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/// ------------------------------------------------------
/// RandomOps - (Pseudo) Random Number Generator For C#
/// Copyright (C) 2003-2010 Magnus Erik Hvass Pedersen.
/// Please see the file license.txt for license details.
/// RandomOps on the internet: http://www.Hvass-Labs.org/
/// ------------------------------------------------------
using System;
using System.Diagnostics;
namespace RandomOps
{
/// <remarks>
/// Implements RNG of a disk.
/// </remarks>
public abstract partial class Random
{
/// <summary>
/// Generate a uniform random point from the unit-radius 2-dimensional disk.
/// Thread-safe if Uniform() is thread-safe.
/// </summary>
public virtual double[] Disk()
{
double[] x = new double[2];
double sumSquares;
Disk(out x[0], out x[1], out sumSquares);
return x;
}
/// <summary>
/// Generate a uniform random point from the unit-radius 2-dimensional disk.
/// Thread-safe if Uniform() is thread-safe.
/// </summary>
/// <param name="x">Random point x</param>
/// <param name="y">Random point y</param>
/// <param name="sumSquares">Equals x*x + y*y</param>
public virtual void Disk(out double x, out double y, out double sumSquares)
{
// Pick two uniform numbers in the square (-1,1) x (-1,1). See if the
// numbers are inside the unit circle, and if they are not, try again.
// Succesful points occupy the inside of the unit circle, whose area is
// pi, or about 3.14. Since we sample uniformly from a square of size 4,
// the probability of the loop succeeding in a single iteration is pi/4,
// or about 0.7854.
// Probability of success in two iterations is therefore 0.954, in three
// iterations it is about 0.990, and the probability of success in
// four successive iterations is approximately 0.998, etc. -- provided there
// is no correlation between calls to Uniform(-1, 1).
// The average number of iterations before success is 1.27
do
{
x = Uniform(-1, 1);
y = Uniform(-1, 1);
sumSquares = x * x + y * y;
}
while (sumSquares > 1);
}
}
}
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