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