// The Lanczos approximation, should only be good for z >= 0.5,
// but we get the right answers anyway.
private static double gamma(double z)
{
double[] p = new double[8]
{
676.5203681218851,
-1259.1392167224028,
771.32342877765313,
-176.61502916214059,
12.507343278686905,
-0.13857109526572012,
9.9843695780195716e-6,
1.5056327351493116e-7
};
z -= 1.0;
double x = 0.99999999999980993; // Unnecessary precision
for (int i = 0; i < 8; i++)
{
double pval = p[i];
x += pval / (z + i + 1);
}
double t = z + 8.0 - 0.5;
return(Math.Sqrt(2.0 * Math.PI) * Math.Pow(t, z + 0.5) * Math.Exp(-t) * x);
}
public static H3.Cell[] CalcCellsSmart(Sphere[] mirrors, H3.Cell[] cells, Settings settings, int desiredCount)
{
double t1 = 80;
double t2 = 130;
// I found that log(1/thresh)/log(count) was relatively constant,
// so we'll extrapolate that to get close to the right number of edges.
double OneOverThresh = t1;
settings.Threshold = 1 / OneOverThresh;
H3.Cell[] result = CalcCells(mirrors, cells, settings);
int count1 = result.Length;
System.Console.WriteLine(string.Format("count1: {0}", count1));
OneOverThresh = t2;
settings.Threshold = 1 / OneOverThresh;
result = CalcCells(mirrors, cells, settings);
int count2 = result.Length;
System.Console.WriteLine(string.Format("count2: {0}", count2));
double slope = (Math.Log(count2) - Math.Log(count1)) / (Math.Log(t2) - Math.Log(t1));
double logDesiredCount = Math.Log((double)desiredCount);
double temp = Math.Log(t2) + (logDesiredCount - Math.Log(count2)) / slope;
settings.Threshold = 1 / Math.Exp(temp);
System.Console.WriteLine(string.Format("Setting threshold to: {0}", settings.Threshold));
return(CalcCells(mirrors, cells, settings));
}
public static float[,] CalculateGaussianKernel(int W, double sigma)
{
float[,] kernel = new float[W, W];
double mean = W / 2.0;
float sum = 0.0f;
for (int x = 0; x < W; ++x)
{
for (int y = 0; y < W; ++y)
{
kernel[x, y] = (float)(Math.Exp(-0.5 * (Math.Pow((x - mean) / sigma, 2.0) + Math.Pow((y - mean) / sigma, 2.0)))
/ (2 * Math.PI * sigma * sigma));
sum += kernel[x, y];
}
}
for (int x = 0; x < W; ++x)
{
for (int y = 0; y < W; ++y)
{
kernel[x, y] *= (1.0f) / sum;
}
}
return(kernel);
}
/// <summary>
/// From the virtual math museum
/// </summary>
public static Vector3D Dini2(Vector3D disk)
{
Vector3D uv = DiskToUpper(disk);
double u = Math.Log(uv.Y);
//double v = DonHatch.acosh( 1 + ( Math.Pow( uv.X, 2 ) + 0 ) / ( 2 * Math.Pow( uv.Y, 2 ) ) ) ;
//if( uv.X < 0 )
// v *= -1;
double v = uv.X;
if (u <= -4 || u > 4 ||
v < -6 * Math.PI || v > 6 * Math.PI)
{
return(Infinity.InfinityVector);
}
double psi = 0.5;
psi *= Math.PI;
double sinpsi = Math.Sin(psi);
double cospsi = Math.Cos(psi);
double g = (u - cospsi * v) / sinpsi;
double s = Math.Exp(g);
double r = (2 * sinpsi) / (s + 1 / s);
double t = r * (s - 1 / s) * 0.5;
return(new Vector3D(u - t, r * Math.Cos(v), r * Math.Sin(v)));
}
/// <summary>
/// Handles the calculation for hyperbolic cosecant.
/// </summary>
/// <param name="x">A double to be evaluated.</param>
/// <returns>Return the hyperbolic cosecant of an angle specified in radians.</returns>
public static double HyperbolicCosecant(double x)
{
if ((MathObj.Exp(x) - MathObj.Exp(-x)) == 0)
{
return(-2);
}
return(2 / (MathObj.Exp(x) - MathObj.Exp(-x)));
}
/// <summary>
/// Handles the calculation for hyperbolic cotangent.
