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#define PJ_LIB__
#include <math.h>
#include "proj.h"
#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) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
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) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
else lp.phi = lp.phi < 0. ? -M_HALFPI : M_HALFPI;
else
lp.phi = asin(lp.phi);
return lp;
}
PJ *PROJECTION(mbtfpq) {
P->es = 0.;
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
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