;
+		blackbody.radius = 6.957e+8;
 		
 		ecs::transform_component transform;
 		transform.local = math::identity_transform<float>;
@@ -139,11 +140,9 @@ void play_state_enter(game_context* ctx)
 		
 		const double earth_radius_m = 6378e3;
 		ecs::atmosphere_component atmosphere;
-		atmosphere.exosphere_radius = earth_radius_m + 100e3;
+		atmosphere.exosphere_altitude = 80e3;
 		atmosphere.rayleigh_scale_height = 8000.0;
 		atmosphere.mie_scale_height = 1200.0;
-		atmosphere.rayleigh_scattering_coefficients = {5.8e-6, 1.35e-5, 3.31e-5};
-		atmosphere.mie_scattering_coefficients = {2e-6, 2e-6, 2e-6};
 		
 		ecs::transform_component transform;
 		transform.local = math::identity_transform<float>;

src/physics/atmosphere.hpp

@@ -0,0 +1,50 @@
+/*
+ * Copyright (C) 2021  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_PHYSICS_ATMOSPHERE_HPP
+#define ANTKEEPER_PHYSICS_ATMOSPHERE_HPP
+
+#include "physics/constants.hpp"
+#include <cmath>
+
+namespace physics {
+
+/// Atmosphere-related functions.
+namespace atmosphere {
+
+/**
+ * Calculates the density of exponentially-distributed atmospheric particles at a given altitude.
+ *
+ * @param d0 Density at sea level.
+ * @param z Height above sea level.
+ * @param sh Scale height of the particle type.
+ * @return Particle density at altitude.
+ *
+ * @see https://en.wikipedia.org/wiki/Scale_height
+ */
+T density(T d0, T z, T sh)
+{
+	return d0 * std::exp(-z / sh);
+}
+
+} // namespace atmosphere
+
+} // namespace physics
+
+#endif // ANTKEEPER_PHYSICS_ATMOSPHERE_HPP

src/physics/constants.hpp

@@ -25,18 +25,34 @@ namespace physics {
 /// Physical constants
 namespace constants {
 
+/**
+ * Avogadro number (N).
+ *
+ * @see https://physics.nist.gov/cgi-bin/cuu/Value?na
+ */
+template <class T>
+constexpr T avogadro = T(6.02214076e+23);
+
 /**
  * Boltzmann constant (k), in joule per kelvin.
  *
- * @see https://physics.nist.gov/cgi-bin/cuu/Value?k|search_for=universal_in!
+ * @see https://physics.nist.gov/cgi-bin/cuu/Value?k
  */
 template <class T>
 constexpr T boltzmann = T(1.380649e-23);
 
+/**
+ * Molar gas constant (R), in joule per kelvin per mole.
+ *
+ * @see https://en.wikipedia.org/wiki/Gas_constant
+ */
+template <class T>
+constexpr T gas = T(8.31446261815324);
+
 /**
  * Gravitational constant (G), in cubic meter per second squared per kilogram.
  *
- * @see https://physics.nist.gov/cgi-bin/cuu/Value?G|search_for=universal_in!
+ * @see https://physics.nist.gov/cgi-bin/cuu/Value?G
  */
 template <class T>
 constexpr T gravitational = T(6.67430e-11);
@@ -44,7 +60,7 @@ constexpr T gravitational = T(6.67430e-11);
 /**
  * Planck constant (h), in joule per hertz.
  *
- * @see https://physics.nist.gov/cgi-bin/cuu/Value?h|search_for=universal_in!
+ * @see https://physics.nist.gov/cgi-bin/cuu/Value?h
  */
 template <class T>
 constexpr T planck = T(6.62607015e-34);
@@ -60,7 +76,7 @@ constexpr T stefan_boltzmann = T(5.670374419184429453970996731889230875840122970
 /**
  * Speed of light in vacuum (c), in meters per second.
  *
- * @see https://physics.nist.gov/cgi-bin/cuu/Value?c|search_for=universal_in!
+ * @see https://physics.nist.gov/cgi-bin/cuu/Value?c
  */
 template <class T>
 constexpr T speed_of_light = T(299792458);

src/physics/light/photometry.hpp

@@ -45,8 +45,8 @@ T luminous_efficiency(UnaryOp1 spd, UnaryOp2 lef, InputIt first, InputIt last)
 		return spd(x) * lef(x);
 	};
 	
-	const T num = math::quadrature::trapezoid(spd_lef, first, last);
-	const T den = math::quadrature::trapezoid(spd, first, last);
+	const T num = math::quadrature::simpson(spd_lef, first, last);
+	const T den = math::quadrature::simpson(spd, first, last);
 	
 	return num / den;
 }

src/renderer/passes/sky-pass.cpp

@@ -43,6 +43,7 @@
 #include "geom/cartesian.hpp"
 #include "geom/spherical.hpp"
 #include "physics/orbit/orbit.hpp"
+#include "physics/light/photometry.hpp"
 #include <cmath>
 #include <stdexcept>
 #include <glad/glad.h>
@@ -68,6 +69,7 @@ sky_pass::sky_pass(gl::rasterizer* rasterizer, const gl::framebuffer* framebuffe
 	julian_day_tween(0.0, math::lerp<float, float>),
 	horizon_color_tween(float3{0.0f, 0.0f, 0.0f}, math::lerp<float3, float>),
 	zenith_color_tween(float3{1.0f, 1.0f, 1.0f}, math::lerp<float3, float>),
+	sun_color_tween(float3{1.0f, 1.0f, 1.0f}, math::lerp<float3, float>),
 	topocentric_frame_translation({0, 0, 0}, math::lerp<float3, float>),
 	topocentric_frame_rotation(math::quaternion<float>::identity(), math::nlerp<float>),
 	sun_object(nullptr)
@@ -122,17 +124,17 @@ sky_pass::sky_pass(gl::rasterizer* rasterizer, const gl::framebuffer* framebuffe
 		// Calculate XYZ color from color temperature
 		double3 color_xyz = color::cct::to_xyz(cct);
 		