/// </summary>
/// <param name="x">A double to be evaluated.</param>
/// <returns>Return the hyperbolic cotangent of a hyperbolic angle.</returns>
public static double HyperbolicCotangent(double x)
{
//This is to handle a rounding diffrence between excel and EPPlus.
var NaNChecker = (MathObj.Exp(x) + MathObj.Exp(-x)) / (MathObj.Exp(x) - MathObj.Exp(-x));
if (NaNChecker.Equals(double.NaN))
{
return(1);
}
return((MathObj.Exp(x) + MathObj.Exp(-x)) / (MathObj.Exp(x) - MathObj.Exp(-x)));
}
expm1(double x)
{
double u = Math.Exp(x);
if (u == 1.0)
{
return(x);
}
if (u - 1.0 == -1.0)
{
return(-1);
}
return((u - 1.0) * x / Math.Log(u));
}
/// <summary>
/// Attempts to calculate approx 1.3M edges when the threshold is a minimum edge length.
/// This is required for honeycombs with ideal or ultra-ideal cells
/// </summary>
public static Edge[] CalcEdgesSmart2(Sphere[] simplex, Edge[] edges, int desiredCount)
{
Settings s = new Settings();
// I found that log(1/thresh)/log(count) was relatively constant,
// so we'll extrapolate that to get close to the right number of edges.
double OneOverThresh = 60;
s.Threshold = 1 / OneOverThresh;
Edge[] result = CalcEdges(simplex, edges, s);
int count1 = result.Length;
OneOverThresh = 80;
s.Threshold = 1 / OneOverThresh;
result = CalcEdges(simplex, edges, s);
int count2 = result.Length;
double slope = (Math.Log(count2) - Math.Log(count1)) / (Math.Log(80) - Math.Log(60));
double logDesiredCount = Math.Log((double)desiredCount);
double temp = Math.Log(80) + (logDesiredCount - Math.Log(count2)) / slope;
s.Threshold = 1 / Math.Exp(temp);
return(CalcEdges(simplex, edges, s));
}
public static float Ease(int esType, float t)
{
switch (esType)
{
case EsType.Quad:
case EsType.QuadIn: return(t * t);
case EsType.QuadOut: return(t * (2 - t));
case EsType.QuadInOut: return((t *= 2) < 1 ? .5f * t * t : .5f * (1 - (t - 1) * (t - 3)));
case EsType.Cubic:
case EsType.CubicIn: return(t * t * t);
case EsType.CubicOut: return((t -= 1) * t * t + 1);
case EsType.CubicInOut: return((t *= 2) < 1 ? .5f * t * t * t : .5f * ((t -= 2) * t * t + 2));
case EsType.Quart:
case EsType.QuartIn: return(t * t * t * t);
case EsType.QuartOut: return(1 - (t -= 1) * t * t * t);
case EsType.QuartInOut: return((t *= 2) < 1 ? .5f * t * t * t * t : .5f * (2 - (t -= 2) * t * t * t));
case EsType.Quint:
case EsType.QuintIn: return(t * t * t * t * t);
case EsType.QuintOut: return((t -= 1) * t * t * t * t + 1);
case EsType.QuintInOut: return((t *= 2) < 1 ? .5f * t * t * t * t * t : .5f * ((t -= 2) * t * t * t * t + 2));
case EsType.Sine:
case EsType.SineIn: return(1 - (float)Math.Cos(t * HalfPi));
case EsType.SineOut: return((float)Math.Sin(t * HalfPi));
case EsType.SineInOut: return(.5f * (1 - (float)Math.Cos(t * Pi)));
case EsType.Expo:
case EsType.ExpoIn: return((float)Math.Exp(7 * (t - 1)));
case EsType.ExpoOut: return(1 - (float)Math.Exp(-7 * t));
case EsType.ExpoInOut: return((t *= 2) < 1 ? .5f * (float)Math.Exp(7 * (t - 1)) : .5f * (2 - (float)Math.Exp(-7 * (t - 1))));
