|
|
- /*
- * 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 "math/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
|