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++ // Copyright (C) 2023 Fernando García Liñán
++ // Copyright (C) 2026 The Qt Company Ltd.
++ // SPDX-License-Identifier: MIT
++
++ // Configurable parameters
++
++ // Ray marching steps. More steps mean better accuracy but worse performance
++ const int TRANSMITTANCE_STEPS = 32;
++ const int IN_SCATTERING_STEPS = 32;
++
++ // Debug
++ #define ENABLE_SPECTRAL 1
++ #define ENABLE_MULTIPLE_SCATTERING 1
++ #define ENABLE_AEROSOLS 1
++
++ //-----------------------------------------------------------------------------
++ // Constants
++
++ // All parameters that depend on wavelength (vec4) are sampled at
++ // 630, 560, 490, 430 nanometers
++
++ const float PI = 3.14159265358979323846;
++ const float INV_PI = 0.31830988618379067154;
++ const float INV_4PI = 0.25 * INV_PI;
++ const float PHASE_ISOTROPIC = INV_4PI;
++ const float RAYLEIGH_PHASE_SCALE = (3.0 / 16.0) * INV_PI;
++ const float g = 0.8;
++ const float gg = g*g;
++
++ const float EARTH_RADIUS = 6371.0; // km
++ const float ATMOSPHERE_THICKNESS = 100.0; // km
++ const float ATMOSPHERE_RADIUS = EARTH_RADIUS + ATMOSPHERE_THICKNESS;
++
++ #if ENABLE_SPECTRAL == 1
++ // Extraterrestial Solar Irradiance Spectra, units W * m^-2 * nm^-1
++ const vec4 sun_spectral_irradiance = vec4(1.679, 1.828, 1.986, 1.307);
++ // Rayleigh scattering coefficient at sea level, units km^-1
++ // "Rayleigh-scattering calculations for the terrestrial atmosphere"
++ // by Anthony Bucholtz (1995).
++ const vec4 molecular_scattering_coefficient_base = vec4(6.605e-3, 1.067e-2, 1.842e-2, 3.156e-2);
++ // Ozone absorption cross section, units m^2 / molecules
++ // "High spectral resolution ozone absorption cross-sections"
++ // by V. Gorshelev et al. (2014).
++ const vec4 ozone_absorption_cross_section = vec4(3.472e-21, 3.914e-21, 1.349e-21, 11.03e-23) * 1e-4f;
++ #else
++ // Same as above but for the following "RGB" wavelengths: 680, 550, 440 nm
++ // The Sun spectral irradiance is also multiplied by a constant factor to
++ // compensate for the fact that we use the spectral samples directly as RGB,
++ // which is incorrect.
++ const vec4 sun_spectral_irradiance = vec4(1.500, 1.864, 1.715, 0.0) * 150.0;
++ const vec4 molecular_scattering_coefficient_base = vec4(4.847e-3, 1.149e-2, 2.870e-2, 0.0);
++ const vec4 ozone_absorption_cross_section = vec4(3.36e-21f, 3.08e-21f, 20.6e-23f, 0.0) * 1e-4f;
++ #endif
++
++ /*
++ * Every aerosol type expects 5 parameters:
++ * - Scattering cross section
++ * - Absorption cross section
++ * - Base density (km^-3)
++ * - Background density (km^-3)
++ * - Height scaling parameter
++ * These parameters can be sent as uniforms.
++ *
++ * This model for aerosols and their corresponding parameters come from
++ * "A Physically-Based Spatio-Temporal Sky Model"
++ * by Guimera et al. (2018).
++ */
++
++ vec3 get_sun_direction(float time)
++ {
++ float a = sin(time*0.5 - 1.5) * 0.55 + 0.45;
++ return vec3(-sqrt(1.0 - a*a), 0.0, a);
++ }
++
++ /*
++ * Helper function to obtain the transmittance to the top of the atmosphere
++ * from Buffer A.
