//calculation of the euler pole from a rotation matrix
public static void calc_matrix2pole(double[,] m,out EulerPole p , out double Angle)
{
double X1,Y1,z1;
X1 = m[2,1]-m[1,2];
Y1 = m[0,2]-m[2,0];
z1 = m[1,0]-m[0,1];
p.Lattd = 0;
p.Longttd = 0;
kart2sphere( out p,X1,Y1,z1);
Angle = deg (Math.Atan (Math.Sqrt ( X1*X1 + Y1*Y1 + z1*z1)/( m[0,0]+m[1,1]+m[2,2] - 1)));
//if the latitude of the EulerPole is less than zero,then change in the below way
//ensure the EulerPole is at north earth,in fact it's the same but the order of the P and P'
if ( p.Lattd < 0 )
{
p.Lattd = -p.Lattd;
p.Longttd = p.Longttd - 180;
Angle = -Angle;
}
//ensure the longtitude of the EulerPole is betwen -180 to 180
if (p.Longttd > 180)
{ p.Longttd = p.Longttd - 360; }
if (p.Longttd < 180)
{ p.Longttd = p.Longttd + 360; }
}
//calculation of euler pole from VGP(virtual paeomagnetic pole)
public static void calc_VGP2pole(EulerPole vgp,out EulerPole p,out double Angle,Boolean polarity)
{
//polarity represent North pole or South pole,true is N ,false is S
p.Lattd = 0;
p.Longttd = vgp.Longttd + 90;
//ensure the longtitude of the EulerPole is betwen -180 to 180
if (p.Longttd > 360)
{p.Longttd = p.Longttd - 360;}
Angle = vgp.Lattd - 90;
}
//calculate the angle between two vectors
public static double calc_angle(EulerPole A,EulerPole B)
{
double a1,a2,a3;
double b1,b2,b3;
double w;
sphere2kart(out a1, out a2, out a3, A);
sphere2kart(out b1, out b2, out b3, B);
w = Math.Acos(a1*b1 + a2*b2 + a3*b3);
return w;
}
//calculation of the rotation matrix from an euler pole,maybe have sth wrong with it
public static void calc_pole2matrix(out double[,] m ,EulerPole p,double Angle1 )
{
double X,Y,z;
double Angle=rad(Angle1);
m = new double[3, 3];
sphere2kart(out X, out Y, out z, p);
m[0,0]= X * X * (1 - Math.Cos(Angle)) + Math.Cos(Angle);
m[0,1] = X * Y * (1 - Math.Cos(Angle)) - z * Math.Sin(Angle);
m[0,2] = X * z * (1 - Math.Cos(Angle)) + Y * Math.Sin(Angle);
m[1,0] = Y * X * (1 - Math.Cos (Angle)) + z * Math.Sin (Angle);
m[1,1] = Y * Y * (1 - Math.Cos (Angle)) + Math.Cos (Angle);
m[1,2] = Y * z * (1 - Math.Cos (Angle)) - X * Math.Sin (Angle);
m[2,0] = z * X * (1 - Math.Cos (Angle)) - Y * Math.Sin (Angle);
m[2,1] = z * Y * (1 - Math.Cos (Angle)) + X * Math.Sin (Angle);
m[2,2] = z * z * (1 - Math.Cos (Angle)) + Math.Cos (Angle);
}
//rotate P to P' with the matrix M
public static void euler_rot(out EulerPole p,double[,] m)
{
double X,Y,z;
double X1,Y1,z1;
//Initialize,otherwise,error
p.Lattd = 0;
p.Longttd = 0;
sphere2kart(out X, out Y, out z, p);
X1 = m[0, 0] * X + m[0, 1] * Y + m[0, 2] * z;
Y1 = m[1, 0] * X + m[1, 1] * Y + m[1, 2] * z;
z1 = m[2, 0] * X + m[2, 1] * Y + m[2, 2] * z;
kart2sphere(out p,X1,Y1,z1);
}
//calculation of the vector product
//OA*OB=(a2b3-a3b2)i-(a1b3-a3b1)j+(a1b2-a2b1)k, |OA|*|OB|sina
public static void vectorproduct(out double X,out double Y,out double z,EulerPole A,EulerPole B)
{
double ax,ay,az;
double bx,by,bz;
sphere2kart(out ax, out ay, out az, A);
sphere2kart(out bx, out by, out bz, B);
X = ay * bz - az * by;
Y = az * bx - ax * bz;
z = ax * by - ay * bx;
}
//mathematic formulas in .net is ready.
//such as Acos(arccos),Asin(arcsin) and so on.And the result and the input parameter of angle is radian!!
//transformation from spherical to orthogonal coordiantes
//use 'out' and 'void' instead of return() because of multi-returned values
public static void sphere2kart(out double X,out double Y,out double z ,EulerPole p)
{
X = Math.Cos (rad (p.Lattd )) * Math.Cos (rad(p.Longttd ));
Y = Math.Cos (rad(p.Lattd )) * Math.Sin (rad(p.Longttd ));
z = Math.Sin (rad(p.Lattd ));
}
//transformation from orthogonal to spherical coordinates
public static void kart2sphere(out EulerPole p, double X, double Y, double z)
{
//Initialize,otherwise,error:
p.Lattd = 0;
p.Longttd = 0;
//lattitude in z-axis or not
if ((X * X + Y * Y)!= 0)
{p.Lattd = Math.Atan (z / Math.Sqrt (X * X + Y * Y));}
else
{if (z > 0)
{p.Lattd = Math.PI /2;}
if (z < 0)
{p.Lattd = -Math.PI /2;}}
//longtitude,decide which quadrant
//first and second quadrant
if (X > 0)
{if (Y > 0)
{p.Longttd = Math.Atan (Y/X);}
if (Y < 0)
{p.Longttd = Math.Atan (Y/X) + 2 * Math.PI;}}
//longtitude in y-axis or pole or not
if (X == 0)
{if (Y > 0)
{p.Longttd = Math.PI /2;}
if (Y < 0)
{p.Longttd = -Math.PI /2;}
if (Y == 0)
{p.Longttd =0;}}
//the third or forth quadrant
if (X < 0)
{p.Longttd = Math.Atan (Y/X) + Math.PI ;}
//transform result from radian to degree
p.Longttd = deg ( p.Longttd );
p.Lattd = deg (p.Lattd );
//ensure the longtitude of the EulerPole is between -180 to 180
if (p.Longttd > 180 )
{p.Longttd = p.Longttd - 360;}
if (p.Longttd < -180)
{p.Longttd = p.Longttd + 360;}
}
