/// <summary>
/// Returns a uniformly distributed vector (corresponds to a
/// uniformly distributed point on the unit sphere) by using
/// 2 random values from the series with the supplied indices.
/// Note, that the returned vector will never be equal to [0, 0, -1].
/// </summary>
public static V3d UniformV3dDirection(this IRandomSeries rnd, int si0, int si1)
{
double phi = rnd.UniformDouble(si0) * Constant.PiTimesTwo;
double z = 1.0 - rnd.UniformDouble(si1) * 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>
/// Uses the 2 random series (seriesIndex, seriesIndex+1)
/// </summary>
public static V3d Spherical(
IRandomSeries rnds, int seriesIndex)
{
double phi = Constant.PiTimesTwo * rnds.UniformDouble(seriesIndex);
double z = 1.0 - 2.0 * rnds.UniformDouble(seriesIndex + 1);
double r = Fun.Max(1.0 - z * z, 0.0).Sqrt();
return(new V3d(r * phi.Cos(), r * phi.Sin(), z));
}
/// <summary>
/// Supplied normal MUST be normalized, uses the 2 random series
/// (seriesIndex, seriesIndex+1).
/// </summary>
public static V3d Lambertian(
V3d normal, IRandomSeries rnds, int seriesIndex)
{
V3d vec;
double squareLen;
do
{
double phi = Constant.PiTimesTwo * rnds.UniformDouble(seriesIndex);
double z = 1.0 - 2.0 * rnds.UniformDouble(seriesIndex + 1);
double r = Fun.Max(1.0 - z * z, 0.0).Sqrt();
vec = new V3d(r * phi.Cos(), r * phi.Sin(), z) + normal;
squareLen = vec.LengthSquared;
}while (squareLen < 0.000001);
vec *= 1.0 / squareLen.Sqrt();
return(vec);
}
/// <summary>
/// Generates a uniform distributed random sample on the given triangle using
/// two random series (seriesIndex, seriesIndex + 1).
/// </summary>
public static V2d Triangle(Triangle2d t, IRandomSeries rnd, int seriesIndex)
{
return(Triangle(t.P0, t.P1, t.P2,
rnd.UniformDouble(seriesIndex),
rnd.UniformDouble(seriesIndex + 1)));
}
/// <summary>
/// Uses the 2 random series (seriesIndex, seriesIndex+1) to generate a random point on a sphere.
/// </summary>
public static V3d Spherical(IRandomSeries rnds, int seriesIndex)
{
return(Spherical(rnds.UniformDouble(seriesIndex), rnds.UniformDouble(seriesIndex + 1)));
}
/// <summary>
/// Generates a uniform distributed 2d random sample on a disk with radius 1.
/// It uses two random series (seriesIndex, seriesIndex+1).
/// </summary>
public static V2d Disk(IRandomSeries rnd, int seriesIndex)
{
return(Disk(rnd.UniformDouble(seriesIndex), rnd.UniformDouble(seriesIndex + 1)));
}
/// <summary>
/// Supplied normal MUST be normalized, uses the 2 random series
/// (seriesIndex, seriesIndex+1).
/// </summary>
public static V3d Lambertian(V3d normal, IRandomSeries rnds, int seriesIndex)
{
return(Lambertian(normal,
rnds.UniformDouble(seriesIndex),
rnds.UniformDouble(seriesIndex + 1)));
}
/// <summary>
/// Generates a uniform distributed random sample on the given triangle using
/// two random series (seriesIndex, seriesIndex + 1).
/// </summary>
public static V3d Triangle(V3d p0, V3d p1, V3d p2, IRandomSeries rnd, int seriesIndex)
{
return(Triangle(p0, p1, p2,
rnd.UniformDouble(seriesIndex),
rnd.UniformDouble(seriesIndex + 1)));
}