/*
** 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.
*/
#define EPS10 1.e-10
#define TOL 1.e-14
#define PROJ_PARMS__ \
  double  sinph0; \
  double  cosph0; \
  void  *en; \
  double  M1; \
  double  N1; \
  double  Mp; \
  double  He; \
  double  G; \
  int    mode;
#define PROJ_LIB__
#include  <lib_proj.h>
PROJ_HEAD(aeqd, "Azimuthal Equidistant") "\n\tAzi, Sph&Ell\n\tlat_0= guam";
#define N_POLE  0
#define S_POLE 1
#define EQUIT  2
#define OBLIQ  3
FORWARD(e_guam_fwd); /* Guam elliptical */
  double  cosphi, sinphi, t;

  cosphi = cos(lp.phi);
  sinphi = sin(lp.phi);
  t = 1. / sqrt(1. - P->es * sinphi * sinphi);
  xy.x = lp.lam * cosphi * t;
  xy.y = proj_mdist(lp.phi, sinphi, cosphi, P->en) - P->M1 +
    .5 * lp.lam * lp.lam * cosphi * sinphi * t;
  return (xy);
}
FORWARD(e_forward); /* elliptical */
  double  coslam, cosphi, sinphi, rho, s, H, H2, c, Az, t, ct, st, cA, sA;

  coslam = cos(lp.lam);
  cosphi = cos(lp.phi);
  sinphi = sin(lp.phi);
  switch (P->mode) {
  case N_POLE:
    coslam = - coslam;
  case S_POLE:
    xy.x = (rho = fabs(P->Mp - proj_mdist(lp.phi, sinphi, cosphi, P->en))) *
      sin(lp.lam);
    xy.y = rho * coslam;
    break;
  case EQUIT:
  case OBLIQ:
    if (fabs(lp.lam) < EPS10 && fabs(lp.phi - P->phi0) < EPS10) {
      xy.x = xy.y = 0.;
      break;
    }
    t = atan2(P->one_es * sinphi + P->es * P->N1 * P->sinph0 *
      sqrt(1. - P->es * sinphi * sinphi), cosphi);
    ct = cos(t); st = sin(t);
    Az = atan2(sin(lp.lam) * ct, P->cosph0 * st - P->sinph0 * coslam * ct);
    cA = cos(Az); sA = sin(Az);
    s = proj_asin( fabs(sA) < TOL ?
      (P->cosph0 * st - P->sinph0 * coslam * ct) / cA :
      sin(lp.lam) * ct / sA );
    H = P->He * cA;
    H2 = H * H;
    c = P->N1 * s * (1. + s * s * (- H2 * (1. - H2)/6. +
      s * ( P->G * H * (1. - 2. * H2 * H2) / 8. +
      s * ((H2 * (4. - 7. * H2) - 3. * P->G * P->G * (1. - 7. * H2)) /
      120. - s * P->G * H / 48.))));
    xy.x = c * sA;
    xy.y = c * cA;
    break;
  }
  return (xy);
}
FORWARD(s_forward); /* spherical */
  double  coslam, cosphi, sinphi;

  sinphi = sin(lp.phi);
  cosphi = cos(lp.phi);
  coslam = cos(lp.lam);
  switch (P->mode) {
  case EQUIT:
    xy.y = cosphi * coslam;
    goto oblcon;
  case OBLIQ:
    xy.y = P->sinph0 * sinphi + P->cosph0 * cosphi * coslam;
oblcon:
    if (fabs(fabs(xy.y) - 1.) < TOL)
      if (xy.y < 0.)
        F_ERROR 
      else
        xy.x = xy.y = 0.;
    else {
      xy.y = acos(xy.y);
      xy.y /= sin(xy.y);
      xy.x = xy.y * cosphi * sin(lp.lam);
      xy.y *= (P->mode == EQUIT) ? sinphi :
           P->cosph0 * sinphi - P->sinph0 * cosphi * coslam;
    }
    break;
  case N_POLE:
    lp.phi = -lp.phi;
    coslam = -coslam;
  case S_POLE:
    if (fabs(lp.phi - HALFPI) < EPS10) F_ERROR;
    xy.x = (xy.y = (HALFPI + lp.phi)) * sin(lp.lam);
    xy.y *= coslam;
    break;
  }
  return (xy);
}
INVERSE(e_guam_inv); /* Guam elliptical */
  double x2, t = 0.;
  int i;

  x2 = 0.5 * xy.x * xy.x;
  lp.phi = P->phi0;
  for (i = 0; i < 3; ++i) {
    t = P->e * sin(lp.phi);
    lp.phi = proj_inv_mdist(P->M1 + xy.y -
      x2 * tan(lp.phi) * (t = sqrt(1. - t * t)), P->en);
  }
  lp.lam = xy.x * t / cos(lp.phi);
  return (lp);
}
INVERSE(e_inverse); /* elliptical */
  double c, Az, cosAz, A, B, D, E, F, psi, t;

