public static float logCurve(float level, float initial, float steepness, float amplification)
{
float s = 1 / (float)Math.Log((steepness + 1), 10);
float b = (float)(Math.Log((level + s), 10) - Math.Log(s, 10));
return(initial + amplification * b);
}
/// <summary>
/// Calculates distance/bearing between two geographic locations on Rhumb line (loxodrome)
/// </summary>
/// <param name="origin">origin location in geographic degrees</param>
/// <param name="destination">destination location in geographic degrees</param>
/// <param name="radius">radius of a geographic sphere, in kilometers</param>
/// <remarks>radius defaults to Earth's mean radius</remarks>
public static GeoRhumb GetRhumb(GeoPoint origin, GeoPoint destination, double radius = GeoGlobal.Earths.Radius)
{
origin = origin.ToRadians();
destination = destination.ToRadians();
var dLat = (destination.Latitude - origin.Latitude);
var dLon = (destination.Longitude - origin.Longitude);
var tDestination = Math.Tan(Math.PI / 4 + destination.Latitude / 2);
var tOrigin = Math.Tan(Math.PI / 4 + origin.Latitude / 2);
var dPhi = Math.Log(tDestination / tOrigin); // E-W line gives dPhi=0
var q = (IsFinite(dLat / dPhi)) ? dLat / dPhi : Math.Cos(origin.Latitude);
// if dLon over 180° take shorter Rhumb across anti-meridian:
if (Math.Abs(dLon) > Math.PI)
{
dLon = dLon > 0 ? -(2 * Math.PI - dLon) : (2 * Math.PI + dLon);
}
var distance = Math.Sqrt(dLat * dLat + q * q * dLon * dLon) * radius;
var bearing = Math.Atan2(dLon, dPhi);
return(new GeoRhumb {
Distance = distance, Bearing = bearing.ToDegreesNormalized()
});
}
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));
}
/// <summary>
/// Attempts to calculate approx 1.3M edges when the threshold is a distance from origin in the ball model.
/// This works for honeycombs with finite cells.
/// </summary>
public static Edge[] CalcEdgesSmart(Sphere[] simplex, Edge[] edges, int desiredCount)
{
Settings s = new Settings();
s.ThreshType = EdgeThreshType.Radial;
// The number of cells increase exponentially with hyperbolic distance,
// so linear on a log scale.
// We'll do to test runs to get the line, then run at the extrapolated value.
double hDist = 5;
s.Threshold = DonHatch.h2eNorm(hDist);
Edge[] result = CalcEdges(simplex, edges, s);
int count1 = result.Length;
hDist = 5.5;
s.Threshold = DonHatch.h2eNorm(hDist);
result = CalcEdges(simplex, edges, s);
int count2 = result.Length;
double slope = (Math.Log(count2) - Math.Log(count1)) / 0.5;
double logDesiredCount = Math.Log(desiredCount);
hDist = 5.5 + (logDesiredCount - Math.Log(count2)) / slope;
s.Threshold = DonHatch.h2eNorm(hDist);
return(CalcEdges(simplex, edges, s));
}
public static Vector3D SpiralToIsometric(Vector3D v, int p, int m, int n)
{
Complex vc = v.ToComplex();
v = new Vector3D(Math.Log(vc.Magnitude), vc.Phase);
Vector3D e1 = new Vector3D(0, 1);
Vector3D e2;
switch (p)
{
case 3:
e2 = new Vector3D(); break;
case 4:
e2 = new Vector3D(); break;
case 6:
e2 = new Vector3D(); break;
default:
throw new System.ArgumentException();
}
double scale = Math.Sqrt(m * m + n * n);
double a = Euclidean2D.AngleToClock(new Vector3D(0, 1), new Vector3D(m, n));
v.RotateXY(a); // Rotate
v *= scale; // Scale
v *= Math.Sqrt(2) * Geometry2D.EuclideanHypotenuse / (2 * Math.PI);
v.RotateXY(Math.PI / 4);
return(v);
}
/// <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)));
}
// Box-Muller Transformation
private float GetRandomPosX(float seedX)
{
double x1 = Random.value;
double x2 = Random.value;
float posX = (float)(_dispersion * Math.Sqrt(-2 * Math.Log(x1)) * Math.Cos(2 * Math.PI * x2) + seedX);
if (!_spawnArea.IsInRange(posX))
{
posX = _spawnArea.Adjust(posX);
}
return(posX);
}
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));
}
private static int Math_Log(ILuaState lua)
{
double x = lua.L_CheckNumber(1);
double res;
if (lua.IsNoneOrNil(2))
{
res = Math.Log(x);
}
else
{
double logBase = lua.L_CheckNumber(2);
if (logBase == 10.0)
{
res = Math.Log10(x);
}
else
{
res = Math.Log(x, logBase);
}
}
lua.PushNumber(res);
return(1);
}
/// <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));
}
/// <summary>
/// Handles the calculation for inverse hyperbolic cosine.
