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#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(vandg4, "van der Grinten IV") "\n\tMisc Sph, no inv.";
#define TOL 1e-10
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
double x1, t, bt, ct, ft, bt2, ct2, dt, dt2;
(void) P;
if (fabs(lp.phi) < TOL) {
xy.x = lp.lam;
xy.y = 0.;
} else if (fabs(lp.lam) < TOL || fabs(fabs(lp.phi) - M_HALFPI) < TOL) {
xy.x = 0.;
xy.y = lp.phi;
} else {
bt = fabs(M_TWO_D_PI * lp.phi);
bt2 = bt * bt;
ct = 0.5 * (bt * (8. - bt * (2. + bt2)) - 5.)
/ (bt2 * (bt - 1.));
ct2 = ct * ct;
dt = M_TWO_D_PI * lp.lam;
dt = dt + 1. / dt;
dt = sqrt(dt * dt - 4.);
if ((fabs(lp.lam) - M_HALFPI) < 0.) dt = -dt;
dt2 = dt * dt;
x1 = bt + ct; x1 *= x1;
t = bt + 3.*ct;
ft = x1 * (bt2 + ct2 * dt2 - 1.) + (1.-bt2) * (
bt2 * (t * t + 4. * ct2) +
ct2 * (12. * bt * ct + 4. * ct2) );
x1 = (dt*(x1 + ct2 - 1.) + 2.*sqrt(ft)) /
(4.* x1 + dt2);
xy.x = M_HALFPI * x1;
xy.y = M_HALFPI * sqrt(1. + dt * fabs(x1) - x1 * x1);
if (lp.lam < 0.) xy.x = -xy.x;
if (lp.phi < 0.) xy.y = -xy.y;
}
return xy;
}
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(vandg4) {
P->es = 0.;
P->fwd = s_forward;
return P;
}
#ifdef PJ_OMIT_SELFTEST
int pj_vandg4_selftest (void) {return 0;}
#else
int pj_vandg4_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char s_args[] = {"+proj=vandg4 +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY s_fwd_expect[] = {
{ 223374.57729435508, 111701.19548415358
},
{ 223374.57729435508, -111701.19548415358
},
{-223374.57729435508, 111701.19548415358
},
{-223374.57729435508, -111701.19548415358
},
};
return pj_generic_selftest (0, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, 0, s_fwd_expect, 0, 0, 0);
}
#endif
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