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/*
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* Copyright (C) 2021 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_PHYSICS_ATMOSPHERE_HPP
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#define ANTKEEPER_PHYSICS_ATMOSPHERE_HPP
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#include "physics/constants.hpp"
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#include "math/constants.hpp"
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#include <cmath>
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namespace physics {
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/// Atmosphere-related functions.
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namespace atmosphere {
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/**
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* Calculates the density of exponentially-distributed atmospheric particles at a given altitude.
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*
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* @param d0 Density at sea level.
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* @param z Height above sea level.
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* @param sh Scale height of the particle type.
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* @return Particle density at altitude.
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*
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* @see https://en.wikipedia.org/wiki/Scale_height
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* @see https://en.wikipedia.org/wiki/Barometric_formula
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*/
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template <class T>
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T density(T d0, T z, T sh)
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{
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return d0 * std::exp(-z / sh);
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}
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/**
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* Calculates a particle polarizability factor used in computing scattering coefficients.
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*
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* @param ior Atmospheric index of refraction.
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* @param density Molecular density.
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* @return Polarization factor.
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*
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* @see Elek, Oskar. (2009). Rendering Parametrizable Planetary Atmospheres with Multiple Scattering in Real-Time.
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* @see Real-Time Spectral Scattering in Large-Scale Natural Participating Media.
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*/
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template <class T>
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T polarization(T ior, T density)
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{
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const T ior2m1 = ior * ior - T(1.0);
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const T num = T(2) * math::pi<T> * math::pi<T> * ior2m1 * ior2m1;
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const T den = T(3) * density * density;
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return num / den;
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}
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/**
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* Calculates a Rayleigh scattering coefficient at sea level (wavelength-dependent).
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*
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* @param wavelength Wavelength of light, in meters.
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* @param density Molecular density of Rayleigh particles at sea level.
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* @param polarization Rayleigh particle polarization factor.
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*
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* @see atmosphere::polarization
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*
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* @see Elek, Oskar. (2009). Rendering Parametrizable Planetary Atmospheres with Multiple Scattering in Real-Time.
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* @see Real-Time Spectral Scattering in Large-Scale Natural Participating Media.
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*/
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template <class T>
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T scattering_rayleigh(T wavelength, T density, T polarization)
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{
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const T wavelength2 = wavelength * wavelength;
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return T(4) * math::pi<T> * density / (wavelength2 * wavelength2) * polarization;
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}
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/**
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* Calculates a Mie scattering coefficient at sea level (wavelength-independent).
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*
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* @param density Molecular density of Mie particles at sea level.
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* @param polarization Mie particle polarization factor.
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*
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* @see atmosphere::polarization
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*
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* @see Elek, Oskar. (2009). Rendering Parametrizable Planetary Atmospheres with Multiple Scattering in Real-Time.
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* @see Real-Time Spectral Scattering in Large-Scale Natural Participating Media.
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*/
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template <class T>
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T scattering_mie(T density, T polarization)
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{
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return T(4) * math::pi<T> * density * polarization;
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}
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/**
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* Calculates attenuation due to extinction (absorption + out-scattering).
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*
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* @param ec Extinction coefficient (absorption coefficient + scattering coefficient).
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* @param s Scale factor.
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* @return Attenuation factor.
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*/
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template <class T>
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T extinction(T ec, T s)
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{
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return std::exp(-(ec * s));
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}
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/**
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* Calculates the single-scattering albedo (SSA) given a scattering coefficient and an extinction coefficient.
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*
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* @param s Scattering coefficient.
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* @param e Extinction coefficient.
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* @return Single-scattering albedo.
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*/
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template <class T>
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T albedo(T s, T e)
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{
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return s / t;
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}
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/**
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* Approximates the optical depth of exponentially-distributed atmospheric particles between two points using the trapezoidal rule.
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*
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* @param a Start point.
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* @param b End point.
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* @param r Radius of the planet.
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* @param sh Scale height of the atmospheric particles.
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* @param n Number of samples.
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* @return Optical depth between @p a and @p b.
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*/
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template <class T>
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T optical_depth(const math::vector3<T>& a, const math::vector3<T>& b, T r, T sh, std::size_t n)
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{
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sh = T(-1) / sh;
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const T h = math::length(b - a) / T(n);
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math::vector3<T> dy = (b - a) / T(n);
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math::vector3<T> y = a + dy;
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T f_x = std::exp((math::length(a) - r) * sh);
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T f_y = std::exp((math::length(y) - r) * sh);
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T sum = (f_x + f_y);
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for (std::size_t i = 1; i < n; ++i)
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{
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f_x = f_y;
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y += dy;
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f_y = std::exp((math::length(y) - r) * sh);
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sum += (f_x + f_y);
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}
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return sum / T(2) * h;
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}
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} // namespace atmosphere
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} // namespace physics
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#endif // ANTKEEPER_PHYSICS_ATMOSPHERE_HPP
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