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#define PJ_LIB__
#include <errno.h>
#include "proj.h"
#include "proj_internal.h"
#include <math.h>
PROJ_HEAD(laea, "Lambert Azimuthal Equal Area") "\n\tAzi, Sph&Ell";
namespace { // anonymous namespace
enum Mode {
N_POLE = 0,
S_POLE = 1,
EQUIT = 2,
OBLIQ = 3
};
} // anonymous namespace
namespace { // anonymous namespace
struct pj_opaque {
double sinb1;
double cosb1;
double xmf;
double ymf;
double mmf;
double qp;
double dd;
double rq;
double *apa;
enum Mode mode;
};
} // anonymous namespace
#define EPS10 1.e-10
static PJ_XY laea_e_forward (PJ_LP lp, PJ *P) { /* Ellipsoidal, forward */
PJ_XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double coslam, sinlam, sinphi, q, sinb=0.0, cosb=0.0, b=0.0;
coslam = cos(lp.lam);
sinlam = sin(lp.lam);
sinphi = sin(lp.phi);
q = pj_qsfn(sinphi, P->e, P->one_es);
if (Q->mode == OBLIQ || Q->mode == EQUIT) {
sinb = q / Q->qp;
cosb = sqrt(1. - sinb * sinb);
}
switch (Q->mode) {
case OBLIQ:
b = 1. + Q->sinb1 * sinb + Q->cosb1 * cosb * coslam;
break;
case EQUIT:
b = 1. + cosb * coslam;
break;
case N_POLE:
b = M_HALFPI + lp.phi;
q = Q->qp - q;
break;
case S_POLE:
b = lp.phi - M_HALFPI;
q = Q->qp + q;
break;
}
if (fabs(b) < EPS10) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
switch (Q->mode) {
case OBLIQ:
b = sqrt(2. / b);
xy.y = Q->ymf * b * (Q->cosb1 * sinb - Q->sinb1 * cosb * coslam);
goto eqcon;
break;
case EQUIT:
b = sqrt(2. / (1. + cosb * coslam));
xy.y = b * sinb * Q->ymf;
eqcon:
xy.x = Q->xmf * b * cosb * sinlam;
break;
case N_POLE:
case S_POLE:
if (q >= 1e-15) {
b = sqrt(q);
xy.x = b * sinlam;
xy.y = coslam * (Q->mode == S_POLE ? b : -b);
} else
xy.x = xy.y = 0.;
break;
}
return xy;
}
static PJ_XY laea_s_forward (PJ_LP lp, PJ *P) { /* Spheroidal, forward */
PJ_XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double coslam, cosphi, sinphi;
sinphi = sin(lp.phi);
cosphi = cos(lp.phi);
coslam = cos(lp.lam);
switch (Q->mode) {
case EQUIT:
xy.y = 1. + cosphi * coslam;
goto oblcon;
case OBLIQ:
xy.y = 1. + Q->sinb1 * sinphi + Q->cosb1 * cosphi * coslam;
oblcon:
if (xy.y <= EPS10) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
xy.y = sqrt(2. / xy.y);
xy.x = xy.y * cosphi * sin(lp.lam);
xy.y *= Q->mode == EQUIT ? sinphi :
Q->cosb1 * sinphi - Q->sinb1 * cosphi * coslam;
break;
case N_POLE:
coslam = -coslam;
/*-fallthrough*/
case S_POLE:
if (fabs(lp.phi + P->phi0) < EPS10) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
xy.y = M_FORTPI - lp.phi * .5;
xy.y = 2. * (Q->mode == S_POLE ? cos(xy.y) : sin(xy.y));
xy.x = xy.y * sin(lp.lam);
xy.y *= coslam;
break;
}
return xy;
}
static PJ_LP laea_e_inverse (PJ_XY xy, PJ *P) { /* Ellipsoidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double cCe, sCe, q, rho, ab=0.0;
switch (Q->mode) {
case EQUIT:
case OBLIQ:
xy.x /= Q->dd;
xy.y *= Q->dd;
rho = hypot(xy.x, xy.y);