-		// Transform XYZ from (assumed) D65 illuminant to ACES illuminant.
-		//color_xyz = color::xyz::cat::d65_to_aces(color_xyz);
-		
 		// Transform XYZ color to ACEScg colorspace
 		double3 color_acescg = color::xyz::to_acescg(color_xyz);
 		
-		// Convert apparent magnitude to lux
+		// Convert apparent magnitude to irradiance W/m2
 		double vmag_lux = astro::vmag_to_lux(vmag);
 		
-		// Normalized color luminance and scale by apparent magnitude
-		double3 scaled_color = color_acescg * vmag_lux;
+		// Convert irradiance to illuminance (using luminous efficiency of sun)
+		double illuminance = physics::light::watts_to_lumens<double>(vmag_lux, 0.13);
+		
+		// Scale color by illuminance
+		double3 scaled_color = color_acescg * illuminance;
 		
 		// Build vertex
 		*(star_vertex++) = static_cast<float>(position_inertial.x);
@@ -204,6 +206,8 @@ void sky_pass::render(render_context* context) const
 	float julian_day = julian_day_tween.interpolate(context->alpha);
 	float3 horizon_color = horizon_color_tween.interpolate(context->alpha);
 	float3 zenith_color = zenith_color_tween.interpolate(context->alpha);
+	float3 sun_color = sun_color_tween.interpolate(context->alpha);
+	
 	
 	// Construct tweened inertial to topocentric frame
 	physics::frame<float> topocentric_frame =
@@ -233,6 +237,8 @@ void sky_pass::render(render_context* context) const
 			horizon_color_input->upload(horizon_color);
 		if (zenith_color_input)
 			zenith_color_input->upload(zenith_color);
+		if (sun_color_input)
+			sun_color_input->upload(sun_color);
 		if (mouse_input)
 			mouse_input->upload(mouse_position);
 		if (resolution_input)
@@ -267,11 +273,14 @@ void sky_pass::render(render_context* context) const
 		rasterizer->draw_arrays(*sky_model_vao, sky_model_drawing_mode, sky_model_start_index, sky_model_index_count);
 	}
 	
+	glEnable(GL_BLEND);
+	//glBlendFunc(GL_SRC_ALPHA, GL_ONE);
+	glBlendFunc(GL_ONE, GL_ONE);
+	
 	// Draw moon model
 	if (moon_position.y >= -moon_angular_radius)
 	{
-		glEnable(GL_BLEND);
-		glBlendFunc(GL_SRC_ALPHA, GL_ONE);
+
 		
 		float moon_distance = (clip_near + clip_far) * 0.5f;		
 		float moon_radius = moon_angular_radius * moon_distance;
@@ -370,6 +379,7 @@ void sky_pass::set_sky_model(const model* model)
 				model_view_projection_input = sky_shader_program->get_input("model_view_projection");
 				horizon_color_input = sky_shader_program->get_input("horizon_color");
 				zenith_color_input = sky_shader_program->get_input("zenith_color");
+				sun_color_input = sky_shader_program->get_input("sun_color");
 				mouse_input = sky_shader_program->get_input("mouse");
 				resolution_input = sky_shader_program->get_input("resolution");
 				time_input = sky_shader_program->get_input("time");
@@ -437,6 +447,7 @@ void sky_pass::update_tweens()
 	zenith_color_tween.update();
 	topocentric_frame_translation.update();
 	topocentric_frame_rotation.update();
+	sun_color_tween.update();
 }
 
 void sky_pass::set_time_of_day(float time)
@@ -503,6 +514,11 @@ void sky_pass::set_zenith_color(const float3& color)
 	zenith_color_tween[1] = color;
 }
 
+void sky_pass::set_sun_color(const float3& color)
+{
+	sun_color_tween[1] = color;
+}
+
 void sky_pass::handle_event(const mouse_moved_event& event)
 {
 	mouse_position = {static_cast<float>(event.x), static_cast<float>(event.y)};

src/renderer/passes/sky-pass.hpp

@@ -55,6 +55,7 @@ public:
 	void set_sky_model(const model* model);
 	void set_horizon_color(const float3& color);
 	void set_zenith_color(const float3& color);
+	void set_sun_color(const float3& color);
 	void set_time_of_day(float time);
 	void set_blue_noise_map(const gl::texture_2d* texture);
 	void set_sky_gradient(const gl::texture_2d* texture, const gl::texture_2d* texture2);
@@ -91,6 +92,7 @@ private:
 	const gl::shader_input* sky_gradient_input;
 	const gl::shader_input* sky_gradient2_input;
 	const gl::shader_input* exposure_input;
+	const gl::shader_input* sun_color_input;
 	
 	gl::shader_program* moon_shader_program;
 	const gl::shader_input* moon_model_view_projection_input;
@@ -133,6 +135,7 @@ private:
 	tween<float> julian_day_tween;
 	tween<float3> horizon_color_tween;
 	tween<float3> zenith_color_tween;
+	tween<float3> sun_color_tween;
 	
 	tween<float3> topocentric_frame_translation;
 	tween<math::quaternion<float>> topocentric_frame_rotation;