// CIRCLE with R=1
public static Vector2 Circle( ref UMT.MersenneTwister _rand )
{
float t = (float) _rand.Next();
float _2pi = (float) Math.PI * 2;
float a = MTRandom.ScaleFloatToRange(t, 0, _2pi, 0, Int32.MaxValue);
return new Vector2( (float) Math.Cos(a) , (float) Math.Sin(a));
}
public static float Normalize(ref UMT.MersenneTwister _rand, int ia)
{
int j;
float am, e, s, v1, v2, x, y;
if (ia < 1)
throw new ArgumentException("Error in Gamma Distribution. Argument ia should be an integer > 1");
if (ia < 6) {
// use direct method, addin waiting times
x = 1.0f;
for (j=1; j<=ia; j++) x *= _rand.NextSingle(true);
x = (float) - (Math.Log(x));
} else {
do {
do {
// This four lines generate the tanget of random angle
// Equivalent to y = tan( pi * rand())
do {
v1 = _rand.NextSingle(true);
v2 = 2.0f * _rand.NextSingle(true) - 1.0f;
} while (v1 * v1+v2 * v2 > 1.0f);
y = v2/v1;
am = ia-1;
s = (float) Math.Sqrt(2.0*am+1.0f);
x = s * y + am;
// We decide wheter to reject x, Reject in 0 probability region
} while (x <= 0.0f);
e = (float) ((1.0f + y*y) * Math.Exp(am * Math.Log(x/am) -s*y));
} while (_rand.NextSingle(true) > e);
}
return x;
}
public static Vector2 Disk( ref UMT.MersenneTwister _rand )
{
// t [0,1] , Theta [0,2pi)
double t = _rand.NextSingle(true);
// in range [0,1) then multiply this number by k to get a random number in the range [0,k)
double theta = _rand.NextSingle(false) * 2 * Math.PI;
return new Vector2( (float) (Math.Sqrt(t) * Math.Cos(theta)), (float) (Math.Sqrt(t) * Math.Sin(theta)) );
}
/// <summary>
/// Returns a point on the unit sphere that is within the outer cone along the z-axis
/// but not inside the inner cone. The resulting area describes a ring on the sphere surface.
/// </summary>
/// <param name="innerSpotAngle">[0..180] specifies the inner cone that should be excluded.</param>
/// <param name="outerSpotAngle">[0..180] specifies the outer cone that should be included.</param>
/// <remarks>FROM: http://unifycommunity.com/wiki/index.php?title=UnitSphere</remarks>
public static Vector3 GetPointOnRing(float innerSpotAngle, float outerSpotAngle, ref UMT.MersenneTwister _rand)
{
float angle1 = MTRandom.ScaleFloatToRange(_rand.NextSingle(true),0.0f, Mathf.PI*2, 0, 1);
float angle2 = MTRandom.ScaleFloatToRange(_rand.NextSingle(true),innerSpotAngle, outerSpotAngle, 0, 1) * Mathf.Deg2Rad;
Vector3 V = new Vector3(Mathf.Sin(angle1),Mathf.Cos(angle1),0);
V *= Mathf.Sin(angle2);
V.z = Mathf.Cos(angle2);
return V;
}
public static Vector2 Circle( ref UMT.MersenneTwister _rand, MTRandom.Normalization n, float t )
{
float r;
switch (n) {
case MTRandom.Normalization.STDNORMAL:
r = MTRandom.ScaleFloatToRange( (float) NormalDistribution.Normalize(_rand.NextSingle(true), t), 0, Int32.MaxValue, 0, 1);
break;
case MTRandom.Normalization.POWERLAW:
r = (float) PowerLaw.Normalize(_rand.NextSingle(true), t, 0, Int32.MaxValue);
break;
default:
r = (float) _rand.Next();
break;
}
float _2pi = (float) Math.PI * 2;
float a = MTRandom.ScaleFloatToRange(r, 0, _2pi, 0, Int32.MaxValue);
return new Vector2( (float) Math.Cos(a) , (float) Math.Sin(a));
}
/// <summary>
/// return as a floating point number an integer value that is a random deviate drawn
/// from a Possion Distribution of mean xm using randx as a source of uniform deviates
/// </summary>
/// <param name="_rand">random generator.</param>
/// <param name="xm">Xm.</param>
public static float Normalize( ref UMT.MersenneTwister _rand, float xm)
{
// Davide Rambaldi: all moved to double precision
double sq, alxm, g, oldm; // oldm is a flag for wheter xm has changed or not sincle last call
sq = alxm = g = oldm = (-1.0);
double em, t, y;
if (xm < 12.0f) { // Use direct method
if (xm != oldm) {
oldm = xm;
g = Math.Exp(-xm); // if x is new, compute the exponential
}
em = -1;
t = 1.0f;
// Instead of adding exponential deviates it is equivalent to multiply unifomr deviates
// We never actually take the log, we compare the precomupted exponential
do {
++em;
t *= _rand.NextSingle(true);
} while (t > g);
} else {
// Use REJECTION method
// xm has changed?
