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#define PJ_LIB__
#include <math.h>
#include "proj.h"
#include "proj_internal.h"
PROJ_HEAD(eck4, "Eckert IV") "\n\tPCyl, Sph";
#define C_x .42223820031577120149
#define C_y 1.32650042817700232218
#define RC_y .75386330736002178205
#define C_p 3.57079632679489661922
#define RC_p .28004957675577868795
#define EPS 1e-7
#define NITER 6
static PJ_XY eck4_s_forward (PJ_LP lp, PJ *P) { /* Spheroidal, forward */
PJ_XY xy = {0.0,0.0};
double p, V, s, c;
int i;
(void) P;
p = C_p * sin(lp.phi);
V = lp.phi * lp.phi;
lp.phi *= 0.895168 + V * ( 0.0218849 + V * 0.00826809 );
for (i = NITER; i ; --i) {
c = cos(lp.phi);
s = sin(lp.phi);
V = (lp.phi + s * (c + 2.) - p) / (1. + c * (c + 2.) - s * s);
lp.phi -= V;
if (fabs(V) < EPS)
break;
}
if (!i) {
xy.x = C_x * lp.lam;
xy.y = lp.phi < 0. ? -C_y : C_y;
} else {
xy.x = C_x * lp.lam * (1. + cos(lp.phi));
xy.y = C_y * sin(lp.phi);
}
return xy;
}
static PJ_LP eck4_s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
lp.phi = aasin(P->ctx,xy.y * RC_y);
const double c = cos(lp.phi);
lp.lam = xy.x / (C_x * (1. + c));
lp.phi = aasin(P->ctx,(lp.phi + sin(lp.phi) * (c + 2.)) * RC_p);
return lp;
}
PJ *PROJECTION(eck4) {
P->es = 0.0;
P->inv = eck4_s_inverse;
P->fwd = eck4_s_forward;
return P;
}
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