💿🐜 Antkeeper source code
https://antkeeper.com
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
168 lines
4.9 KiB
168 lines
4.9 KiB
/*
|
|
* 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
|
|
* @see https://en.wikipedia.org/wiki/Barometric_formula
|
|
*/
|
|
template <class T>
|
|
T density(T d0, T z, T sh)
|
|
{
|
|
return d0 * std::exp(-z / sh);
|
|
}
|
|
|
|
/**
|
|
* Calculates a particle polarizability factor used in computing scattering coefficients.
|
|
*
|
|
* @param ior Atmospheric index of refraction.
|
|
* @param density Molecular density.
|
|
* @return Polarization factor.
|
|
*
|
|
* @see Elek, Oskar. (2009). Rendering Parametrizable Planetary Atmospheres with Multiple Scattering in Real-Time.
|
|
* @see Real-Time Spectral Scattering in Large-Scale Natural Participating Media.
|
|
*/
|
|
template <class T>
|
|
T polarization(T ior, T density)
|
|
{
|
|
const T ior2m1 = ior * ior - T(1.0);
|
|
const T num = T(2) * math::pi<T> * math::pi<T> * ior2m1 * ior2m1;
|
|
const T den = T(3) * density * density;
|
|
return num / den;
|
|
}
|
|
|
|
/**
|
|
* Calculates a Rayleigh scattering coefficient at sea level (wavelength-dependent).
|
|
*
|
|
* @param wavelength Wavelength of light, in meters.
|
|
* @param density Molecular density of Rayleigh particles at sea level.
|
|
* @param polarization Rayleigh particle polarization factor.
|
|
*
|
|
* @see atmosphere::polarization
|
|
*
|
|
* @see Elek, Oskar. (2009). Rendering Parametrizable Planetary Atmospheres with Multiple Scattering in Real-Time.
|
|
* @see Real-Time Spectral Scattering in Large-Scale Natural Participating Media.
|
|
*/
|
|
template <class T>
|
|
T scattering_rayleigh(T wavelength, T density, T polarization)
|
|
{
|
|
const T wavelength2 = wavelength * wavelength;
|
|
return T(4) * math::pi<T> * density / (wavelength2 * wavelength2) * polarization;
|
|
}
|
|
|
|
/**
|
|
* Calculates a Mie scattering coefficient at sea level (wavelength-independent).
|
|
*
|
|
* @param density Molecular density of Mie particles at sea level.
|
|
* @param polarization Mie particle polarization factor.
|
|
*
|
|
* @see atmosphere::polarization
|
|
*
|
|
* @see Elek, Oskar. (2009). Rendering Parametrizable Planetary Atmospheres with Multiple Scattering in Real-Time.
|
|
* @see Real-Time Spectral Scattering in Large-Scale Natural Participating Media.
|
|
*/
|
|
template <class T>
|
|
T scattering_mie(T density, T polarization)
|
|
{
|
|
return T(4) * math::pi<T> * density * polarization;
|
|
}
|
|
|
|
/**
|
|
* Calculates attenuation due to extinction (absorption + out-scattering).
|
|
*
|
|
* @param ec Extinction coefficient (absorption coefficient + scattering coefficient).
|
|
* @param s Scale factor.
|
|
* @return Attenuation factor.
|
|
*/
|
|
template <class T>
|
|
T extinction(T ec, T s)
|
|
{
|
|
return std::exp(-(ec * s));
|
|
}
|
|
|
|
/**
|
|
* Calculates the single-scattering albedo (SSA) given a scattering coefficient and an extinction coefficient.
|
|
*
|
|
* @param s Scattering coefficient.
|
|
* @param e Extinction coefficient.
|
|
* @return Single-scattering albedo.
|
|
*/
|
|
template <class T>
|
|
T albedo(T s, T e)
|
|
{
|
|
return s / t;
|
|
}
|
|
|
|
/**
|
|
* Approximates the optical depth of exponentially-distributed atmospheric particles between two points using the trapezoidal rule.
|
|
*
|
|
* @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.
|
|
* @return Optical depth between @p a and @p b.
|
|
*/
|
|
template <class T>
|
|
T optical_depth(const math::vector3<T>& a, const math::vector3<T>& b, T r, T sh, std::size_t n)
|
|
{
|
|
sh = T(-1) / sh;
|
|
|
|
const T h = math::length(b - a) / T(n);
|
|
|
|
math::vector3<T> dy = (b - a) / T(n);
|
|
math::vector3<T> y = a + dy;
|
|
|
|
T f_x = std::exp((math::length(a) - r) * sh);
|
|
T f_y = std::exp((math::length(y) - r) * sh);
|
|
T sum = (f_x + f_y);
|
|
|
|
for (std::size_t i = 1; i < n; ++i)
|
|
{
|
|
f_x = f_y;
|
|
y += dy;
|
|
f_y = std::exp((math::length(y) - r) * sh);
|
|
sum += (f_x + f_y);
|
|
}
|
|
|
|
return sum / T(2) * h;
|
|
}
|
|
|
|
} // namespace atmosphere
|
|
|
|
} // namespace physics
|
|
|
|
#endif // ANTKEEPER_PHYSICS_ATMOSPHERE_HPP
|