/// </summary>
/// <param name="x">A double to be evaluated.</param>
/// <returns>Returns the inverse hyperbolic cosine of a number.</returns>
public static double InverseHyperbolicCosine(double x)
{
return(MathObj.Log(x + MathObj.Sqrt(x * x - 1)));
}
/// <summary>
/// Handles the calculation for inverse hyperbolic cotangent.
/// </summary>
/// <param name="x">A double to be evaluated.</param>
/// <returns>Returns the inverse hyperbolic cotangent of a number.</returns>
public static double InverseHyperbolicCotangent(double x)
{
return(MathObj.Log((x + 1.0) / (x - 1.0)) / 2.0);
}
/// <summary>
/// Handles the calculation for Inverse Hyperbolic Tangent.
/// </summary>
/// <param name="x">A double to be evaluated.</param>
/// <returns>Returns the inverse hyperbolic tangent of a number.</returns>
public static double InverseHyperbolicTangent(double x)
{
return(MathObj.Log((1 + x) / (1 - x)) / 2);
}
// Inverse Hyperbolic Tangent
public static double HArctan(double x)
{
return(MathObj.Log((1 + x) / (1 - x)) / 2);
}
log1p(double x)
{
double u = 1.0 + x;
return(Math.Log(u) - ((u - 1.0) - x) / u);
}
public static double Log(object self, double x)
{
return(DomainCheck(SM.Log(x), "log"));
}
/// <summary>
///
/// </summary>
/// <param name="c">Kamera g³ówna</param>
/// <param name="playerPlane">Obiekt samolotu gracza (model)</param>
/// <param name="evt">FrameEvent (chodzi o czas od ostatniej klatki)</param>
/// <param name="manualZoom"></param>
/// <returns></returns>
public static void Manage(Camera c, Plane playerPlane, FrameEvent evt, float manualZoom)
{
Plane p = null;
if (playerPlane != null)
{
p = playerPlane;
}
Vector3 translateVector = Vector3.ZERO;
float t = evt.timeSinceLastFrame;
if (t >= 1.0f)
{
t = 0.99f;
}
float minCamDistance = 15;
float halfMaxHeight = (float)GameConsts.GenericPlane.CurrentUserPlane.MaxHeight / 2.0f;
float realHalfMaxHeight = halfMaxHeight * 0.95f;
float camAlt = c.RealPosition.y + c.Position.y;
// float camAlt = c.RealPosition.y;
float minCamAlt = 4.0f;
/* bool duringEmergency = false;
*
* // awaryjne wynurzenie kamery;)
* if (c._getDerivedPosition().y + c.Position.y <= 0)
* {
* // metr nad wod¹
* Vector3 emergency = new Vector3(0, c.Position.y + c._getDerivedPosition().y + 1.0f, 0);
* c.MoveRelative(emergency);
* duringEmergency = true;
* }*/
// wysokosc
if (camAlt < minCamAlt)
{
translateVector.y = 40 * (minCamAlt - camAlt); // wynurzenie kamery znad powierchni wody
}
else if (camAlt > 10)
{
// powrot w ozi Y
if (c.Position.y > 0.01f && EngineConfig.CurrentGameSpeedMultiplier != EngineConfig.GameSpeedMultiplierSlow)
{
translateVector.y = -(c.Position.y) / 10.0f;
}
}
// ZOOMING
float speed = (float)p.Speed;
float speedFactor = 0;
float altFactor = 0;
// wspolczynnik wysokosci
if (c.RealPosition.y > 0)
{
altFactor = (float)Math.Log(c.RealPosition.y + 1, 1.011);
altFactor = Math.Max(0, altFactor);
}
float zoomFactor;
speedFactor = speed; // wsp. szybkosci
//altFactor*=altFactor * altFactor;
