343 lines
11 KiB
GLSL
343 lines
11 KiB
GLSL
/*
|
|
* Common atmosphere rendering functions
|
|
*
|
|
* See https://www.shadertoy.com/view/msXXDS for a more complete description
|
|
* of what the shader does and more references.
|
|
*
|
|
* All 4-component vectors in this file represent values sampled for the
|
|
* following wavelengths: 630, 560, 490, 430 nm
|
|
*/
|
|
|
|
#version 330 core
|
|
|
|
uniform vec4 aerosol_absorption_cross_section;
|
|
uniform vec4 aerosol_scattering_cross_section;
|
|
uniform float aerosol_base_density;
|
|
uniform float aerosol_relative_background_density;
|
|
uniform float aerosol_scale_height;
|
|
uniform float aerosol_turbidity;
|
|
uniform float fog_density;
|
|
uniform float fog_scale_height;
|
|
uniform float fog_height_offset;
|
|
uniform float ozone_mean_dobson;
|
|
uniform vec4 ground_albedo;
|
|
|
|
uniform float fg_EarthRadius;
|
|
|
|
const float RAYLEIGH_PHASE_SCALE = 0.05968310365946075091; // 3/(16*pi)
|
|
const float HENYEY_ASYMMETRY = 0.8;
|
|
const float HENYEY_ASYMMETRY2 = HENYEY_ASYMMETRY*HENYEY_ASYMMETRY;
|
|
|
|
/*
|
|
* Rayleigh scattering coefficient at sea level, units m^-1
|
|
* "Rayleigh-scattering calculations for the terrestrial atmosphere"
|
|
* by Anthony Bucholtz (1995).
|
|
*/
|
|
const vec4 molecular_scattering_coefficient_base =
|
|
vec4(6.605e-6, 1.067e-5, 1.842e-5, 3.156e-5);
|
|
|
|
/*
|
|
* Fog scattering/extinction cross section, units m^2 / molecules
|
|
* Mie theory results for IOR of 1.333. Particle size is a log normal
|
|
* distribution of mean diameter=15 and std deviation=0.4
|
|
*/
|
|
const vec4 fog_scattering_cross_section =
|
|
vec4(5.015e-10, 4.987e-10, 4.966e-10, 4.949e-10);
|
|
|
|
/*
|
|
* 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-25, 3.914e-25, 1.349e-25, 11.03e-27);
|
|
|
|
// math.glsl
|
|
float M_PI();
|
|
float M_2PI();
|
|
float M_1_PI();
|
|
float M_1_4PI();
|
|
float sqr(float x);
|
|
|
|
//------------------------------------------------------------------------------
|
|
|
|
float get_earth_radius()
|
|
{
|
|
return fg_EarthRadius;
|
|
}
|
|
|
|
float get_atmosphere_radius()
|
|
{
|
|
return 6471e3; // m
|
|
}
|
|
|
|
/*
|
|
* Helper function to obtain the transmittance to the top of the atmosphere
|
|
* from the precomputed transmittance LUT.
|
|
*/
|
|
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 + HENYEY_ASYMMETRY2 + 2.0 * HENYEY_ASYMMETRY * cos_theta;
|
|
return M_1_4PI() * (1.0 - HENYEY_ASYMMETRY2) / (den * sqrt(den));
|
|
}
|
|
|
|
/*
|
|
* Get the approximated multiple scattering contribution for a given point
|
|
* within the atmosphere.
|
|
*/
|
|
vec4 get_multiple_scattering(sampler2D transmittance_lut,
|
|
float cos_theta,
|
|
float normalized_height,
|
|
float d)
|
|
{
|
|
// Solid angle subtended by the planet from a point at d distance
|
|
// from the planet center.
|
|
float omega = M_2PI() * (1.0 - sqrt(sqr(d) - sqr(get_earth_radius())) / d);
|
|
omega = max(0.0, omega);
|
|
|
|
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 = M_1_4PI() * omega * (ground_albedo * M_1_PI())
|
|
* T_to_ground * T_ground_to_sample * max(0.0, 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;
|
|
}
|
|
|
|
/*
|
|
* Return the molecular volume scattering coefficient (m^-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 (m^-1) for a given altitude
|
|
* in kilometers.
|
|
*/
|
|
vec4 get_molecular_absorption_coefficient(float h)
|
|
{
|
|
h += 1e-4; // Avoid division by 0
|
|
float t = log(h) - 3.22261;
|
|
float density = 3.78547397e17 * (1.0 / h) * exp(-t * t * 5.55555555);
|
|
return ozone_absorption_cross_section * ozone_mean_dobson * density;
|
|
}
|
|
|
|
/*
|
|
* Return the aerosol density for a given altitude in kilometers.
|
|
*/
|
|
float get_aerosol_density(float h)
|
|
{
|
|
return aerosol_turbidity * aerosol_base_density
|
|
* (exp(-h / aerosol_scale_height) + aerosol_relative_background_density);
|
|
}
|
|
|
|
/*
|
|
* Return the fog volume scattering coefficient (m^-1) for a given altitude in
|
|
* kilometers.
|
|
*
|
|
* Fog (or mist, depending on density) is a special kind of aerosol consisting
|
|
* of water droplets or ice crystals. Visibility is mostly dependent on fog.
|
|
*/
|
|
vec4 get_fog_scattering_coefficient(float h)
|
|
{
|
|
if (fog_density > 0.0) {
|
|
return fog_scattering_cross_section * fog_density
|
|
* min(1.0, exp((-h + fog_height_offset) / fog_scale_height));
|
|
} else {
|
|
return vec4(0.0);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* Get the collision coefficients (scattering and absorption) of the
|
|
* atmospheric medium for a given point at an altitude h in meters.