case EsType.Circ:
case EsType.CircIn: return(1 - (float)Math.Sqrt(1 - t * t));
case EsType.CircOut: return((float)Math.Sqrt(1 - (t -= 1) * t));
case EsType.CircInOut: return((t *= 2) < 1 ? .5f * (1 - (float)Math.Sqrt(1 - t * t)) : .5f * ((float)Math.Sqrt(1 - (t -= 2) * t) + 1));
case EsType.Back:
case EsType.BackIn: return(t * t * (2.70158f * t - 1.70158f));
case EsType.BackOut: return((t -= 1) * t * (2.70158f * t + 1.70158f) + 1);
case EsType.BackInOut: return((t *= 2) < 1 ? .5f * (t * t * (3.5949095f * t - 2.5949095f)) : .5f * ((t -= 2) * t * (3.5949095f * t + 2.5949095f) + 2));
case EsType.Elastic:
case EsType.ElasticIn: return((float)(-Math.Exp(7 * (t -= 1)) * Math.Sin((t - 0.075) * 20.9439510239)));
case EsType.ElasticOut: return((float)(Math.Exp(-7 * t) * Math.Sin((t - 0.075) * 20.9439510239) + 1));
case EsType.ElasticInOut: return((t *= 2) < 1 ? (float)(-.5 * Math.Exp(7 * (t -= 1)) * Math.Sin((t - 0.1125) * 13.962634016)) : (float)(Math.Exp(-7 * (t -= 1)) * Math.Sin((t - 0.1125) * 13.962634016) * .5 + 1));
case EsType.Bounce:
case EsType.BounceIn: return(1 - Es.Ease(EsType.BounceOut, 1 - t));
case EsType.BounceOut: return(t < 0.363636363636f ? 7.5625f * t * t : t < 0.727272727273f ? 7.5625f * (t -= 0.545454545455f) * t + .75f : t < 0.909090909091f ? 7.5625f * (t -= 0.818181818182f) * t + .9375f : 7.5625f * (t -= 0.954545454545f) * t + .984375f);
case EsType.BounceInOut: return((t *= 2) < 1 ? .5f * (1 - Es.Ease(EsType.BounceOut, 1 - t)) : .5f * (Es.Ease(EsType.BounceOut, t - 1) + 1));
}
return(t);
}
/// <summary>
/// http://www.wolframalpha.com/input/?i=1%2F+%281%2Be%5E%28-10*%28x-0.5%29%29%29
/// </summary>
private double Sigmoid(double input)
{
return(1 / (1 + Math.Exp(-BorderDiv * (input - 0.5))));
}
cosh(double x)
{
double e_x = Math.Exp(x);
return((e_x + 1.0 / e_x) * .5);
}
// Hyperbolic Cosecant
public static double HCosec(double x)
{
return(2 / (MathObj.Exp(x) - MathObj.Exp(-x)));
}
// Hyperbolic Cosine
public static double HCos(double x)
{
return((MathObj.Exp(x) + MathObj.Exp(-x)) / 2);
}
/// <summary>
/// Handles the calculation for Hyperbolic Secant.
/// </summary>
/// <param name="x">A double to be evaluated.</param>
/// <returns>Returns the hyperbolic secant of an angle.</returns>
public static double HyperbolicSecant(double x)
{
return(2 / (MathObj.Exp(x) + MathObj.Exp(-x)));
}
private static int Math_Exp(ILuaState lua)
{
lua.PushNumber(Math.Exp(lua.L_CheckNumber(1)));
return(1);
}
public static double Exp(object self, double x)
{
return(SM.Exp(x));
}
// Hyperbolic Secant
public static double HSec(double x)
{
return(2 / (MathObj.Exp(x) + MathObj.Exp(-x)));
}
public static double Exp(object self, [DefaultProtocol] double x)
{
return(SM.Exp(x));
}
// Hyperbolic Tangent
public static double HTan(double x)
{
return((MathObj.Exp(x) - MathObj.Exp(-x)) / (MathObj.Exp(x) + MathObj.Exp(-x)));
}
// Hyperbolic Sine
public static double HSin(double x)
{
return((MathObj.Exp(x) - MathObj.Exp(-x)) / 2);
}