++ */
++ vec4 transmittance_from_lut(sampler2D lut, float cos_theta, float normalized_altitude)
++ {
++ float u = clamp(cos_theta * 0.5 + 0.5, 0.0, 1.0);
++ float v = clamp(normalized_altitude, 0.0, 1.0);
++ return texture(lut, vec2(u, v));
++ }
++
++ /*
++ * Returns the distance between ro and the first intersection with the sphere
++ * or -1.0 if there is no intersection. The sphere's origin is (0,0,0).
++ * -1.0 is also returned if the ray is pointing away from the sphere.
++ */
++ float ray_sphere_intersection(vec3 ro, vec3 rd, float radius)
++ {
++ float b = dot(ro, rd);
++ float c = dot(ro, ro) - radius*radius;
++ if (c > 0.0 && b > 0.0) return -1.0;
++ float d = b*b - c;
++ if (d < 0.0) return -1.0;
++ if (d > b*b) return (-b+sqrt(d));
++ return (-b-sqrt(d));
++ }
++
++ /*
++ * Rayleigh phase function.
++ */
++ float molecular_phase_function(float cos_theta)
++ {
++ return RAYLEIGH_PHASE_SCALE * (1.0 + cos_theta*cos_theta);
++ }
++
++ /*
++ * Henyey-Greenstrein phase function.
++ */
++ float aerosol_phase_function(float cos_theta)
++ {
++ float den = 1.0 + gg + 2.0 * g * cos_theta;
++ return INV_4PI * (1.0 - gg) / (den * sqrt(den));
++ }
++
++ vec4 get_multiple_scattering(sampler2D transmittance_lut, float cos_theta, float normalized_height, float d, vec4 ground_albedo)
++ {
++ #if ENABLE_MULTIPLE_SCATTERING == 1
++ // Solid angle subtended by the planet from a point at d distance
++ // from the planet center.
++ float omega = 2.0 * PI * (1.0 - sqrt(d*d - EARTH_RADIUS*EARTH_RADIUS) / d);
++
++ vec4 T_to_ground = transmittance_from_lut(transmittance_lut, cos_theta, 0.0);
++
++ vec4 T_ground_to_sample =
++ transmittance_from_lut(transmittance_lut, 1.0, 0.0) /
++ transmittance_from_lut(transmittance_lut, 1.0, normalized_height);
++
++ // 2nd order scattering from the ground
++ vec4 L_ground = PHASE_ISOTROPIC * omega * (ground_albedo / PI) * T_to_ground * T_ground_to_sample * cos_theta;
++
++ // Fit of Earth's multiple scattering coming from other points in the atmosphere
++ vec4 L_ms = 0.02 * vec4(0.217, 0.347, 0.594, 1.0) * (1.0 / (1.0 + 5.0 * exp(-17.92 * cos_theta)));
++
++ return L_ms + L_ground;
++ #else
++ return vec4(0.0);
++ #endif
++ }
++
++ /*
++ * Return the molecular volume scattering coefficient (km^-1) for a given altitude
++ * in kilometers.
++ */
++ vec4 get_molecular_scattering_coefficient(float h)
++ {
++ return molecular_scattering_coefficient_base * exp(-0.07771971 * pow(h, 1.16364243));
++ }
++
++ /*
++ * Return the molecular volume absorption coefficient (km^-1) for a given altitude
++ * in kilometers.
++ */
++ vec4 get_molecular_absorption_coefficient(float h, float ozone_mean_monthly_dobson)
++ {
++ h += 1e-4; // Avoid division by 0
++ float t = log(h) - 3.22261;
++ float density = 3.78547397e20 * (1.0 / h) * exp(-t * t * 5.55555555);
++ return ozone_absorption_cross_section * ozone_mean_monthly_dobson * density;
++ }
++
++ float get_aerosol_density(float h,
++ int aerosol_type,
++ float aerosol_base_density,
++ float aerosol_height_scale,
++ float aerosol_background_divided_by_base_density
++ )
++ {
++ if (aerosol_type == 0) { // Only for the Background aerosol type, no dependency on height
++ return aerosol_base_density * (1.0 + aerosol_background_divided_by_base_density);
++ } else {
++ return aerosol_base_density * (exp(-h / aerosol_height_scale)
++ + aerosol_background_divided_by_base_density);
++ }
++ }
++
++ /*
++ * Get the collision coefficients (scattering and absorption) of the
++ * atmospheric medium for a given point at an altitude h.
