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#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj.h"
#include "proj_internal.h"
PROJ_HEAD(poly, "Polyconic (American)")
"\n\tConic, Sph&Ell";
namespace { // anonymous namespace
struct pj_opaque {
double ml0; \
double *en;
};
} // anonymous namespace
#define TOL 1e-10
#define CONV 1e-10
#define N_ITER 10
#define I_ITER 20
#define ITOL 1.e-12
static PJ_XY poly_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 ms, sp, cp;
if (fabs(lp.phi) <= TOL) {
xy.x = lp.lam;
xy.y = -Q->ml0;
} else {
sp = sin(lp.phi);
cp = cos(lp.phi);
ms = fabs(cp) > TOL ? pj_msfn(sp, cp, P->es) / sp : 0.;
lp.lam *= sp;
xy.x = ms * sin(lp.lam);
xy.y = (pj_mlfn(lp.phi, sp, cp, Q->en) - Q->ml0) + ms * (1. - cos(lp.lam));
}
return xy;
}
static PJ_XY poly_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);
if (fabs(lp.phi) <= TOL) {
xy.x = lp.lam;
xy.y = Q->ml0;
} else {
const double cot = 1. / tan(lp.phi);
const double E = lp.lam * sin(lp.phi);
xy.x = sin(E) * cot;
xy.y = lp.phi - P->phi0 + cot * (1. - cos(E));
}
return xy;
}
static PJ_LP poly_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);
xy.y += Q->ml0;
if (fabs(xy.y) <= TOL) {
lp.lam = xy.x;
lp.phi = 0.;
} else {
int i;
const double r = xy.y * xy.y + xy.x * xy.x;
lp.phi = xy.y;
for (i = I_ITER; i ; --i) {
const double sp = sin(lp.phi);
const double cp = cos(lp.phi);
const double s2ph = sp * cp;
if (fabs(cp) < ITOL) {
proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);
return lp;
}
double mlp = sqrt(1. - P->es * sp * sp);
const double c = sp * mlp / cp;
const double ml = pj_mlfn(lp.phi, sp, cp, Q->en);
const double mlb = ml * ml + r;
mlp = P->one_es / (mlp * mlp * mlp);
const double dPhi =
( ml + ml + c * mlb - 2. * xy.y * (c * ml + 1.) ) / (
P->es * s2ph * (mlb - 2. * xy.y * ml) / c +
2.* (xy.y - ml) * (c * mlp - 1. / s2ph) - mlp - mlp );
lp.phi += dPhi;
if (fabs(dPhi) <= ITOL)
break;
}
if (!i) {
proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);
return lp;
}
const double c = sin(lp.phi);
lp.lam = asin(xy.x * tan(lp.phi) * sqrt(1. - P->es * c * c)) / sin(lp.phi);
}
return lp;
}
static PJ_LP poly_s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
if (fabs(xy.y = P->phi0 + xy.y) <= TOL) {
lp.lam = xy.x;
lp.phi = 0.;
} else {
lp.phi = xy.y;
const double B = xy.x * xy.x + xy.y * xy.y;
int i = N_ITER;
while(true) {
const double tp = tan(lp.phi);
const double dphi = (xy.y * (lp.phi * tp + 1.) - lp.phi -
.5 * ( lp.phi * lp.phi + B) * tp) /
((lp.phi - xy.y) / tp - 1.);
lp.phi -= dphi;
if( !(fabs(dphi) > CONV) )
break;
--i;
if( i == 0 ) {
proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);
return lp;
}
}
lp.lam = asin(xy.x * tan(lp.phi)) / sin(lp.phi);
}
return lp;
}
static PJ *destructor(PJ *P, int errlev) {
if (nullptr==P)
return nullptr;
if (nullptr==P->opaque)
return pj_default_destructor (P, errlev);
if (static_cast<struct pj_opaque*>(P->opaque)->en)
free (static_cast<struct pj_opaque*>(P->opaque)->en);
return pj_default_destructor(P, errlev);
}
PJ *PROJECTION(poly) {
struct pj_opaque *Q = static_cast<struct pj_opaque*>(calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, PROJ_ERR_OTHER /*ENOMEM*/);
P->opaque = Q;
P->destructor = destructor;
if (P->es != 0.0) {
if (!(Q->en = pj_enfn(P->es)))
return pj_default_destructor (P, PROJ_ERR_OTHER /*ENOMEM*/);
Q->ml0 = pj_mlfn(P->phi0, sin(P->phi0), cos(P->phi0), Q->en);
P->inv = poly_e_inverse;
P->fwd = poly_e_forward;
} else {
Q->ml0 = -P->phi0;
P->inv = poly_s_inverse;
P->fwd = poly_s_forward;
}
return P;
}
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