/*
** 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_LIB__
# include  <lib_proj.h>
PROJ_HEAD(vandg, "van der Grinten (I)") "\n\tMisc Sph";
# define TOL    1.e-10
# define THIRD    .33333333333333333333
# define TWO_THRD  .66666666666666666666
# define C2_27    .07407407407407407407
# define PI4_3    4.18879020478639098458
# define PISQ    9.86960440108935861869
# define TPISQ    19.73920880217871723738
# define HPISQ    4.93480220054467930934
FORWARD(s_forward); /* spheroid */
  double  al, al2, g, g2, p2;
  (void) P; /* avoid warning */

  p2 = fabs(lp.phi / HALFPI);
  if ((p2 - TOL) > 1.) F_ERROR;
  if (p2 > 1.)
    p2 = 1.;
  if (fabs(lp.phi) <= TOL) {
    xy.x = lp.lam;
    xy.y = 0.;
  } else if (fabs(lp.lam) <= TOL || fabs(p2 - 1.) < TOL) {
    xy.x = 0.;
    xy.y = PI * tan(.5 * asin(p2));
    if (lp.phi < 0.) xy.y = -xy.y;
  } else {
    al = .5 * fabs(PI / lp.lam - lp.lam / PI);
    al2 = al * al;
    g = sqrt(1. - p2 * p2);
    g = g / (p2 + g - 1.);
    g2 = g * g;
    p2 = g * (2. / p2 - 1.);
    p2 = p2 * p2;
    xy.x = g - p2; g = p2 + al2;
    xy.x = PI * (al * xy.x + sqrt(al2 * xy.x * xy.x - g * (g2 - p2))) / g;
    if (lp.lam < 0.) xy.x = -xy.x;
    xy.y = fabs(xy.x / PI);
    xy.y = 1. - xy.y * (xy.y + 2. * al);
    if (xy.y < -TOL) F_ERROR;
    if (xy.y < 0.)  xy.y = 0.;
    else    xy.y = sqrt(xy.y) * (lp.phi < 0. ? -PI : PI);
  }
  return (xy);
}
INVERSE(s_inverse); /* spheroid */
  double t, c0, c1, c2, c3, al, r2, r, m, d, ay, x2, y2;
  (void) P; /* avoid warning */

  x2 = xy.x * xy.x;
  if ((ay = fabs(xy.y)) < TOL) {
    lp.phi = 0.;
    t = x2 * x2 + TPISQ * (x2 + HPISQ);
    lp.lam = fabs(xy.x) <= TOL ? 0. :
       .5 * (x2 - PISQ + sqrt(t)) / xy.x;
    return (lp);
  }
  y2 = xy.y * xy.y;
  r = x2 + y2;  r2 = r * r;
  c1 = - PI * ay * (r + PISQ);
  c3 = r2 + TWOPI * (ay * r + PI * (y2 + PI * (ay + HALFPI)));
  c2 = c1 + PISQ * (r - 3. *  y2);
  c0 = PI * ay;
  c2 /= c3;
  al = c1 / c3 - THIRD * c2 * c2;
  m = 2. * sqrt(-THIRD * al);
  d = C2_27 * c2 * c2 * c2 + (c0 * c0 - THIRD * c2 * c1) / c3;
  if (((t = fabs(d = 3. * d / (al * m))) - TOL) <= 1.) {
    d = t > 1. ? (d > 0. ? 0. : PI) : acos(d);
    lp.phi = PI * (m * cos(d * THIRD + PI4_3) - THIRD * c2);
    if (xy.y < 0.) lp.phi = -lp.phi;
    t = r2 + TPISQ * (x2 - y2 + HPISQ);
    lp.lam = fabs(xy.x) <= TOL ? 0. :
       .5 * (r - PISQ + (t <= 0. ? 0. : sqrt(t))) / xy.x;
  } else
    I_ERROR;
  return (lp);
}
FREEUP; if (P) free(P); }
ENTRY0(vandg) P->es = 0.; P->inv = s_inverse; P->fwd = s_forward; ENDENTRY(P)
/*
** Log: proj_vandg.c
** Revision 3.1  2006/01/11 01:38:18  gie
** Initial
**
*/
