PJ_aea.c
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/******************************************************************************
* $Id: PJ_aea.c 1504 2009-01-06 02:11:57Z warmerdam $
*
* Project: PROJ.4
* Purpose: Implementation of the aea (Albers Equal Area) 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.
*****************************************************************************/
#define PROJ_PARMS__ \
double ec; \
double n; \
double c; \
double dd; \
double n2; \
double rho0; \
double rho; \
double phi1; \
double phi2; \
double *en; \
int ellips;
#define PJ_LIB__
#include <projects.h>
PJ_CVSID("$Id: PJ_aea.c 1504 2009-01-06 02:11:57Z warmerdam $");
# define EPS10 1.e-10
# define TOL7 1.e-7
PROJ_HEAD(aea, "Albers Equal Area")
"\n\tConic Sph&Ell\n\tlat_1= lat_2=";
PROJ_HEAD(leac, "Lambert Equal Area Conic")
"\n\tConic, Sph&Ell\n\tlat_1= south";
/* determine latitude angle phi-1 */
# define N_ITER 15
# define EPSILON 1.0e-7
# define TOL 1.0e-10
static double
phi1_(double qs, double Te, double Tone_es) {
int i;
double Phi, sinpi, cospi, con, com, dphi;
Phi = asin (.5 * qs);
if (Te < EPSILON)
return( Phi );
i = N_ITER;
do {
sinpi = sin (Phi);
cospi = cos (Phi);
con = Te * sinpi;
com = 1. - con * con;
dphi = .5 * com * com / cospi * (qs / Tone_es -
sinpi / com + .5 / Te * log ((1. - con) /
(1. + con)));
Phi += dphi;
} while (fabs(dphi) > TOL && --i);
return( i ? Phi : HUGE_VAL );
}
FORWARD(e_forward); /* ellipsoid & spheroid */
if ((P->rho = P->c - (P->ellips ? P->n * pj_qsfn(sin(lp.phi),
P->e, P->one_es) : P->n2 * sin(lp.phi))) < 0.) F_ERROR
P->rho = P->dd * sqrt(P->rho);
xy.x = P->rho * sin( lp.lam *= P->n );
xy.y = P->rho0 - P->rho * cos(lp.lam);
return (xy);
}
INVERSE(e_inverse) /* ellipsoid & spheroid */;
if( (P->rho = hypot(xy.x, xy.y = P->rho0 - xy.y)) != 0.0 ) {
if (P->n < 0.) {
P->rho = -P->rho;
xy.x = -xy.x;
xy.y = -xy.y;
}
lp.phi = P->rho / P->dd;
if (P->ellips) {
lp.phi = (P->c - lp.phi * lp.phi) / P->n;
if (fabs(P->ec - fabs(lp.phi)) > TOL7) {
if ((lp.phi = phi1_(lp.phi, P->e, P->one_es)) == HUGE_VAL)
I_ERROR
} else
lp.phi = lp.phi < 0. ? -HALFPI : HALFPI;
} else if (fabs(lp.phi = (P->c - lp.phi * lp.phi) / P->n2) <= 1.)
lp.phi = asin(lp.phi);
else
lp.phi = lp.phi < 0. ? -HALFPI : HALFPI;
lp.lam = atan2(xy.x, xy.y) / P->n;
} else {
lp.lam = 0.;
lp.phi = P->n > 0. ? HALFPI : - HALFPI;
}
return (lp);
}
FREEUP; if (P) { if (P->en) pj_dalloc(P->en); pj_dalloc(P); } }
static PJ *
setup(PJ *P) {
double cosphi, sinphi;
int secant;
if (fabs(P->phi1 + P->phi2) < EPS10) E_ERROR(-21);
P->n = sinphi = sin(P->phi1);
cosphi = cos(P->phi1);
secant = fabs(P->phi1 - P->phi2) >= EPS10;
if( (P->ellips = (P->es > 0.))) {
double ml1, m1;
if (!(P->en = pj_enfn(P->es))) E_ERROR_0;
m1 = pj_msfn(sinphi, cosphi, P->es);
ml1 = pj_qsfn(sinphi, P->e, P->one_es);
if (secant) { /* secant cone */
double ml2, m2;
sinphi = sin(P->phi2);
cosphi = cos(P->phi2);
m2 = pj_msfn(sinphi, cosphi, P->es);
ml2 = pj_qsfn(sinphi, P->e, P->one_es);
P->n = (m1 * m1 - m2 * m2) / (ml2 - ml1);
}
P->ec = 1. - .5 * P->one_es * log((1. - P->e) /
(1. + P->e)) / P->e;
P->c = m1 * m1 + P->n * ml1;
P->dd = 1. / P->n;
P->rho0 = P->dd * sqrt(P->c - P->n * pj_qsfn(sin(P->phi0),
P->e, P->one_es));
} else {
if (secant) P->n = .5 * (P->n + sin(P->phi2));
P->n2 = P->n + P->n;
P->c = cosphi * cosphi + P->n2 * sinphi;
P->dd = 1. / P->n;
P->rho0 = P->dd * sqrt(P->c - P->n2 * sin(P->phi0));
}
P->inv = e_inverse; P->fwd = e_forward;
return P;
}
ENTRY1(aea,en)
P->phi1 = pj_param(P->params, "rlat_1").f;
P->phi2 = pj_param(P->params, "rlat_2").f;
ENDENTRY(setup(P))
ENTRY1(leac,en)
P->phi2 = pj_param(P->params, "rlat_1").f;
P->phi1 = pj_param(P->params, "bsouth").i ? - HALFPI: HALFPI;
ENDENTRY(setup(P))