if (playerPlane.Position.Y < 30)
{
altFactor /= (30 - (float)playerPlane.Position.Y) * 0.15f;
}
if (altFactor > 250)
{
altFactor = 250;
}
zoomFactor = speedFactor * 0.1f + altFactor * 0.53f + (-manualZoom + minCamDistance - c.Position.z);
// Bullet-time
if (EngineConfig.CurrentGameSpeedMultiplier == EngineConfig.GameSpeedMultiplierSlow)
{
zoomFactor += -manualZoom + minCamDistance - c.Position.z + 30.0f;
}
translateVector.z += zoomFactor;
// ruch kamery w zaleznosci od wysokosci
if (c.RealPosition.y >= realHalfMaxHeight && EngineConfig.CurrentGameSpeedMultiplier != EngineConfig.GameSpeedMultiplierSlow)
{
translateVector.y -= (camAlt - realHalfMaxHeight);
}
else if (c.RealPosition.y < (realHalfMaxHeight * 0.75f))
{
if (c.Position.y < 0)
{
translateVector.y -= c.Position.y;
}
}
// ograniczenia awaryjne
// translateVector.z += manualZoom;
translateVector.x = Math.Min(translateVector.x, 500);
translateVector.y = Math.Min(translateVector.y, 500);
translateVector.z = Math.Min(translateVector.z, 500);
translateVector.x = Math.Max(translateVector.x, -500);
translateVector.y = Math.Max(translateVector.y, -500);
translateVector.z = Math.Max(translateVector.z, -500);
// uzaleznij od czasu
translateVector *= t;
c.MoveRelative(translateVector);
}
// Inverse Hyperbolic Secant
public static double HArcsec(double x)
{
return(MathObj.Log((MathObj.Sqrt(-x * x + 1) + 1) / x));
}
// Inverse Hyperbolic Cotangent
public static double HArccotan(double x)
{
return(MathObj.Log((x + 1) / (x - 1)) / 2);
}
// Inverse Hyperbolic Cosecant
public static double HArccosec(double x)
{
return(MathObj.Log((MathObj.Sign(x) * MathObj.Sqrt(x * x + 1) + 1) / x));
}
// Inverse Hyperbolic Cosine
public static double HArccos(double x)
{
return(MathObj.Log(x + MathObj.Sqrt(x * x - 1)));
}
// Logarithm to base N
public static double LogN(double x, double n)
{
return(MathObj.Log(x) / MathObj.Log(n));
}
public static double Asinh(object self, double x)
{
//ln(x + sqrt(x*x + 1))
return(SM.Log(x + SM.Sqrt(x * x + 1)));
}
public static double Atanh(object self, double x)
{
//(1/2) * ln((1+x)/(1-x))
return(DomainCheck((1 / 2) * SM.Log((1 + x) / (1 - x)), "atanh"));
}
public static double Log2(object self, [DefaultProtocol] double x)
{
return(DomainCheck(SM.Log(x) / SM.Log(2), "log2"));
}
public static double Acosh(object self, [DefaultProtocol] double x)
{
//ln(x + sqrt(x*x - 1)) for x >= 1
return(DomainCheck(SM.Log(x + SM.Sqrt(x * x - 1)), "acosh"));
}
acosh(double x)
{
return(2 * Math.Log(Math.Sqrt((x + 1) * .5) + Math.Sqrt((x - 1) * .5)));
}
public static double Asinh(object self, [DefaultProtocol] double x)
{
//ln(x + sqrt(x*x + 1))
return(SM.Log(x + SM.Sqrt(x * x + 1)));
}
public static double Atanh(object self, [DefaultProtocol] double x)
{
//(1/2) * ln((1+x)/(1-x))
return(DomainCheck(0.5 * SM.Log((1 + x) / (1 - x)), "atanh"));
}
// Inverse Hyperbolic Sine
public static double HArcsin(double x)
{
return(MathObj.Log(x + MathObj.Sqrt(x * x + 1)));
}