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#define PJ_LIB__
#include <projects.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 XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
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);
lp.phi -= V = (lp.phi + s * (c + 2.) - p) /
(1. + c * (c + 2.) - s * s);
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 LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
double c;
lp.phi = aasin(P->ctx,xy.y / C_y);
lp.lam = xy.x / (C_x * (1. + (c = cos(lp.phi))));
lp.phi = aasin(P->ctx,(lp.phi + sin(lp.phi) * (c + 2.)) / C_p);
return lp;
}
static void *freeup_new (PJ *P) { /* Destructor */
if (0==P)
return 0;
return pj_dealloc(P);
}
static void freeup (PJ *P) {
freeup_new (P);
return;
}
PJ *PROJECTION(eck4) {
P->es = 0.0;
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
#ifdef PJ_OMIT_SELFTEST
int pj_eck4_selftest (void) {return 0;}
#else
int pj_eck4_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char s_args[] = {"+proj=eck4 +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY s_fwd_expect[] = {
{ 188646.38935641639, 132268.54017406539},
{ 188646.38935641639, -132268.54017406539},
{-188646.38935641639, 132268.54017406539},
{-188646.38935641639, -132268.54017406539},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP s_inv_expect[] = {
{ 0.0021202405520236059, 0.00075601458836610643},
{ 0.0021202405520236059, -0.00075601458836610643},
{-0.0021202405520236059, 0.00075601458836610643},
{-0.0021202405520236059, -0.00075601458836610643},
};
return pj_generic_selftest (0, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, 0, s_fwd_expect, inv_in, 0, s_inv_expect);
}
#endif
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