/usr/include/libwildmagic/Wm5RandomHypersphere.h is in libwildmagic-dev 5.13-1+b2.
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// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.1 (2010/10/01)
#ifndef WM5RANDOMHYPERSPHERE_H
#define WM5RANDOMHYPERSPHERE_H
#include "Wm5MathematicsLIB.h"
namespace Wm5
{
// Generate N random points on the hypersphere in D-space,
//
// x_1^2 + ... + x_D^2 = 1
//
// The function selects a random angle in [0,2*pi) and partitions
// the equation into
//
// x_1^2 + ... + x_{D/2}^2 = (cos(A))^2
//
// and
//
// x_{D/2+1}^2 + ... + x_D^2 = (sin(A))^2
//
// The function initializes all components of P to 1. The partitioned
// components are updated as x_i *= cos(A) for 0 <= i < D/2 and
// x_i *= sin(A) for D/2 <= i < D. The function is recursively called
// on the partitioned components.
WM5_MATHEMATICS_ITEM void RandomPointOnHypersphere (int dimension,
double* point);
// An attempt to determine the uniformity of N randomly generated
// points P[0] through P[N-1] on the hypersphere. Select a positive
// angle. For each point P[i] count the number H[i] of random points
// P[j] which lie in the cone with axis P[i] and specified angle. For
// N suitably large, H[i] should be constant for all i. To be really
// sure of the uniformity, you should look at other cones whose axes
// are not the sample points. However, this requires generating random
// points to get the axes and, well, you can see the problem...
WM5_MATHEMATICS_ITEM void Histogram (int dimension, double angle,
int numPoints, double** points, int* histogram);
//An example of how to use these functions.
//
//void TestRandomHyperspherePoints ()
//{
// const int numPoints = 4096;
// const int dimension = 3;
// int i;
//
// double** points = new2 <double>(numPoints, dimension);
// for (i = 0; i < numPoints; ++i)
// {
// RandomPointOnHypersphere(dimension, points[i]);
// }
//
// int* histogram = new1<int>(numPoints);
// double angle = 0.5;
// Histogram(dimension, angle, numPoints, points, histogram);
//
// ofstream ostr("histo.txt");
// for (i = 0; i < numPoints; ++i)
// {
// ostr << i << ' ' << histogram[i] << endl;
// }
//
// delete1(histogram);
// delete2(points);
//}
}
#endif
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