|
|
*/
|
|
void get_atmosphere_collision_coefficients(in float h,
|
|
out vec4 aerosol_absorption,
|
|
out vec4 aerosol_scattering,
|
|
out vec4 molecular_absorption,
|
|
out vec4 molecular_scattering,
|
|
out vec4 fog_scattering,
|
|
out vec4 extinction)
|
|
{
|
|
h = max(h, 1e-3); // In case height is negative
|
|
h *= 1e-3; // To km
|
|
|
|
// Molecules
|
|
molecular_absorption = get_molecular_absorption_coefficient(h);
|
|
molecular_scattering = get_molecular_scattering_coefficient(h);
|
|
|
|
// Aerosols
|
|
float aerosol_density = get_aerosol_density(h);
|
|
aerosol_absorption = aerosol_absorption_cross_section * aerosol_density;
|
|
aerosol_scattering = aerosol_scattering_cross_section * aerosol_density;
|
|
|
|
// Fog
|
|
fog_scattering = get_fog_scattering_coefficient(h);
|
|
|
|
extinction =
|
|
aerosol_absorption + aerosol_scattering +
|
|
molecular_absorption + molecular_scattering +
|
|
fog_scattering;
|
|
}
|
|
|
|
/*
|
|
* Any given ray inside the atmospheric medium can end in one of 3 places:
|
|
* 1. The Earth's surface.
|
|
* 2. Outer space. We define the boundary between space and the atmosphere
|
|
* at the Kármán line (100 km above sea level).
|
|
* 3. Any object within the atmosphere.
|
|
*/
|
|
float get_ray_end(vec3 ray_origin, vec3 ray_dir, float t_max)
|
|
{
|
|
float ray_altitude = length(ray_origin);
|
|
// If the ray origin is underground, put the ground a bit below it
|
|
float earth_radius = min(get_earth_radius(), ray_altitude - 1.0);
|
|
|
|
if (ray_altitude >= get_atmosphere_radius()) {
|
|
// We are in outer space, move the ray origin to the atmospheric boundary
|
|
// XXX: No atmosphere rendering from space yet
|
|
return -1.0;
|
|
}
|
|
|
|
float t_atmos = ray_sphere_intersection(ray_origin, ray_dir, get_atmosphere_radius());
|
|
float t_ground = ray_sphere_intersection(ray_origin, ray_dir, earth_radius);
|
|
float t_d = 0.0;
|
|
if (t_ground < 0.0) {
|
|
if (t_atmos < 0.0) {
|
|
t_d = -1.0;
|
|
} else {
|
|
t_d = t_atmos;
|
|
}
|
|
} else {
|
|
if (t_atmos > 0.0) {
|
|
t_d = min(t_atmos, t_ground);
|
|
}
|
|
}
|
|
return min(t_d, t_max);
|
|
}
|
|
|
|
/*
|
|
* Compute the in-scattering integral of the volume rendering equation (VRE)
|
|
*
|
|
* The integral is solved numerically by ray marching. The final in-scattering
|
|
* returned by this function is a 4D vector of the spectral radiance sampled for
|
|
* the 4 wavelengths at the top of this file. To obtain an RGB triplet, the
|
|
* spectral radiance must be multiplied by the spectral irradiance of the Sun
|
|
* and converted to sRGB.
|
|
*/
|
|
vec4 compute_inscattering(in vec3 ray_origin,
|
|
in vec3 ray_dir,
|
|
in float t_max,
|
|
in vec3 sun_dir,
|
|
in int steps,
|
|
in sampler2D transmittance_lut,
|
|
out vec4 transmittance)
|
|
{
|
|
float t_d = get_ray_end(ray_origin, ray_dir, t_max);
|
|
if (t_d < 1e-3) {
|
|
// No intersection with the atmosphere or the ray origin and end points
|
|
// are too close too each other. In both cases there is no inscattering.
|
|
return vec4(0.0);
|
|
}
|
|
float dt = t_d / float(steps);
|
|
|
|
float cos_theta = dot(-ray_dir, sun_dir);
|
|
|
|
float molecular_phase = molecular_phase_function(cos_theta);
|
|
float aerosol_phase = aerosol_phase_function(cos_theta);
|
|
|
|
vec4 L_inscattering = vec4(0.0);
|
|
transmittance = vec4(1.0);
|
|
|
|
for (int i = 0; i < 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 - get_earth_radius();
|
|
float normalized_altitude = altitude / (get_atmosphere_radius() - get_earth_radius());
|
|
|
|
float sample_cos_theta = dot(zenith_dir, sun_dir);
|
|
|
|
vec4 aerosol_absorption, aerosol_scattering;
|
|
vec4 molecular_absorption, molecular_scattering;
|
|
vec4 fog_scattering;
|
|
vec4 extinction;
|
|
get_atmosphere_collision_coefficients(
|
|
altitude,
|
|
aerosol_absorption, aerosol_scattering,
|
|
molecular_absorption, molecular_scattering,
|
|
fog_scattering,
|
|
extinction);
|
|
|
|
vec4 transmittance_to_sun = transmittance_from_lut(
|
|
transmittance_lut, sample_cos_theta, normalized_altitude);
|
|
|
|
vec4 ms = get_multiple_scattering(
|
|
transmittance_lut, sample_cos_theta, normalized_altitude,
|
|
distance_to_earth_center);
|
|
|
|
vec4 S =
|
|
molecular_scattering * (molecular_phase * transmittance_to_sun + ms) +
|
|
(aerosol_scattering + fog_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;
|
|
}
|