/*
** libproj -- library of cartographic projections
**
** Copyright (c) 2003, 2006   Gerald I. Evenden
*/
static const char
LIBPROJ_ID[] = "Id";
/*
** Permission is hereby granted, free of charge, to any person obtaining
** a copy of this software and associated documentation files (the
** "Software"), to deal in the Software without restriction, including
** without limitation the rights to use, copy, modify, merge, publish,
** distribute, sublicense, and/or sell copies of the Software, and to
** permit persons to whom the Software is furnished to do so, subject to
** the following conditions:
**
** The above copyright notice and this permission notice shall be
** included in all copies or substantial portions of the Software.
**
** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
** EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
** MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
** IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
** CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
** TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
** SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
/* Computes distance from equator along the meridian to latitude phi
** and inverse on unit ellipsoid.
** Precision commensurate with double precision.
*/
#define PROJ_LIB__
#include <lib_proj.h>
#define MAX_ITER 20
#define TOL 1e-14

struct MDIST {
  int nb;
  double es;
  double E;
  double b[1];
};
#define B ((struct MDIST *)b)
  void *
proj_mdist_ini(double es) {
  double numf, numfi, twon1, denf, denfi, ens, T, twon;
  double den, El, Es;
  double E[MAX_ITER];
  struct MDIST *b;
  int i, j;

/* generate E(e^2) and its terms E[] */
  ens = es;
  numf = twon1 = denfi = 1.;
  denf = 1.;
  twon = 4.;
  Es = El = E[0] = 1.;
  for (i = 1; i < MAX_ITER ; ++i) {
    numf *= (twon1 * twon1);
    den = twon * denf * denf * twon1;
    T = numf/den;
    Es -= (E[i] = T * ens);
    ens *= es;
    twon *= 4.;
    denf *= ++denfi;
    twon1 += 2.;
    if (Es == El) /* jump out if no change */
      break;
    El = Es;
  }
  if ((b = (struct MDIST *)malloc(sizeof(struct MDIST)+
    (i*sizeof(double)))) == NULL)
    return(NULL);
  b->nb = i - 1;
  b->es = es;
  b->E = Es;
  /* generate b_n coefficients--note: collapse with prefix ratios */
  b->b[0] = Es = 1. - Es;
  numf = denf = 1.;
  numfi = 2.;
  denfi = 3.;
  for (j = 1; j < i; ++j) {
    Es -= E[j];
    numf *= numfi;
    denf *= denfi;
    b->b[j] = Es * numf / denf;
    numfi += 2.;
    denfi += 2.;
  }
  return (b);
}
  double
proj_mdist(double phi, double sphi, double cphi, const void *b) {
  double sc, sum, sphi2, D;
  int i;

  sc = sphi * cphi;
  sphi2 = sphi * sphi;
  D = phi * B->E - B->es * sc / sqrt(1. - B->es * sphi2);
  sum = B->b[i = B->nb];
  while (i) sum = B->b[--i] + sphi2 * sum;
  return(D + sc * sum);
}
  double
proj_inv_mdist(double dist, const void *b) {
  double s, t, phi, k;
  int i;

  k = 1./(1.- B->es);
  i = MAX_ITER;
  phi = dist;
  while ( i-- ) {
    s = sin(phi);
    t = 1. - B->es * s * s;
    phi -= t = (proj_mdist(phi, s, cos(phi), b) - dist) *
      (t * sqrt(t)) * k;
    if (fabs(t) < TOL) /* that is no change */
      return phi;
  }
    /* convergence failed */
  proj_errno = -17;
  return phi;
}
/* Revision Log:
** Log: proj_mdist.c
** Revision 3.1  2006/01/11 01:38:18  gie
** Initial
**
*/
