79 lines
2.2 KiB
C++
79 lines
2.2 KiB
C++
// intersections.cpp
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//
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// Copyright (c) 2018
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// Justinas V. Daugmaudis
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//
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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//[intersections
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/*`
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For the source of this example see
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[@boost://libs/random/example/intersections.cpp intersections.cpp].
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This example demonstrates generating quasi-randomly distributed chord
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entry and exit points on an S[sup 2] sphere.
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First we include the headers we need for __niederreiter_base2
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and __uniform_01 distribution.
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*/
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#include <boost/random/niederreiter_base2.hpp>
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#include <boost/random/uniform_01.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/tuple/tuple.hpp>
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/*`
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We use 4-dimensional __niederreiter_base2 as a source of randomness.
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*/
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boost::random::niederreiter_base2 gen(4);
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int main()
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{
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typedef boost::tuple<double, double, double> point_t;
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const std::size_t n_points = 100; // we will generate 100 points
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std::vector<point_t> points;
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points.reserve(n_points);
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/*<< __niederreiter_base2 produces integers in the range [0, 2[sup 64]-1].
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However, we want numbers in the range [0, 1). The distribution
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__uniform_01 performs this transformation.
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>>*/
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boost::random::uniform_01<double> dist;
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for (std::size_t i = 0; i != n_points; ++i)
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{
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/*`
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Using formula from J. Rovira et al., "Point sampling with uniformly distributed lines", 2005
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to compute uniformly distributed chord entry and exit points on the surface of a sphere.
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*/
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double cos_theta = 1 - 2 * dist(gen);
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double sin_theta = std::sqrt(1 - cos_theta * cos_theta);
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double phi = boost::math::constants::two_pi<double>() * dist(gen);
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double sin_phi = std::sin(phi), cos_phi = std::cos(phi);
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point_t point_on_sphere(sin_theta*sin_phi, cos_theta, sin_theta*cos_phi);
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/*`
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Here we assume that our sphere is a unit sphere at origin. If your sphere was
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different then now would be the time to scale and translate the `point_on_sphere`.
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*/
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points.push_back(point_on_sphere);
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}
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/*`
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Vector `points` now holds generated 3D points on a sphere.
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*/
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return 0;
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}
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//]
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