++ */
++ void get_atmosphere_collision_coefficients(in float h,
++ in vec4 aerosol_absorption_cross_section,
++ in vec4 aerosol_scattering_cross_section,
++ in float aerosol_base_density,
++ in float aerosol_height_scale,
++ in float aerosol_background_divided_by_base_density,
++ in int aerosol_type,
++ in float ozone_mean_monthly_dobson,
++ in float aerosol_turbidity,
++ out vec4 aerosol_absorption,
++ out vec4 aerosol_scattering,
++ out vec4 molecular_absorption,
++ out vec4 molecular_scattering,
++ out vec4 extinction)
++ {
++ h = max(h, 0.0); // In case height is negative
++ #if ENABLE_AEROSOLS == 0
++ aerosol_absorption = vec4(0.0);
++ aerosol_scattering = vec4(0.0);
++ #else
++ float aerosol_density = get_aerosol_density(h, aerosol_type, aerosol_base_density, aerosol_height_scale, aerosol_background_divided_by_base_density);
++ aerosol_absorption = aerosol_absorption_cross_section * aerosol_density * aerosol_turbidity;
++ aerosol_scattering = aerosol_scattering_cross_section * aerosol_density * aerosol_turbidity;
++ #endif
++ molecular_absorption = get_molecular_absorption_coefficient(h, ozone_mean_monthly_dobson);
++ molecular_scattering = get_molecular_scattering_coefficient(h);
++ extinction = aerosol_absorption + aerosol_scattering + molecular_absorption + molecular_scattering;
++ }
++
++ //-----------------------------------------------------------------------------
++ // Spectral rendering stuff
++
++ const mat4 M = mat4(
++ 137.672389239975, -8.632904716299537, -1.7181567391931372, 0,
++ 32.549094028629234, 91.29801417199785, -12.005406444382531, 0,
++ -38.91428392614275, 34.31665471469816, 29.89044807197628, 0,
++ 8.572844237945445, -11.103384660054624, 117.47585277566478, 0
++ );
++
++ vec3 linear_srgb_from_spectral_samples(vec4 L)
++ {
++ return (M * L).xyz;
++ }
++
++ /*
++ * Buffer B: Sky texture
++ *
++ * "A Scalable and Production Ready Sky and Atmosphere Rendering Technique"
++ * by Sébastien Hillaire (2020).
++ *
++ * We render the sky to a texture instead of raymarching on the entire screen.
++ * This is not very useful in Shadertoy, but very useful for someone looking
++ * to implement this on a real application.
++ *
++ * It is important to note that quality decreases significantly when rendering
++ * space views. To avoid this, the compute_inscattering() function can be used
++ * directly when rendering to a fullscreen quad.
++ */
++
++ vec4 compute_inscattering(vec3 ray_origin, vec3 ray_dir, float t_d, out vec4 transmittance)
++ {
++
++ float cos_theta = dot(-ray_dir, sun_direction);
++
++ float molecular_phase = molecular_phase_function(cos_theta);
++ float aerosol_phase = aerosol_phase_function(cos_theta);
++
++ float dt = t_d / float(IN_SCATTERING_STEPS);
++
++ vec4 L_inscattering = vec4(0.0);
++ transmittance = vec4(1.0);
++
++ for (int i = 0; i < IN_SCATTERING_STEPS; ++i) {
++ float t = (float(i) + 0.5) * dt;
++ vec3 x_t = ray_origin + ray_dir * t;
++
++ float distance_to_earth_center = length(x_t);
++ vec3 zenith_dir = x_t / distance_to_earth_center;
++ float altitude = distance_to_earth_center - EARTH_RADIUS;
++ float normalized_altitude = altitude / ATMOSPHERE_THICKNESS;
++
++ float sample_cos_theta = dot(zenith_dir, sun_direction);
++
++ vec4 aerosol_absorption, aerosol_scattering;
