/*
** 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 PROJ_PARMS__ \
  double  sinb1; \
  double  cosb1; \
  double  xmf; \
  double  ymf; \
  double  mmf; \
  double  qp; \
  double  dd; \
  double  rq; \
  double  *apa; \
  int    mode;
#define PROJ_LIB__
#include  <lib_proj.h>
PROJ_HEAD(laea, "Lambert Azimuthal Equal Area") "\n\tAzi, Sph&Ell";
#define sinph0  P->sinb1
#define cosph0  P->cosb1
#define EPS10  1.e-10
#define NITER  20
#define CONV  1.e-10
#define N_POLE  0
#define S_POLE  1
#define EQUIT  2
#define OBLIQ  3
FORWARD(e_forward); /* ellipsoid */
  double coslam, sinlam, sinphi, q, sinb=0., cosb=0., b=0.;

  coslam = cos(lp.lam);
  sinlam = sin(lp.lam);
  sinphi = sin(lp.phi);
  q = proj_qsfn(lp.phi, P->apa);
  if (P->mode == OBLIQ || P->mode == EQUIT) {
    sinb = q / P->qp;
    cosb = sqrt(1. - sinb * sinb);
  }
  switch (P->mode) {
  case OBLIQ:
    b = 1. + P->sinb1 * sinb + P->cosb1 * cosb * coslam;
    break;
  case EQUIT:
    b = 1. + cosb * coslam;
    break;
  case N_POLE:
    b = HALFPI + lp.phi;
    q = P->qp - q;
    break;
  case S_POLE:
    b = lp.phi - HALFPI;
    q = P->qp + q;
    break;
  }
  if (fabs(b) < EPS10) F_ERROR;
  switch (P->mode) {
  case OBLIQ:
    xy.y = P->ymf * ( b = sqrt(2. / b) )
       * (P->cosb1 * sinb - P->sinb1 * cosb * coslam);
    goto eqcon;
    break;
  case EQUIT:
    xy.y = (b = sqrt(2. / (1. + cosb * coslam))) * sinb * P->ymf; 
eqcon:
    xy.x = P->xmf * b * cosb * sinlam;
    break;
  case N_POLE:
  case S_POLE:
    if (q >= 0.) {
      xy.x = (b = sqrt(q)) * sinlam;
      xy.y = coslam * (P->mode == S_POLE ? b : -b);
    } else
      xy.x = xy.y = 0.;
    break;
  }
  return (xy);
}
FORWARD(s_forward); /* spheroid */
  double  coslam, cosphi, sinphi;

  sinphi = sin(lp.phi);
  cosphi = cos(lp.phi);
  coslam = cos(lp.lam);
  switch (P->mode) {
  case EQUIT:
    xy.y = 1. + cosphi * coslam;
    goto oblcon;
  case OBLIQ:
    xy.y = 1. + sinph0 * sinphi + cosph0 * cosphi * coslam;
oblcon:
    if (xy.y <= EPS10) F_ERROR;
    xy.x = (xy.y = sqrt(2. / xy.y)) * cosphi * sin(lp.lam);
    xy.y *= P->mode == EQUIT ? sinphi :
       cosph0 * sinphi - sinph0 * cosphi * coslam;
    break;
  case N_POLE:
    coslam = -coslam;
  case S_POLE:
    if (fabs(lp.phi + P->phi0) < EPS10) F_ERROR;
    xy.y = FORTPI - lp.phi * .5;
    xy.y = 2. * (P->mode == S_POLE ? cos(xy.y) : sin(xy.y));
    xy.x = xy.y * sin(lp.lam);
    xy.y *= coslam;
    break;
  }
  return (xy);
}
INVERSE(e_inverse); /* ellipsoid */
  double cCe, sCe, q, rho, ab=0.;