if ( xm != oldm) {
oldm = xm;
sq = Math.Sqrt(2.0 * xm);
alxm = Math.Log(xm);
// Gammln is the natural log of a gamma function
g = xm * alxm - gammln(xm + 1.0f);
}
do {
do {
// y is the deviate from a Lorentzian comparison function
y = Math.Tan(Math.PI*_rand.NextSingle(true));
em=sq*y+xm;
} while (em < 0.0);
em = Math.Floor(em);
t = 0.9 * (1.0+y*y) * Math.Exp(em*alxm-gammln(em+1.0f)-g);
} while (_rand.NextSingle(true) > t);
}
return (float) em;
}
public static Vector2 Disk( ref UMT.MersenneTwister _rand, MTRandom.Normalization n, float temp )
{
double t, theta;
switch (n) {
case MTRandom.Normalization.STDNORMAL:
t = NormalDistribution.Normalize(_rand.NextSingle(true), temp);
theta = NormalDistribution.Normalize(_rand.NextSingle(true), temp) * 2 * Math.PI;
break;
case MTRandom.Normalization.POWERLAW:
t = PowerLaw.Normalize(_rand.NextSingle(true), temp, 0, 1);
theta = PowerLaw.Normalize(_rand.NextSingle(true), temp, 0, 1) * 2 * Math.PI;
break;
default:
t = (float) _rand.NextSingle(true);
theta = _rand.NextSingle(false) * 2 * Math.PI;
break;
}
return new Vector2( (float) (Math.Sqrt(t) * Math.Cos(theta)), (float) (Math.Sqrt(t) * Math.Sin(theta)) );
}
public static Vector2 Area( ref UMT.MersenneTwister _rand, MTRandom.Normalization n, float t )
{
float x,y;
x = y = 0;
switch (n) {
case MTRandom.Normalization.STDNORMAL:
x = (float) NormalDistribution.Normalize(_rand.NextSingle(true), t);
y = (float) NormalDistribution.Normalize(_rand.NextSingle(true), t);
break;
case MTRandom.Normalization.POWERLAW:
x = (float) PowerLaw.Normalize(_rand.NextSingle(true), t, 0, 1);
y = (float) PowerLaw.Normalize(_rand.NextSingle(true), t, 0, 1);
break;
default:
x = _rand.NextSingle(true);
y = _rand.NextSingle(true);
break;
}
// Move to -1, 1 space as for CIRCLE and SPHERE
return new Vector2((2*x - 1), (2*y - 1));
}
public static Vector3 Surface(ref UMT.MersenneTwister _rand, MTRandom.Normalization n, float t)
{
Vector3 pos = new Vector3();
switch (n) {
case MTRandom.Normalization.STDNORMAL:
pos = GetPointOnCubeSurface(
(float) NormalDistribution.Normalize(_rand.NextSingle(true), t),
(float) NormalDistribution.Normalize(_rand.NextSingle(true), t),
_rand.Next(5));
break;
case MTRandom.Normalization.POWERLAW:
pos = GetPointOnCubeSurface(
(float) PowerLaw.Normalize(_rand.NextSingle(true), t, 0, 1),
(float) PowerLaw.Normalize(_rand.NextSingle(true), t, 0, 1),
_rand.Next(5));
break;
default:
pos = GetPointOnCubeSurface(_rand.NextSingle(true),_rand.NextSingle(true),_rand.Next(6));
break;
}
// Move to -1, 1 space as for CIRCLE and SPHERE
return new Vector3((2*pos.x)-1, (2*pos.y)-1, (2*pos.z)-1);
}
public static Vector3 Surface(ref UMT.MersenneTwister _rand)
{
// Move to -1, 1 space as for CIRCLE and SPHERE
Vector3 pos = GetPointOnCubeSurface(_rand.NextSingle(true),_rand.NextSingle(true),_rand.Next(6));
return new Vector3((2*pos.x)-1, (2*pos.y)-1, (2*pos.z)-1);
}
public static Vector2 Area( ref UMT.MersenneTwister _rand )
{
// Move to -1, 1 space as for CIRCLE and SPHERE
return new Vector2((2*_rand.NextSingle(true) - 1), (2*_rand.NextSingle(true) - 1));
}
public static Vector3 Volume(ref UMT.MersenneTwister _rand)
{
Vector3 pos = new Vector3(_rand.NextSingle(true), _rand.NextSingle(true), _rand.NextSingle(true));
// Move to -1, 1 space as for CIRCLE and SPHERE
return new Vector3((2*pos.x)-1, (2*pos.y)-1, (2*pos.z)-1);
}
/// <summary>
/// Gets the point on ring.
