/// <summary>
/// Returns a fully uniformly distributed vector (corresponds to a
/// uniformly distributed point on the surface of the unit sphere).
/// Note however, that the returned vector will never be equal to
/// [0, 0, -1].
/// </summary>
public static V3d UniformV3dFullDirection(this IRandomUniform rnd)
{
double phi = rnd.UniformDoubleFull() * Constant.PiTimesTwo;
double z = 1.0 - rnd.UniformDoubleFull() * 2.0;
double s = System.Math.Sqrt(1.0 - z * z);
return(new V3d(System.Math.Cos(phi) * s, System.Math.Sin(phi) * s, z));
}
/// <summary>
/// Returns a uniformly distributed long in the interval [0, size-1].
/// NOTE: If count has more than about 48 bits, aliasing leads to
/// noticeable (greater 5%) shifts in the probabilities (i.e. one
/// long has a probability of x and the other a probability of
/// x * (2^(52-b)-1)/(2^(52-b)), where b is log(size)/log(2)).
/// </summary>
public static long UniformLong(this IRandomUniform rnd, long size)
{
if (rnd.GeneratesFullDoubles || size < 16777216)
{
return((long)(rnd.UniformDouble() * size));
}
else
{
return((long)(rnd.UniformDoubleFull() * size));
}
}
/// <summary>
/// Returns a uniformly distributed int in the interval [0, count-1].
/// In order to avoid excessive aliasing, two random numbers are used
/// when count is greater or equal 2^24 and the random generator
/// delivers 32 random bits or less. The method thus works fairly
/// decently for all integers.
/// </summary>
public static int UniformInt(this IRandomUniform rnd, int size)
{
if (rnd.GeneratesFullDoubles || size < 16777216)
{
return((int)(rnd.UniformDouble() * size));
}
else
{
return((int)(rnd.UniformDoubleFull() * size));
}
}
/// <summary>
/// Fills the specified array with fully random doubles (53 random
/// bits) in the half-open interval [0.0, 1.0).
/// </summary>
public static void FillUniformFull(
this IRandomUniform rnd, double[] array)
{
long count = array.LongLength;
if (rnd.GeneratesFullDoubles)
{
for (long i = 0; i < count; i++)
{
array[i] = rnd.UniformDoubleFull();
}
}
else
{
for (long i = 0; i < count; i++)
{
array[i] = rnd.UniformDouble();
}
}
}
public static V3d UniformV3dFull(this IRandomUniform rnd, Box3d box)
{
return(box.Lerp(rnd.UniformDoubleFull(),
rnd.UniformDoubleFull(),
rnd.UniformDoubleFull()));
}
public static V3d UniformV3dFull(this IRandomUniform rnd)
{
return(new V3d(rnd.UniformDoubleFull(),
rnd.UniformDoubleFull(),
rnd.UniformDoubleFull()));
}
public static V2d UniformV2dFull(this IRandomUniform rnd, Box2d box)
{
return(new V2d(box.Min.X + rnd.UniformDoubleFull() * (box.Max.X - box.Min.X),
box.Min.Y + rnd.UniformDoubleFull() * (box.Max.Y - box.Min.Y)));
}