  if ((c = hypot(xy.x, xy.y)) < EPS10) {
    lp.phi = P->phi0;
    lp.lam = 0.;
    return (lp);
  }
  if (P->mode == OBLIQ || P->mode == EQUIT) {
    cosAz = cos(Az = atan2(xy.x, xy.y));
    t = P->cosph0 * cosAz;
    B = P->es * t / P->one_es;
    A = - B * t;
    B *= 3. * (1. - A) * P->sinph0;
    D = c / P->N1;
    E = D * (1. - D * D * (A * (1. + A) / 6. + B * (1. + 3.*A) * D / 24.));
    F = 1. - E * E * (A / 2. + B * E / 6.);
    psi = proj_asin(P->sinph0 * cos(E) + t * sin(E));
    lp.lam = proj_asin(sin(Az) * sin(E) / cos(psi));
    if ((t = fabs(psi)) < EPS10)
      lp.phi = 0.;
    else if (fabs(t - HALFPI) < 0.)
      lp.phi = HALFPI;
    else
      lp.phi = atan((1. - P->es * F * P->sinph0 / sin(psi)) * tan(psi) /
        P->one_es);
  } else { /* Polar */
    lp.phi = proj_inv_mdist(P->mode == N_POLE ? P->Mp - c : P->Mp + c,
      P->en);
    lp.lam = atan2(xy.x, P->mode == N_POLE ? -xy.y : xy.y);
  }
  return (lp);
}
INVERSE(s_inverse); /* spherical */
  double cosc, c_rh, sinc;

  if ((c_rh = hypot(xy.x, xy.y)) > PI) {
    if (c_rh - EPS10 > PI) I_ERROR;
    c_rh = PI;
  } else if (c_rh < EPS10) {
    lp.phi = P->phi0;
    lp.lam = 0.;
    return (lp);
  }
  if (P->mode == OBLIQ || P->mode == EQUIT) {
    sinc = sin(c_rh);
    cosc = cos(c_rh);
    if (P->mode == EQUIT) {
      lp.phi = proj_asin(xy.y * sinc / c_rh);
      xy.x *= sinc;
      xy.y = cosc * c_rh;
    } else {
      lp.phi = proj_asin(cosc * P->sinph0 + xy.y * sinc * P->cosph0 /
        c_rh);
      xy.y = (cosc - P->sinph0 * sin(lp.phi)) * c_rh;
      xy.x *= sinc * P->cosph0;
    }
    lp.lam = xy.y == 0. ? 0. : atan2(xy.x, xy.y);
  } else if (P->mode == N_POLE) {
    lp.phi = HALFPI - c_rh;
    lp.lam = atan2(xy.x, -xy.y);
  } else {
    lp.phi = c_rh - HALFPI;
    lp.lam = atan2(xy.x, xy.y);
  }
  return (lp);
}
FREEUP;
    if (P) {
    if (P->en)
      free(P->en);
    free(P);
  }
}
ENTRY1(aeqd, en)
  P->phi0 = proj_param(P->params, "rlat_0").f;
  if (fabs(fabs(P->phi0) - HALFPI) < EPS10) {
    P->mode = P->phi0 < 0. ? S_POLE : N_POLE;
    P->sinph0 = P->phi0 < 0. ? -1. : 1.;
    P->cosph0 = 0.;
  } else if (fabs(P->phi0) < EPS10) {
    P->mode = EQUIT;
    P->sinph0 = 0.;
    P->cosph0 = 1.;
  } else {
    P->mode = OBLIQ;
    P->sinph0 = sin(P->phi0);
    P->cosph0 = cos(P->phi0);
  }
  if (! P->es) {
    P->inv = s_inverse; P->fwd = s_forward;
  } else {
    if (!(P->en = proj_mdist_ini(P->es))) E_ERROR_0;
    if (proj_param(P->params, "bguam").i) {
      P->M1 = proj_mdist(P->phi0, P->sinph0, P->cosph0, P->en);
      P->inv = e_guam_inv; P->fwd = e_guam_fwd;
    } else {
      switch (P->mode) {
      case N_POLE:
        P->Mp = proj_mdist(HALFPI, 1., 0., P->en);
        break;
      case S_POLE:
        P->Mp = proj_mdist(-HALFPI, -1., 0., P->en);
        break;
      case EQUIT:
      case OBLIQ:
        P->inv = e_inverse; P->fwd = e_forward;
        P->N1 = 1. / sqrt(1. - P->es * P->sinph0 * P->sinph0);
        P->G = P->sinph0 * (P->He = P->e / sqrt(P->one_es));
        P->He *= P->cosph0;
        break;
      }
      P->inv = e_inverse; P->fwd = e_forward;
    }
  }
ENDENTRY(P)
/*
** Log: proj_aeqd.c
** Revision 1.1  2008-11-07 16:41:13  jeff
** ENH: Adding a 2D geoview. Adding the geographic projection library libproj4
** to Utilities. Updating the architecture of the geospatial views. All
** multi-resolution sources are now subclasses of vtkGeoSource. Each source
** has its own worker thread for fetching refined images or geometry.
** On the 3D side, vtkGeoGlobeSource is an appropriate source for vtkGeoTerrain,
** and vtkGeoAlignedImageSource is an appropriate source for
** vtkGeoAlignedImageRepresentation. On the 2D side, vtkGeoProjectionSource is an
** appropriate source for vtkGeoTerrain2D, and the image source is the same.
**
** Revision 3.1  2006/01/11 01:38:18  gie
** Initial
**
*/