💿🐜 Antkeeper source code
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252 lines
7.3 KiB
252 lines
7.3 KiB
/*
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* Copyright (C) 2023 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_GAS_ATMOSPHERE_HPP
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#define ANTKEEPER_PHYSICS_GAS_ATMOSPHERE_HPP
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#include "physics/constants.hpp"
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#include "math/numbers.hpp"
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#include <algorithm>
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#include <cmath>
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namespace physics {
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namespace gas {
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/// Atmosphere-related functions.
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namespace atmosphere {
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/**
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* Calculates a particle polarizability factor.
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*
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* @param ior Atmospheric index of refraction.
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* @param density Molecular number density, in mol/m-3.
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* @return Polarizability factor.
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*
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* @see Elek, O., & Kmoch, P. (2010). Real-time spectral scattering in large-scale natural participating media. Proceedings of the 26th Spring Conference on Computer Graphics - SCCG ’10. doi:10.1145/1925059.1925074
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* @see Elek, Oskar. (2009). Rendering Parametrizable Planetary Atmospheres with Multiple Scattering in Real-Time.
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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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constexpr T k = T(2) * math::pi<T> * math::pi<T>;
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const T ior2m1 = ior * ior - T(1);
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const T num = k * 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 wavelength-dependent scattering coefficient.
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*
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* @param density Molecular number density of the particles, in mol/m-3.
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* @param polarization Particle polarizability factor.
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* @param wavelength Wavelength of light, in meters.
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*
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* @return Scattering coefficient.
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*
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* @see atmosphere::polarization
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*
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* @see Elek, O., & Kmoch, P. (2010). Real-time spectral scattering in large-scale natural participating media. Proceedings of the 26th Spring Conference on Computer Graphics - SCCG ’10. doi:10.1145/1925059.1925074
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* @see Elek, Oskar. (2009). Rendering Parametrizable Planetary Atmospheres with Multiple Scattering in Real-Time.
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*/
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template <class T>
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T scattering(T density, T polarization, T wavelength)
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{
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const T wavelength2 = wavelength * wavelength;
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return math::four_pi<T> * (density / (wavelength2 * wavelength2)) * polarization;
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}
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/**
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* Calculates a wavelength-independent scattering coefficient.
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*
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* @param density Molecular number density of the particles, in mol/m-3.
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* @param polarization Particle polarizability factor.
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*
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* @return Scattering coefficient.
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*
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* @see atmosphere::polarization
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*
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* @see Elek, O., & Kmoch, P. (2010). Real-time spectral scattering in large-scale natural participating media. Proceedings of the 26th Spring Conference on Computer Graphics - SCCG ’10. doi:10.1145/1925059.1925074
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* @see Elek, Oskar. (2009). Rendering Parametrizable Planetary Atmospheres with Multiple Scattering in Real-Time.
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*/
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template <class T>
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T scattering(T density, T polarization)
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{
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return math::four_pi<T> * density * polarization;
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}
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/**
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* Calculates an absorption coefficient.
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*
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* @param scattering Scattering coefficient.
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* @param albedo Single-scattering albedo.
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*
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* @return Absorption coefficient.
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*
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* @see https://en.wikipedia.org/wiki/Single-scattering_albedo
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*/
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template <class T>
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T absorption(T scattering, T albedo)
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{
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return scattering * (T(1) / albedo - T(1));
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}
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/**
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* Calculates an extinction coefficient.
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*
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* @param scattering Scattering coefficient.
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* @param albedo Single-scattering albedo.
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*
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* @return Extinction coefficient.
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*
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* @see https://en.wikipedia.org/wiki/Single-scattering_albedo
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*/
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template <class T>
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T extinction(T scattering, T albedo)
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{
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return scattering / albedo;
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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_exp(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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/**
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* Approximates the optical depth of triangularly-distributed atmospheric particles between two points using the trapezoidal rule.
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*
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* @param p0 Start point.
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* @param p1 End point.
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* @param r Radius of the planet.
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* @param a Distribution lower limit.
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* @param b Distribution upper limit.
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* @param c Distribution upper mode.
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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_tri(const math::vector3<T>& p0, const math::vector3<T>& p1, T r, T a, T b, T c, std::size_t n)
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{
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a = T(1) / (a - c);
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b = T(1) / (b - c);
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const T h = math::length(p1 - p0) / T(n);
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math::vector3<T> dy = (p1 - p0) / T(n);
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math::vector3<T> y = p0 + dy;
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T z = math::length(p0) - r;
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T f_x = std::max(T(0), std::max(T(0), c - z) * a - std::max(T(0), z - c) * b + T(1));
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z = math::length(y) - r;
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T f_y = std::max(T(0), std::max(T(0), c - z) * a - std::max(T(0), z - c) * b + T(1));
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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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z = math::length(y) - r;
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f_y = std::max(T(0), std::max(T(0), c - z) * a - std::max(T(0), z - c) * b + T(1));
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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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/// Atmospheric density functions.
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namespace density {
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/**
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* Calculates the density of exponentially-distributed atmospheric particles at a given elevation.
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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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*
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* @return Particle density at elevation @p z.
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*
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* @see https://en.wikipedia.org/wiki/Barometric_formula
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* @see https://en.wikipedia.org/wiki/Scale_height
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*/
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template <class T>
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T exponential(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 the density of triangularly-distributed atmospheric particles at a given elevation.
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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 a Distribution lower limit.
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* @param b Distribution upper limit.
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* @param c Distribution mode.
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*
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* @return Particle density at elevation @p z.
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*
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* @see https://en.wikipedia.org/wiki/Triangular_distribution
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*/
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template <class T>
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T triangular(T d0, T z, T a, T b, T c)
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{
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return d0 * max(T(0), max(T(0), c - z) / (a - c) - max(T(0), z - c) / (b - c) + T(1));
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}
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} // namespace density
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} // namespace atmosphere
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} // namespace gas
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} // namespace physics
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#endif // ANTKEEPER_PHYSICS_GAS_ATMOSPHERE_HPP
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