++ vec4 molecular_absorption, molecular_scattering;
++ vec4 extinction;
++ get_atmosphere_collision_coefficients(
++ altitude,
++ aerosol_absorption_cross_section,
++ aerosol_scattering_cross_section,
++ aerosol_base_density,
++ aerosol_height_scale,
++ aerosol_background_divided_by_base_density,
++ aerosol_type,
++ ozone_mean_monthly_dobson,
++ aerosol_turbidity,
++ aerosol_absorption, aerosol_scattering,
++ molecular_absorption, molecular_scattering,
++ extinction);
++
++ vec4 transmittance_to_sun = transmittance_from_lut(
++ transmittanceBuffer, sample_cos_theta, normalized_altitude);
++
++ vec4 ms = get_multiple_scattering(
++ transmittanceBuffer, sample_cos_theta, normalized_altitude,
++ distance_to_earth_center,
++ ground_albedo);
++
++ vec4 S = sun_spectral_irradiance *
++ (molecular_scattering * (molecular_phase * transmittance_to_sun + ms) +
++ aerosol_scattering * (aerosol_phase * transmittance_to_sun + ms));
++
++ vec4 step_transmittance = exp(-dt * extinction);
++
++ // Energy-conserving analytical integration
++ // "Physically Based Sky, Atmosphere and Cloud Rendering in Frostbite"
++ // by Sébastien Hillaire
++ vec4 S_int = (S - S * step_transmittance) / max(extinction, 1e-7);
++ L_inscattering += transmittance * S_int;
++ transmittance *= step_transmittance;
++ }
++
++ return L_inscattering;
++ }
++
++ void MAIN()
++ {
++ vec2 uv = INPUT_UV;
++ const float EYE_DISTANCE_TO_EARTH_CENTER = EARTH_RADIUS + eye_altitude;
++
++ float azimuth = 2.0 * PI * uv.x;
++
++ // Apply a non-linear transformation to the elevation to dedicate more
++ // texels to the horizon, where having more detail matters.
++ float l = uv.y * 2.0 - 1.0;
++ float elev = l*l * sign(l) * PI * 0.5; // [-pi/2, pi/2]
++
++ vec3 ray_dir = vec3(cos(elev) * cos(azimuth),
++ cos(elev) * sin(azimuth),
++ sin(elev));
++
++ vec3 ray_origin = vec3(0.0, 0.0, EYE_DISTANCE_TO_EARTH_CENTER);
++
++ float atmos_dist = ray_sphere_intersection(ray_origin, ray_dir, ATMOSPHERE_RADIUS);
++ float ground_dist = ray_sphere_intersection(ray_origin, ray_dir, EARTH_RADIUS);
++ float t_d;
++ if (eye_altitude < ATMOSPHERE_THICKNESS) {
++ // We are inside the atmosphere
++ if (ground_dist < 0.0) {
++ // No ground collision, use the distance to the outer atmosphere
++ t_d = atmos_dist;
++ } else {
++ // We have a collision with the ground, use the distance to it
++ t_d = ground_dist;
++ }
++ } else {
++ // We are in outer space
++ if (atmos_dist < 0.0) {
++ // No collision with the atmosphere, just return black
++ FRAGCOLOR = vec4(0.0, 0.0, 0.0, 1.0);
++ return;
++ } else {
++ // Move the ray origin to the atmosphere intersection
++ ray_origin = ray_origin + ray_dir * (atmos_dist + 1e-3);
++ if (ground_dist < 0.0) {
++ // No collision with the ground, so the ray is exiting through
++ // the atmosphere.
++ float second_atmos_dist = ray_sphere_intersection(
++ ray_origin, ray_dir, ATMOSPHERE_RADIUS);
++ t_d = second_atmos_dist;
++ } else {
++ t_d = ground_dist - atmos_dist;
++ }
++ }
++ }
++
++ vec4 transmittance;
++ vec4 L = compute_inscattering(ray_origin, ray_dir, t_d, transmittance);
++
++ #if ENABLE_SPECTRAL == 1
++ FRAGCOLOR = vec4(linear_srgb_from_spectral_samples(L), 1.0);
++ #else
++ FRAGCOLOR = vec4(L.rgb, 1.0);
++ #endif
++
++
++ }