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/******************************************************************************
* Project: PROJ.4
* Purpose: Implementation of the aea (Albers Equal Area) projection.
* and the leac (Lambert Equal Area Conic) projection
* Author: Gerald Evenden (1995)
* Thomas Knudsen (2016) - revise/add regression tests
*
******************************************************************************
* 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 PJ_LIB__
#include "proj.h"
#include <errno.h>
#include "projects.h"
#include "proj_math.h"
# 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 );
}
struct pj_opaque {
double ec;
double n;
double c;
double dd;
double n2;
double rho0;
double rho;
double phi1;
double phi2;
double *en;
int ellips;
};
static void *destructor (PJ *P, int errlev) { /* Destructor */
if (0==P)
return 0;
if (0==P->opaque)
return pj_default_destructor (P, errlev);
pj_dealloc (P->opaque->en);
return pj_default_destructor (P, errlev);
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoid/spheroid, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
Q->rho = Q->c - (Q->ellips ? Q->n * pj_qsfn(sin(lp.phi), P->e, P->one_es) : Q->n2 * sin(lp.phi));;
if (Q->rho < 0.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
Q->rho = Q->dd * sqrt(Q->rho);
xy.x = Q->rho * sin( lp.lam *= Q->n );
xy.y = Q->rho0 - Q->rho * cos(lp.lam);
return xy;
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoid/spheroid, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
if( (Q->rho = hypot(xy.x, xy.y = Q->rho0 - xy.y)) != 0.0 ) {
if (Q->n < 0.) {
Q->rho = -Q->rho;
xy.x = -xy.x;
xy.y = -xy.y;
}
lp.phi = Q->rho / Q->dd;
if (Q->ellips) {
lp.phi = (Q->c - lp.phi * lp.phi) / Q->n;
if (fabs(Q->ec - fabs(lp.phi)) > TOL7) {
if ((lp.phi = phi1_(lp.phi, P->e, P->one_es)) == HUGE_VAL) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
} else
lp.phi = lp.phi < 0. ? -M_HALFPI : M_HALFPI;
} else if (fabs(lp.phi = (Q->c - lp.phi * lp.phi) / Q->n2) <= 1.)
lp.phi = asin(lp.phi);
else
lp.phi = lp.phi < 0. ? -M_HALFPI : M_HALFPI;
lp.lam = atan2(xy.x, xy.y) / Q->n;
} else {
lp.lam = 0.;
lp.phi = Q->n > 0. ? M_HALFPI : - M_HALFPI;
}
return lp;
}
static PJ *setup(PJ *P) {
double cosphi, sinphi;
int secant;
struct pj_opaque *Q = P->opaque;
P->inv = e_inverse;
P->fwd = e_forward;
if (fabs(Q->phi1 + Q->phi2) < EPS10)
return destructor(P, PJD_ERR_CONIC_LAT_EQUAL);
Q->n = sinphi = sin(Q->phi1);
cosphi = cos(Q->phi1);
secant = fabs(Q->phi1 - Q->phi2) >= EPS10;
if( (Q->ellips = (P->es > 0.))) {
double ml1, m1;
if (!(Q->en = pj_enfn(P->es)))
return destructor(P, 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(Q->phi2);
cosphi = cos(Q->phi2);
m2 = pj_msfn(sinphi, cosphi, P->es);
ml2 = pj_qsfn(sinphi, P->e, P->one_es);
if (ml2 == ml1)
return destructor(P, 0);
Q->n = (m1 * m1 - m2 * m2) / (ml2 - ml1);
}
Q->ec = 1. - .5 * P->one_es * log((1. - P->e) /
(1. + P->e)) / P->e;
Q->c = m1 * m1 + Q->n * ml1;
Q->dd = 1. / Q->n;
Q->rho0 = Q->dd * sqrt(Q->c - Q->n * pj_qsfn(sin(P->phi0),
P->e, P->one_es));
} else {
if (secant) Q->n = .5 * (Q->n + sin(Q->phi2));
Q->n2 = Q->n + Q->n;
Q->c = cosphi * cosphi + Q->n2 * sinphi;
Q->dd = 1. / Q->n;
Q->rho0 = Q->dd * sqrt(Q->c - Q->n2 * sin(P->phi0));
}
return P;
}
PJ *PROJECTION(aea) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
P->destructor = destructor;
Q->phi1 = pj_param(P->ctx, P->params, "rlat_1").f;
Q->phi2 = pj_param(P->ctx, P->params, "rlat_2").f;
return setup(P);
}
PJ *PROJECTION(leac) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
P->destructor = destructor;
Q->phi2 = pj_param(P->ctx, P->params, "rlat_1").f;
Q->phi1 = pj_param(P->ctx, P->params, "bsouth").i ? - M_HALFPI: M_HALFPI;
return setup(P);
}
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