/// </summary>
/// <returns>The point on ring.</returns>
/// <param name="innerSpotAngle">Inner spot angle.</param>
/// <param name="outerSpotAngle">Outer spot angle.</param>
/// <param name="_rand">_rand.</param>
/// <param name="relativeTo">Relative to.</param>
/// <param name="radius">Radius.</param>
public static Vector3 GetPointOnRing(float innerSpotAngle, float outerSpotAngle, ref UMT.MersenneTwister _rand, Transform relativeTo, float radius)
{
return relativeTo.TransformPoint( GetPointOnRing(innerSpotAngle, outerSpotAngle, ref _rand)*radius );
}
/// <summary>
/// Surface.
/// </summary>
/// <param name="_rand">random generator.</param>
public static Vector3 Surface(ref UMT.MersenneTwister _rand)
{
Vector3 pos = PickCubePoints(ref _rand);
while ( IsNotOnSurface(pos) )
{
pos = PickCubePoints(ref _rand);
}
return Normalize(pos);
}
/// <summary>
/// Volume.
/// </summary>
/// <param name="_rand">random generator.</param>
public static Vector3 Volume(ref UMT.MersenneTwister _rand)
{
Vector3 pos = PickCubePoints(ref _rand);
while ( isNotInsideSphere(pos) )
{
pos = PickCubePoints(ref _rand);
}
return pos;
}
/// <summary>
/// Gets the point on ring.
/// </summary>
/// <returns>The point on ring.</returns>
/// <param name="innerSpotAngle">Inner spot angle.</param>
/// <param name="outerSpotAngle">Outer spot angle.</param>
/// <param name="_rand">_rand.</param>
/// <param name="orientation">Orientation.</param>
public static Vector3 GetPointOnRing(float innerSpotAngle, float outerSpotAngle, ref UMT.MersenneTwister _rand, Quaternion orientation)
{
return orientation * GetPointOnRing(innerSpotAngle, outerSpotAngle, ref _rand);
}
/// <summary>
/// Gets the point on cap.
/// </summary>
/// <returns>The point on cap.</returns>
/// <param name="spotAngle">Spot angle.</param>
/// <param name="_rand">_rand.</param>
/// <param name="relativeTo">Relative to.</param>
/// <param name="radius">Radius.</param>
public static Vector3 GetPointOnCap(float spotAngle, ref UMT.MersenneTwister _rand, Transform relativeTo, float radius)
{
return relativeTo.TransformPoint( GetPointOnCap(spotAngle, ref _rand)*radius );
}
/// <summary>
/// Gets the point on cap.
/// </summary>
/// <returns>The point on cap.</returns>
/// <param name="spotAngle">Spot angle.</param>
/// <param name="_rand">_rand.</param>
/// <param name="orientation">Orientation.</param>
public static Vector3 GetPointOnCap(float spotAngle, ref UMT.MersenneTwister _rand, Quaternion orientation)
{
return orientation * GetPointOnCap(spotAngle, ref _rand);
}
private static Vector3 PickCubePoints( ref UMT.MersenneTwister _rand )
{
float x = MTRandom.ScaleFloatToRange( _rand.NextSingle(true), -1, 1, 0, 1 );
float y = MTRandom.ScaleFloatToRange( _rand.NextSingle(true), -1, 1, 0, 1 );
float z = MTRandom.ScaleFloatToRange( _rand.NextSingle(true), -1, 1, 0, 1 );
return new Vector3(x,y,z);
}
