/*
Functions that calculate the gravitational potential and its first and second
derivatives for the MAG_tesseroid.

The gravity gradients can be calculated using the general formula of
Grombein et al. (2010).
The integrals are solved using the Gauss-Legendre Quadrature rule
(Asgharzadeh et al., 2007).

The derivatives of the potential are made with respect to the local coordinate
system x->North, y->East, z->Up (away from center of the Earth).

To maintain the standard convention, only for component gz the z axis is
inverted, so a positive density results in positive gz.

Example
-------

To calculate the gzz component due to a MAG_tesseroid on a regular grid:

    #include <stdio.h>
    #include "glq.h"r
    #include "constants.h"
    #include "grav_tess.h"

    int main()
    {
        MAG_TESSEROID tess = {1000, 44, 46, -1, 1, MEAN_EARTH_RADIUS - 100000,
                          MEAN_EARTH_RADIUS};
        GLQ *glqlon, *glqlat, *glqr;
        double lon, lat, r = MEAN_EARTH_RADIUS + 1500000, res;
        int order = 8;

        glqlon = glq_new(order, tess.w, tess.e);
        glqlat = glq_new(order, tess.s, tess.n);
        glqr = glq_new(order, tess.r1, tess.r2);

        for(lat = 20; lat <= 70; lat += 0.5)
        {
            for(lon = -25; lon <= 25; lon += 0.5)
            {
                res = tess_gzz(tess, lon, lat, r, *glqlon, *glqlat, *glqr);
                printf("%g %g %g\n", lon, lat, res);
            }
        }

        glq_free(glqlon);
        glq_free(glqlat);
        glq_free(glqr);

        return 0;
    }

References
----------

Asgharzadeh, M.F., von Frese, R.R.B., Kim, H.R., Leftwich, T.E. & Kim, J.W.
(2007): Spherical prism gravity effects by Gauss-Legendre quadrature integration.
Geophysical Journal International, 169, 1-11.

Grombein, T.; Seitz, K.; Heck, B. (2010): Untersuchungen zur effizienten
Berechnung topographischer Effekte auf den Gradiententensor am Fallbeispiel der
Satellitengradiometriemission GOCE.
KIT Scientific Reports 7547, ISBN 978-3-86644-510-9, KIT Scientific Publishing,
Karlsruhe, Germany.
*/

#ifndef _MAG_TESSEROIDS_GRAV_TESS_H_
#define _MAG_TESSEROIDS_GRAV_TESS_H_


/* Needed for definition of MAG_TESSEROID */
#include "geometry.h"
/* Needed for definition of GLQ */
#include "glq.h"

double calc_tess_model(MAG_TESSEROID *model, int size, double lonp, double latp, double rp, GLQ *glq_lon, GLQ *glq_lat, GLQ *glq_r, double (*field)(MAG_TESSEROID, double, double, double, GLQ, GLQ, GLQ));
void calc_tess_model_triple(MAG_TESSEROID *model, int size, double lonp, double latp, double rp, GLQ *glq_lon, GLQ *glq_lat, GLQ *glq_r,
  void (*field_triple)(MAG_TESSEROID, double, double, double, GLQ, GLQ, GLQ, double*), double *res);
double calc_tess_model_adapt(MAG_TESSEROID *model, int size, double lonp, double latp, double rp, GLQ *glq_lon, GLQ *glq_lat, GLQ *glq_r, double (*field)(MAG_TESSEROID, double, double, double, GLQ, GLQ, GLQ), double ratio);

double tess_gxx(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
double tess_gxy(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
double tess_gxz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
double tess_gyy(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
double tess_gyz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);
double tess_gzz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r);

void tess_gxz_gyz_gzz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r, double *res);
void tess_gxx_gxy_gxz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r, double *res);
void tess_gxy_gyy_gyz(MAG_TESSEROID tess, double lonp, double latp, double rp, GLQ glq_lon, GLQ glq_lat, GLQ glq_r, double *res);

#endif