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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;
}
float ease(float x, float c)
{
x = clamp(x, 0.0, 1.0);
if (c > 0.0) {
if (c < 1.0)
return 1.0 - pow(1.0 - x, 1.0 / c);
return pow(x, c);
}
if (c < 0.0) {
if (x < 0.5)
return pow(x * 2.0, -c) * 0.5;
return (1.0 - pow(1.0 - (x - 0.5) * 2.0, -c)) * 0.5 + 0.5;
}
return 0.0;
}
vec2 sampleSphericalMap(vec3 v)
{
// Linear azimuth/elevation
float azimuth = atan(v.z, v.x); // [-pi, pi]
float theta = asin(v.y); // [-pi/2, pi/2]
// Non-linear LUT warp: undo the warp applied during LUT generation
float elev_warp = sqrt(abs(theta) / (PI * 0.5)) * sign(theta) * 0.5 + 0.5;
// Map azimuth to [0,1]
float azimuth_uv = azimuth / (2.0 * PI) + 0.5;
return vec2(azimuth_uv, elev_warp);
}
/*
* ACES tonemapping fit for the sRGB color space
*/
// sRGB => XYZ => D65_2_D60 => AP1 => RRT_SAT
const mat3 aces_input_mat = mat3(
0.59719, 0.07600, 0.02840,
0.35458, 0.90834, 0.13383,
0.04823, 0.01566, 0.83777
);
// ODT_SAT => XYZ => D60_2_D65 => sRGB
const mat3 aces_output_mat = mat3(
1.60475, -0.10208, -0.00327,
-0.53108, 1.10813, -0.07276,
-0.07367, -0.00605, 1.07602
);
vec3 rrt_and_odt_fit(vec3 v)
{
vec3 a = v * (v + 0.0245786) - 0.000090537;
vec3 b = v * (0.983729 * v + 0.4329510) + 0.238081;
return a / b;
}
vec3 aces_fitted(vec3 color)
{
color = aces_input_mat * color;
color = rrt_and_odt_fit(color);
color = aces_output_mat * color;
return clamp(color, 0.0, 1.0);
}
//-----------------------------------------------------------------------------
vec3 gamma_correct(vec3 linear_srgb)
{
vec3 a = 12.92 * linear_srgb;
vec3 b = 1.055 * pow(linear_srgb, vec3(1.0 / 2.4)) - 0.055;
vec3 c = step(vec3(0.0031308), linear_srgb);
return mix(a, b, c);
}
vec2 octEncode(vec3 n) {
n = normalize(n);
n /= (abs(n.x) + abs(n.y) + abs(n.z));
if (n.z < 0.0) n.xy = (1.0 - abs(n.yx)) * sign(n.xy);
return n.xy * 0.5 + 0.5;
}
vec3 octDecode(vec2 uv) {
uv = uv * 2.0 - 1.0;
vec3 n = vec3(uv.xy, 1.0 - abs(uv.x) - abs(uv.y));
if (n.z < 0.0) n.xy = (1.0 - abs(n.yx)) * sign(n.xy);
return normalize(n);
}
void MAIN()
{
vec3 direction = normalize(qt_eyeDir);
vec2 uv = sampleSphericalMap(direction);
vec3 col = texture(skytextureBuffer, uv).rgb;
vec3 sunCol = vec3(0.0);
if (direction.y > 0.0) {
vec3 sunDirWorld = vec3(-sunDirection.x, sunDirection.z, -sunDirection.y);
float sunDot = clamp(dot(normalize(sunDirWorld), direction), -1.0, 1.0);
float sunAngle = degrees(acos(sunDot));
vec3 sunLinear = qt_sRGBToLinear(vec4(sunColor, 1.0)).rgb * sunEnergy;
if (sunAngle < sunDiskInnerAngle) {
sunCol = sunLinear * sunAlpha;
} else if (sunAngle < sunDiskOuterAngle) {
float t = (sunAngle - sunDiskInnerAngle) / (sunDiskOuterAngle - sunDiskInnerAngle);
t = ease(t, sunDiskFalloff);
sunCol = sunLinear * sunAlpha * (1.0 - t);
}
}
col += sunCol;
col = max(col, vec3(0.0));
// Output linear HDR values — skybox.frag applies exposure + tonemapping.
// The 0.01 factor normalizes physical radiance (W/m²/sr) to display units.
FRAGCOLOR = vec4(col * 0.01, 1.0);
}