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#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(mbtfpq, "McBryde-Thomas Flat-Polar Quartic") "\n\tCyl., Sph.";
#define NITER 20
#define EPS 1e-7
#define ONETOL 1.000001
#define C 1.70710678118654752440
#define RC 0.58578643762690495119
#define FYC 1.87475828462269495505
#define RYC 0.53340209679417701685
#define FXC 0.31245971410378249250
#define RXC 3.20041258076506210122
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
double th1, c;
int i;
(void) P;
c = C * sin(lp.phi);
for (i = NITER; i; --i) {
lp.phi -= th1 = (sin(.5*lp.phi) + sin(lp.phi) - c) /
(.5*cos(.5*lp.phi) + cos(lp.phi));
if (fabs(th1) < EPS) break;
}
xy.x = FXC * lp.lam * (1.0 + 2. * cos(lp.phi)/cos(0.5 * lp.phi));
xy.y = FYC * sin(0.5 * lp.phi);
return xy;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
double t;
lp.phi = RYC * xy.y;
if (fabs(lp.phi) > 1.) {
if (fabs(lp.phi) > ONETOL) I_ERROR
else if (lp.phi < 0.) { t = -1.; lp.phi = -M_PI; }
else { t = 1.; lp.phi = M_PI; }
} else
lp.phi = 2. * asin(t = lp.phi);
lp.lam = RXC * xy.x / (1. + 2. * cos(lp.phi)/cos(0.5 * lp.phi));
lp.phi = RC * (t + sin(lp.phi));
if (fabs(lp.phi) > 1.)
if (fabs(lp.phi) > ONETOL) I_ERROR
else lp.phi = lp.phi < 0. ? -M_HALFPI : M_HALFPI;
else
lp.phi = asin(lp.phi);
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(mbtfpq) {
P->es = 0.;
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
#ifndef PJ_SELFTEST
int pj_mbtfpq_selftest (void) {return 0;}
#else
int pj_mbtfpq_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char s_args[] = {"+proj=mbtfpq +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY s_fwd_expect[] = {
{ 209391.854738393013, 119161.040199054827},
{ 209391.854738393013, -119161.040199054827},
{-209391.854738393013, 119161.040199054827},
{-209391.854738393013, -119161.040199054827},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP s_inv_expect[] = {
{ 0.00191010555824111571, 0.000839185447792341723},
{ 0.00191010555824111571, -0.000839185447792341723},
{-0.00191010555824111571, 0.000839185447792341723},
{-0.00191010555824111571, -0.000839185447792341723},
};
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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