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#include <stdio.h>
#include <gsl/gsl_integration.h>
#include <math.h> /* For M_PI */
/* From Google maps. Probably not very accurate, but should be good enough for
* this calculation. */
double latitude = 46.471857;
double longitude = -81.186755;
/* Radius of the earth in mm. */
double radius_earth = 6.371e9;
/* Depth of the SNO detector in mm. Don't be fooled by all the digits. I just
* converted 6800 feet -> mm. */
double sno_depth = 2072640;
/* Fiducial volume in mm. */
double radius_fiducial = 5000;
/* Cartesian coordinates of SNO in earth frame. They need to be global since
* they are used in some functions. */
double x_sno[3];
double deg2rad(double deg)
{
return deg*M_PI/180.0;
}
double rad2deg(double rad)
{
return rad*180.0/M_PI;
}
/* Convert spherical coordinates to cartesian coordinates.
*
* See https://en.wikipedia.org/wiki/Spherical_coordinate_system. */
void sphere2cartesian(double r, double theta, double phi, double *x, double *y, double *z)
{
*x = r*sin(theta)*cos(phi);
*y = r*sin(theta)*sin(phi);
*z = r*cos(theta);
}
/* Convert cartesian coordinates to spherical coordinates.
*
* See https://en.wikipedia.org/wiki/Spherical_coordinate_system. */
void cartesian2sphere(double x, double y, double z, double *r, double *theta, double *phi)
{
*r = sqrt(x*x + y*y + z*z);
*theta = acos(z/(*r));
*phi = atan2(y,x);
}
void cross(double *a, double *b, double *c)
{
c[0] = a[1]*b[2] - a[2]*b[1];
c[1] = a[2]*b[0] - a[0]*b[2];
c[2] = a[0]*b[1] - a[1]*b[0];
}
double dot(double *a, double *b)
{
return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
}
double norm(double *a)
{
return sqrt(dot(a,a));
}
void normalize(double *a)
{
double n = norm(a);
a[0] /= n;
a[1] /= n;
a[2] /= n;
}
/* Rotate a vector x around the vector dir by an angle theta. */
void rotate(double *result, double *x, double *dir, double theta)
{
double a = dot(dir,x);
double b[3];
double sin_theta = sin(theta);
double cos_theta = cos(theta);
/* Make sure the direction vector is normalized. */
normalize(dir);
cross(x,dir,b);
result[0] = x[0]*cos_theta + dir[0]*a*(1-cos_theta) + b[0]*sin_theta;
result[1] = x[1]*cos_theta + dir[1]*a*(1-cos_theta) + b[1]*sin_theta;
result[2] = x[2]*cos_theta + dir[2]*a*(1-cos_theta) + b[2]*sin_theta;
}
/* Rotate a vector in earth centered coordinates to SNO coordinates (doesn't do
* the translation). */
void rotate_earth_to_sno(double *x_earth, double *x_sno)
{
double dir[3];
double z[3] = {0,0,1};
cross(x_sno, z, dir);
/* Normalize. */
normalize(dir);
double theta = acos(dot(x_sno,z)/norm(x_sno));
rotate(x_sno, x_earth, dir, theta);
}
int main(int argc, char **argv)
{
/* Spherical angles for the SNO detector in the earth frame which has z
* along the north and south poles and the x axis passing through Greenwich.
* Should double check this. */
double sno_theta = deg2rad(latitude + 90.0);
double sno_phi = deg2rad(longitude);
sphere2cartesian(radius_earth - sno_depth, sno_theta, sno_phi, x_sno, x_sno+1, x_sno+2);
return 0;
}
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