public static Vector3D Dini(Vector3D uv, double a, double b)
{
uv = DiskToUpper(uv);
// Eq 1.86 on p36 of book Backlund and Darboux Transformations
double eta = Math.PI / 2 - Math.PI / 20;
//double eta = Math.PI / 2;
double p = 1; // curvature
double x = DonHatch.acosh(uv.Y); // Used info on mathworld for tractrix to figure this out.
//double x = DonHatch.acosh( Math.Exp( DonHatch.acosh( ( uv.Y * uv.Y + 1 ) / ( 2 * uv.Y ) ) ) );
//double x = Math.Log( uv.Y );
double y = uv.X;
double pSinEta = p * Math.Sin(eta);
double chi = (x - y * Math.Cos(eta)) / pSinEta;
if (x <= -4 || x > 4 ||
y < -3 * Math.PI || y > 3 * Math.PI)
{
return(Infinity.InfinityVector);
}
Vector3D result = new Vector3D(
pSinEta * Sech(chi) * Math.Cos(y / p),
pSinEta * Sech(chi) * Math.Sin(y / p),
x - pSinEta * Math.Tanh(chi));
return(result);
/*
* System.Func<double, Complex> tractrix = new System.Func<double, Complex>(
* ( t ) =>
* {
* //return new Complex( t - Math.Tanh( t ), 1.0 / Math.Cosh( t ) );
* return new Complex( - Math.Sqrt( 1 - 1 / (t*t) ) + DonHatch.acosh( t ), 1.0 / t );
* } );
*
* double logy = Math.Log( uv.Y );
* //Complex tract = tractrix( logy );
* Complex tract = tractrix( uv.Y );
* return new Vector3D(
* a * Math.Cos( uv.X ) * tract.Imaginary,
* a * Math.Sin( uv.X ) * tract.Imaginary,
* a * tract.Real + b * uv.X );
*/
/*
* return new Vector3D(
* a * Math.Cos( uv.X ) / Math.Cosh( uv.Y ),
* a * Math.Sin( uv.X ) / Math.Cosh( uv.Y ),
* a * (uv.Y - Math.Tanh( uv.Y )) + b * uv.X ); */
/*return new Vector3D(
* a * Math.Cos( uv.X ) * Math.Sin( uv.Y ),
* a * Math.Sin( uv.X ) * Math.Sin( uv.Y ),
* a * (Math.Cos( uv.Y ) + Math.Log( Math.Tan( 0.5 * uv.Y ) )) + b * uv.X );*/
}
private static int Math_Tanh(ILuaState lua)
{
lua.PushNumber(Math.Tanh(lua.L_CheckNumber(1)));
return(1);
}
public static double Tanh(object self, [DefaultProtocol] double x)
{
return(SM.Tanh(x));
}
public static float Tanh(float value)
{
return((float)SMath.Tanh(value));
}
public static double Tanh(object self, double x)
{
return(SM.Tanh(x));
}
/// <summary>
/// Returns the hyperbolic tangent of the specified angle.
/// </summary>
/// <param name="radians">The angle in radians.</param>
/// <returns>System.Double.</returns>
public static double TanH(double radians)
{
return(NMath.Tanh(radians));
}