1 // intersections.cpp
2 //
3 // Copyright (c) 2018
4 // Justinas V. Daugmaudis
5 //
6 // Distributed under the Boost Software License, Version 1.0. (See
7 // accompanying file LICENSE_1_0.txt or copy at
8 // http://www.boost.org/LICENSE_1_0.txt)
9
10 //[intersections
11 /*`
12 For the source of this example see
13 [@boost://libs/random/example/intersections.cpp intersections.cpp].
14
15 This example demonstrates generating quasi-randomly distributed chord
16 entry and exit points on an S[sup 2] sphere.
17
18 First we include the headers we need for __niederreiter_base2
19 and __uniform_01 distribution.
20 */
21
22 #include <boost/random/niederreiter_base2.hpp>
23 #include <boost/random/uniform_01.hpp>
24
25 #include <boost/math/constants/constants.hpp>
26
27 #include <boost/tuple/tuple.hpp>
28
29 /*`
30 We use 4-dimensional __niederreiter_base2 as a source of randomness.
31 */
32 boost::random::niederreiter_base2 gen(4);
33
34
main()35 int main()
36 {
37 typedef boost::tuple<double, double, double> point_t;
38
39 const std::size_t n_points = 100; // we will generate 100 points
40
41 std::vector<point_t> points;
42 points.reserve(n_points);
43
44 /*<< __niederreiter_base2 produces integers in the range [0, 2[sup 64]-1].
45 However, we want numbers in the range [0, 1). The distribution
46 __uniform_01 performs this transformation.
47 >>*/
48 boost::random::uniform_01<double> dist;
49
50 for (std::size_t i = 0; i != n_points; ++i)
51 {
52 /*`
53 Using formula from J. Rovira et al., "Point sampling with uniformly distributed lines", 2005
54 to compute uniformly distributed chord entry and exit points on the surface of a sphere.
55 */
56 double cos_theta = 1 - 2 * dist(gen);
57 double sin_theta = std::sqrt(1 - cos_theta * cos_theta);
58 double phi = boost::math::constants::two_pi<double>() * dist(gen);
59 double sin_phi = std::sin(phi), cos_phi = std::cos(phi);
60
61 point_t point_on_sphere(sin_theta*sin_phi, cos_theta, sin_theta*cos_phi);
62
63 /*`
64 Here we assume that our sphere is a unit sphere at origin. If your sphere was
65 different then now would be the time to scale and translate the `point_on_sphere`.
66 */
67
68 points.push_back(point_on_sphere);
69 }
70
71 /*`
72 Vector `points` now holds generated 3D points on a sphere.
73 */
74
75 return 0;
76 }
77
78 //]
79