if (rho < EPS10) {
lp.lam = 0.;
lp.phi = P->phi0;
return lp;
}
sCe = 2. * asin(.5 * rho / Q->rq);
cCe = cos(sCe);
sCe = sin(sCe);
xy.x *= sCe;
if (Q->mode == OBLIQ) {
ab = cCe * Q->sinb1 + xy.y * sCe * Q->cosb1 / rho;
xy.y = rho * Q->cosb1 * cCe - xy.y * Q->sinb1 * sCe;
} else {
ab = xy.y * sCe / rho;
xy.y = rho * cCe;
}
break;
case N_POLE:
xy.y = -xy.y;
/*-fallthrough*/
case S_POLE:
q = (xy.x * xy.x + xy.y * xy.y);
if (q == 0.0) {
lp.lam = 0.;
lp.phi = P->phi0;
return (lp);
}
ab = 1. - q / Q->qp;
if (Q->mode == S_POLE)
ab = - ab;
break;
}
lp.lam = atan2(xy.x, xy.y);
lp.phi = pj_authlat(asin(ab), Q->apa);
return lp;
}
static PJ_LP laea_s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double cosz=0.0, rh, sinz=0.0;
rh = hypot(xy.x, xy.y);
if ((lp.phi = rh * .5 ) > 1.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
lp.phi = 2. * asin(lp.phi);
if (Q->mode == OBLIQ || Q->mode == EQUIT) {
sinz = sin(lp.phi);
cosz = cos(lp.phi);
}
switch (Q->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 * Q->sinb1 + xy.y * sinz * Q->cosb1 / rh);
xy.x *= sinz * Q->cosb1;
xy.y = (cosz - sin(lp.phi) * Q->sinb1) * rh;
break;
case N_POLE:
xy.y = -xy.y;
lp.phi = M_HALFPI - lp.phi;
break;
case S_POLE:
lp.phi -= M_HALFPI;
break;
}
lp.lam = (xy.y == 0. && (Q->mode == EQUIT || Q->mode == OBLIQ)) ?
0. : atan2(xy.x, xy.y);
return (lp);
}
static PJ *destructor (PJ *P, int errlev) {
if (nullptr==P)
return nullptr;
if (nullptr==P->opaque)
return pj_default_destructor (P, errlev);
pj_dealloc (static_cast<struct pj_opaque*>(P->opaque)->apa);
return pj_default_destructor(P, errlev);
}
PJ *PROJECTION(laea) {
double t;
struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
P->destructor = destructor;
t = fabs(P->phi0);
if (t > M_HALFPI + EPS10 ) {
return destructor(P, PJD_ERR_LAT_LARGER_THAN_90);
}
if (fabs(t - M_HALFPI) < EPS10)
Q->mode = P->phi0 < 0. ? S_POLE : N_POLE;
else if (fabs(t) < EPS10)
Q->mode = EQUIT;
else
Q->mode = OBLIQ;
if (P->es != 0.0) {
double sinphi;
P->e = sqrt(P->es);
Q->qp = pj_qsfn(1., P->e, P->one_es);
Q->mmf = .5 / (1. - P->es);
Q->apa = pj_authset(P->es);
if (nullptr==Q->apa)
return destructor(P, ENOMEM);
switch (Q->mode) {
case N_POLE:
case S_POLE:
Q->dd = 1.;
break;
case EQUIT:
Q->dd = 1. / (Q->rq = sqrt(.5 * Q->qp));
Q->xmf = 1.;
Q->ymf = .5 * Q->qp;
break;
case OBLIQ:
Q->rq = sqrt(.5 * Q->qp);
sinphi = sin(P->phi0);
Q->sinb1 = pj_qsfn(sinphi, P->e, P->one_es) / Q->qp;
Q->cosb1 = sqrt(1. - Q->sinb1 * Q->sinb1);
Q->dd = cos(P->phi0) / (sqrt(1. - P->es * sinphi * sinphi) *
Q->rq * Q->cosb1);
Q->ymf = (Q->xmf = Q->rq) / Q->dd;
Q->xmf *= Q->dd;
break;
}
P->inv = laea_e_inverse;
P->fwd = laea_e_forward;
} else {
if (Q->mode == OBLIQ) {
Q->sinb1 = sin(P->phi0);
Q->cosb1 = cos(P->phi0);
}
P->inv = laea_s_inverse;
P->fwd = laea_s_forward;
}
return P;
}
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