public static float Normalize(ref NPack.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;
}
// CIRCLE with R=1
public static Vector2 Circle( ref NPack.MersenneTwister _rand )
{
float t = (float) _rand.Next();
float _2pi = (float) Math.PI * 2;
float a = SpecialFunctions.ScaleFloatToRange(t, 0, _2pi, 0, Int32.MaxValue);
return new Vector2( (float) Math.Cos(a) , (float) Math.Sin(a));
}
public static Vector2 Disk( ref NPack.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)) );
}
/// FROM: http://unifycommunity.com/wiki/index.php?title=UnitSphere
/// <summary>
/// Returns a point on the unit sphere that is within a cone along the z-axis
/// </summary>
/// <param name="spotAngle">[0..180] specifies the angle of the cone. </param>
public static Vector3 GetPointOnCap(float spotAngle, ref NPack.MersenneTwister _rand)
{
float angle1 = SpecialFunctions.ScaleFloatToRange(_rand.NextSingle(true),0.0f, Mathf.PI*2, 0, 1);
float angle2 = SpecialFunctions.ScaleFloatToRange(_rand.NextSingle(true), 0.0f,spotAngle * Mathf.Deg2Rad, 0, 1);
Vector3 V = new Vector3(Mathf.Sin(angle1),Mathf.Cos(angle1),0);
V *= Mathf.Sin(angle2);
V.z = Mathf.Cos(angle2);
return V;
}
public static Vector3 Volume(ref NPack.MersenneTwister _rand)
{
Vector3 pos = PickCubePoints(ref _rand);
while ( isNotInsideSphere(pos) )
{
pos = PickCubePoints(ref _rand);
}
return pos;
}
// RADIUS = 1
// Marsaglia Method (1972) I use for Surface and Volume
// FROM http://stackoverflow.com/questions/5531827/random-point-on-a-given-sphere
// ALSO: http://mathworld.wolfram.com/SpherePointPicking.html
// 1. Pick a random point inside the [-1,1]x[-1,1]x[-1,1] cube
// 2. If x*x + y*y + z*z > 1 repeat from 1
// 3. Normalize dividing x, y and z by Math.sqrt(x*x + y*y + z*z)
public static Vector3 Surface(ref NPack.MersenneTwister _rand)
{
Vector3 pos = PickCubePoints(ref _rand);
while ( IsNotOnSurface(pos) )
{
pos = PickCubePoints(ref _rand);
}
return Normalize(pos);
}
private static Vector3 PickCubePoints( ref NPack.MersenneTwister _rand )
{
float x = SpecialFunctions.ScaleFloatToRange( _rand.NextSingle(true), -1, 1, 0, 1 );
float y = SpecialFunctions.ScaleFloatToRange( _rand.NextSingle(true), -1, 1, 0, 1 );
float z = SpecialFunctions.ScaleFloatToRange( _rand.NextSingle(true), -1, 1, 0, 1 );
return new Vector3(x,y,z);
}
// INIT
private void init(int size, DiceType type, ref NPack.MersenneTwister _rand)
{
_result = new int[size];
_dice_type = type;
_size = size;
for (int i = 0; i < _size; i++) {
// Cast enum to int to get the value
_result[i] = _rand.Next( 1, (int) type);
}
}
public static Vector2 Circle( ref NPack.MersenneTwister _rand, UnityRandom.Normalization n, float t )
{
float r;
switch (n) {
case UnityRandom.Normalization.STDNORMAL:
r = SpecialFunctions.ScaleFloatToRange( (float) NormalDistribution.Normalize(_rand.NextSingle(true), t), 0, Int32.MaxValue, 0, 1);
break;
case UnityRandom.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 = SpecialFunctions.ScaleFloatToRange(r, 0, _2pi, 0, Int32.MaxValue);
return new Vector2( (float) Math.Cos(a) , (float) Math.Sin(a));
}
// 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
public static float Normalize( ref NPack.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 - SpecialFunctions.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-SpecialFunctions.gammln(em+1.0f)-g);
} while (_rand.NextSingle(true) > t);
}
return (float) em;
}
public static Vector2 Disk( ref NPack.MersenneTwister _rand, UnityRandom.Normalization n, float temp )
{
double t, theta;
switch (n) {
case UnityRandom.Normalization.STDNORMAL:
t = NormalDistribution.Normalize(_rand.NextSingle(true), temp);
theta = NormalDistribution.Normalize(_rand.NextSingle(true), temp) * 2 * Math.PI;
break;
case UnityRandom.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 NPack.MersenneTwister _rand, UnityRandom.Normalization n, float t )
{
float x,y;
x = y = 0;
switch (n) {
case UnityRandom.Normalization.STDNORMAL:
x = (float) NormalDistribution.Normalize(_rand.NextSingle(true), t);
y = (float) NormalDistribution.Normalize(_rand.NextSingle(true), t);
break;
case UnityRandom.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 NPack.MersenneTwister _rand, UnityRandom.Normalization n, float t)
{
Vector3 pos = new Vector3();
switch (n) {
case UnityRandom.Normalization.STDNORMAL:
pos = GetPointOnCubeSurface(
(float) NormalDistribution.Normalize(_rand.NextSingle(true), t),
(float) NormalDistribution.Normalize(_rand.NextSingle(true), t),
_rand.Next(5));
break;
case UnityRandom.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(5));
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 Vector2 Area( ref NPack.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));
}
// CONSTRUCTOR
public DiceRoll(int size, DiceType type, ref NPack.MersenneTwister _rand)
{
if (size < 1) throw new ArgumentOutOfRangeException ("Number of dices shlud be > 0");
init(size,type,ref _rand);
}
public static Vector3 Surface(ref NPack.MersenneTwister _rand)
{
// Move to -1, 1 space as for CIRCLE and SPHERE
Vector3 pos = GetPointOnCubeSurface(_rand.NextSingle(true),_rand.NextSingle(true),_rand.Next(5));
return new Vector3((2*pos.x)-1, (2*pos.y)-1, (2*pos.z)-1);
}
// FIXME: NOT YET IMPLEMENTED IN UNITYRANDOM
public static Vector3 GetPointOnRing(float innerSpotAngle, float outerSpotAngle, ref NPack.MersenneTwister _rand, Quaternion orientation)
{
return orientation * GetPointOnRing(innerSpotAngle, outerSpotAngle, ref _rand);
}
// FIXME: NOT YET IMPLEMENTED IN UNITYRANDOM
public static Vector3 GetPointOnRing(float innerSpotAngle, float outerSpotAngle, ref NPack.MersenneTwister _rand, Transform relativeTo, float radius)
{
return relativeTo.TransformPoint( GetPointOnRing(innerSpotAngle, outerSpotAngle, ref _rand)*radius );
}
public static Vector3 Volume(ref NPack.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);
}
// FIXME: NOT YET IMPLEMENTED IN UNITYRANDOM
public static Vector3 GetPointOnCap(float spotAngle, ref NPack.MersenneTwister _rand, Quaternion orientation)
{
return orientation * GetPointOnCap(spotAngle, ref _rand);
}
// FIXME: NOT YET IMPLEMENTED IN UNITYRANDOM
public static Vector3 GetPointOnCap(float spotAngle, ref NPack.MersenneTwister _rand, Transform relativeTo, float radius)
{
return relativeTo.TransformPoint( GetPointOnCap(spotAngle, ref _rand)*radius );
}
