#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;

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);
}

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);

    return 0;
}