/******************************************************************************
* $Id$
*
* Project: PROJ.4
* Purpose: Implementation of the aeqd (Azimuthal Equidistant) projection.
* Author: Gerald Evenden
*
******************************************************************************
* Copyright (c) 1995, Gerald Evenden
*
* 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.
******************************************************************************
*
* $Log$
* Revision 1.1 2005/02/01 22:08:43 jdh2358
* Initial revision
*
* Revision 1.3 2002/12/14 19:27:06 warmerda
* updated header
*
*/
#define PROJ_PARMS__ \
double sinph0; \
double cosph0; \
double *en; \
double M1; \
double N1; \
double Mp; \
double He; \
double G; \
int mode;
#define PJ_LIB__
#include <projects.h>
PJ_CVSID("$Id$");
PROJ_HEAD(aeqd, "Azimuthal Equidistant") "\n\tAzi, Sph&Ell\n\tlat_0 guam";
#define EPS10 1.e-10
#define TOL 1.e-14
#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 = pj_mlfn(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 - pj_mlfn(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 = aasin( 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;
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 = pj_inv_mlfn(P->M1 + xy.y -
x2 * tan(lp.phi) * (t = sqrt(1. - t * t)), P->es, 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 = aasin(P->sinph0 * cos(E) + t * sin(E));
lp.lam = aasin(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 = pj_inv_mlfn(P->mode == N_POLE ? P->Mp - c : P->Mp + c,
P->es, 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 = aasin(xy.y * sinc / c_rh);
xy.x *= sinc;
xy.y = cosc * c_rh;
} else {
lp.phi = aasin(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)
pj_dalloc(P->en);
pj_dalloc(P);
}
}
ENTRY1(aeqd, en)
P->phi0 = pj_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 = pj_enfn(P->es))) E_ERROR_0;
if (pj_param(P->params, "bguam").i) {
P->M1 = pj_mlfn(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 = pj_mlfn(HALFPI, 1., 0., P->en);
break;
case S_POLE:
P->Mp = pj_mlfn(-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)