  switch (P->mode) {
  case EQUIT:
  case OBLIQ:
    if ((rho = hypot(xy.x /= P->dd, xy.y *=  P->dd)) < EPS10) {
      lp.lam = 0.;
      lp.phi = P->phi0;
      return (lp);
    }
    cCe = cos(sCe = 2. * asin(.5 * rho / P->rq));
    xy.x *= (sCe = sin(sCe));
    if (P->mode == OBLIQ) {
      q = P->qp * (ab = cCe * P->sinb1 + xy.y * sCe * P->cosb1 / rho);
      xy.y = rho * P->cosb1 * cCe - xy.y * P->sinb1 * sCe;
    } else {
      q = P->qp * (ab = xy.y * sCe / rho);
      xy.y = rho * cCe;
    }
    break;
  case N_POLE:
    xy.y = -xy.y;
  case S_POLE:
    if (!(q = (xy.x * xy.x + xy.y * xy.y)) ) {
      lp.lam = 0.;
      lp.phi = P->phi0;
      return (lp);
    }
    /*
    q = P->qp - q;
    */
    ab = 1. - q / P->qp;
    if (P->mode == S_POLE)
      ab = - ab;
    break;
  }
  lp.lam = atan2(xy.x, xy.y);
  lp.phi = proj_auth_inv(asin(ab), P->apa);
  return (lp);
}
INVERSE(s_inverse); /* spheroid */
  double  cosz=0., rh, sinz=0.;

  rh = hypot(xy.x, xy.y);
  if ((lp.phi = rh * .5 ) > 1.) I_ERROR;
  lp.phi = 2. * asin(lp.phi);
  if (P->mode == OBLIQ || P->mode == EQUIT) {
    sinz = sin(lp.phi);
    cosz = cos(lp.phi);
  }
  switch (P->mode) {
  case EQUIT:
    lp.phi = fabs(rh) <= EPS10 ? 0. : asin(xy.y * sinz / rh);
    xy.x *= sinz;
    xy.y = cosz * rh;
    break;
  case OBLIQ:
    lp.phi = fabs(rh) <= EPS10 ? P->phi0 :
       asin(cosz * sinph0 + xy.y * sinz * cosph0 / rh);
    xy.x *= sinz * cosph0;
    xy.y = (cosz - sin(lp.phi) * sinph0) * rh;
    break;
  case N_POLE:
    xy.y = -xy.y;
    lp.phi = HALFPI - lp.phi;
    break;
  case S_POLE:
    lp.phi -= HALFPI;
    break;
  }
  lp.lam = (xy.y == 0. && (P->mode == EQUIT || P->mode == OBLIQ)) ?
    0. : atan2(xy.x, xy.y);
  return (lp);
}
FREEUP;
  if (P) {
    if (P->apa)
      free(P->apa);
    free(P);
  }
}
ENTRY1(laea, apa)
  double t;

  if (fabs((t = fabs(P->phi0)) - HALFPI) < EPS10)
    P->mode = P->phi0 < 0. ? S_POLE : N_POLE;
  else if (fabs(t) < EPS10)
    P->mode = EQUIT;
  else
    P->mode = OBLIQ;
  if (P->es) {
    double sinphi;

    P->e = sqrt(P->es);
    if (!(P->apa = proj_auth_ini(P->es, &t))) E_ERROR_0;
    P->qp = proj_qsfn(HALFPI, P->apa);
    P->mmf = .5 / (1. - P->es);
    switch (P->mode) {
    case N_POLE:
    case S_POLE:
      P->dd = 1.;
      break;
    case EQUIT:
      P->dd = 1. / (P->rq = sqrt(.5 * P->qp));
      P->xmf = 1.;
      P->ymf = .5 * P->qp;
      break;
    case OBLIQ:
      P->rq = sqrt(.5 * P->qp);
      sinphi = sin(P->phi0);
      P->sinb1 = proj_qsfn(P->phi0, P->apa) / P->qp;
      P->cosb1 = sqrt(1. - P->sinb1 * P->sinb1);
      P->dd = cos(P->phi0) / (sqrt(1. - P->es * sinphi * sinphi) *
         P->rq * P->cosb1);
      P->ymf = (P->xmf = P->rq) / P->dd;
      P->xmf *= P->dd;
      break;
    }
    P->inv = e_inverse;
    P->fwd = e_forward;
  } else {
    if (P->mode == OBLIQ) {
      sinph0 = sin(P->phi0);
      cosph0 = cos(P->phi0);
    }
    P->inv = s_inverse;
    P->fwd = s_forward;
  }
ENDENTRY(P)
/*
** Log: proj_laea.c
** Revision 3.1  2006/01/11 01:38:18  gie
** Initial
**
*/
