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#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj.h"
#include "proj_internal.h"
#include <math.h>
PROJ_HEAD(bipc, "Bipolar conic of western hemisphere") "\n\tConic Sph";
# define EPS 1e-10
# define EPS10 1e-10
# define ONEEPS 1.000000001
# define NITER 10
# define lamB -.34894976726250681539
# define n .63055844881274687180
# define F 1.89724742567461030582
# define Azab .81650043674686363166
# define Azba 1.82261843856185925133
# define T 1.27246578267089012270
# define rhoc 1.20709121521568721927
# define cAzc .69691523038678375519
# define sAzc .71715351331143607555
# define C45 .70710678118654752469
# define S45 .70710678118654752410
# define C20 .93969262078590838411
# define S20 -.34202014332566873287
# define R110 1.91986217719376253360
# define R104 1.81514242207410275904
namespace { // anonymous namespace
struct pj_opaque {
int noskew;
};
} // anonymous namespace
static PJ_XY bipc_s_forward (PJ_LP lp, PJ *P) { /* Spheroidal, forward */
PJ_XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double cphi, sphi, tphi, t, al, Az, z, Av, cdlam, sdlam, r;
int tag;
cphi = cos(lp.phi);
sphi = sin(lp.phi);
cdlam = cos(sdlam = lamB - lp.lam);
sdlam = sin(sdlam);
if (fabs(fabs(lp.phi) - M_HALFPI) < EPS10) {
Az = lp.phi < 0. ? M_PI : 0.;
tphi = HUGE_VAL;
} else {
tphi = sphi / cphi;
Az = atan2(sdlam , C45 * (tphi - cdlam));
}
if( (tag = (Az > Azba)) ) {
sdlam = lp.lam + R110;
cdlam = cos(sdlam);
sdlam = sin(sdlam);
z = S20 * sphi + C20 * cphi * cdlam;
if (fabs(z) > 1.) {
if (fabs(z) > ONEEPS) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
else z = z < 0. ? -1. : 1.;
} else
z = acos(z);
if (tphi != HUGE_VAL)
Az = atan2(sdlam, (C20 * tphi - S20 * cdlam));
Av = Azab;
xy.y = rhoc;
} else {
z = S45 * (sphi + cphi * cdlam);
if (fabs(z) > 1.) {
if (fabs(z) > ONEEPS) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
else z = z < 0. ? -1. : 1.;
} else
z = acos(z);
Av = Azba;
xy.y = -rhoc;
}
if (z < 0.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
t = pow(tan(.5 * z), n);
r = F * t;
if ((al = .5 * (R104 - z)) < 0.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
al = (t + pow(al, n)) / T;
if (fabs(al) > 1.) {
if (fabs(al) > ONEEPS) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
else al = al < 0. ? -1. : 1.;
} else
al = acos(al);
t = n * (Av - Az);
if (fabs(t) < al)
r /= cos(al + (tag ? t : -t));
xy.x = r * sin(t);
xy.y += (tag ? -r : r) * cos(t);
if (Q->noskew) {
t = xy.x;
xy.x = -xy.x * cAzc - xy.y * sAzc;
xy.y = -xy.y * cAzc + t * sAzc;
}
return (xy);
}
static PJ_LP bipc_s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double t, r, rp, rl, al, z = 0.0, fAz, Az, s, c, Av;
int neg, i;
if (Q->noskew) {
t = xy.x;
xy.x = -xy.x * cAzc + xy.y * sAzc;
xy.y = -xy.y * cAzc - t * sAzc;
}
if( (neg = (xy.x < 0.)) ) {
xy.y = rhoc - xy.y;
s = S20;
c = C20;
Av = Azab;
} else {
xy.y += rhoc;
s = S45;
c = C45;
Av = Azba;
}
r = hypot(xy.x, xy.y);
rl = rp = r;
Az = atan2(xy.x, xy.y);
fAz = fabs(Az);
for (i = NITER; i ; --i) {
z = 2. * atan(pow(r / F,1 / n));
al = acos((pow(tan(.5 * z), n) +
pow(tan(.5 * (R104 - z)), n)) / T);
if (fAz < al)
r = rp * cos(al + (neg ? Az : -Az));
if (fabs(rl - r) < EPS)
break;
rl = r;
}
if (! i) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
Az = Av - Az / n;
lp.phi = asin(s * cos(z) + c * sin(z) * cos(Az));
lp.lam = atan2(sin(Az), c / tan(z) - s * cos(Az));
if (neg)
lp.lam -= R110;
else
lp.lam = lamB - lp.lam;
return (lp);
}
PJ *PROJECTION(bipc) {
struct pj_opaque *Q = static_cast<struct pj_opaque*>(calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
Q->noskew = pj_param(P->ctx, P->params, "bns").i;
P->inv = bipc_s_inverse;
P->fwd = bipc_s_forward;
P->es = 0.;
return P;
}
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