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#define PJ_LIB__
#include <projects.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
struct pj_opaque {
int noskew;
};
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = 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)) ) {
cdlam = cos(sdlam = lp.lam + R110);
sdlam = sin(sdlam);
z = S20 * sphi + C20 * cphi * cdlam;
if (fabs(z) > 1.) {
if (fabs(z) > ONEEPS) F_ERROR
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) F_ERROR
else z = z < 0. ? -1. : 1.;
} else
z = acos(z);
Av = Azba;
xy.y = -rhoc;
}
if (z < 0.) F_ERROR;
r = F * (t = pow(tan(.5 * z), n));
if ((al = .5 * (R104 - z)) < 0.) F_ERROR;
al = (t + pow(al, n)) / T;
if (fabs(al) > 1.) {
if (fabs(al) > ONEEPS) F_ERROR
else al = al < 0. ? -1. : 1.;
} else
al = acos(al);
if (fabs(t = n * (Av - Az)) < 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 LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = 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;
}
rl = rp = r = hypot(xy.x, xy.y);
fAz = fabs(Az = atan2(xy.x, xy.y));
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) I_ERROR;
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);
}
static void *freeup_new (PJ *P) { /* Destructor */
if (0==P)
return 0;
pj_dealloc (P->opaque);
return pj_dealloc(P);
}
static void freeup (PJ *P) {
freeup_new (P);
return;
}
PJ *PROJECTION(bipc) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
Q->noskew = pj_param(P->ctx, P->params, "bns").i;
P->inv = s_inverse;
P->fwd = s_forward;
P->es = 0.;
return P;
}
#ifndef PJ_SELFTEST
int pj_bipc_selftest (void) {return 0;}
#else
int pj_bipc_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char e_args[] = {"+proj=bipc +ellps=GRS80 +lat_1=0.5 +lat_2=2"};
char s_args[] = {"+proj=bipc +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY e_fwd_expect[] = {
{2452160.2177257561, -14548450.759654747},
{2447915.213725341, -14763427.21279873},
{2021695.5229349085, -14540413.695283702},
{2018090.5030046992, -14755620.651414108},
};
XY s_fwd_expect[] = {
{2460565.7409749646, -14598319.9893308},
{2456306.1859352002, -14814033.339502094},
{2028625.4978190989, -14590255.375482792},
{2025008.1205891429, -14806200.018759441},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP e_inv_expect[] = {
{-73.038700284978702, 17.248118466239116},
{-73.03730373933017, 17.249414978178777},
{-73.03589317304332, 17.245536403008771},
{-73.034496627213585, 17.246832895573739},
};
LP s_inv_expect[] = {
{-73.038693104942126, 17.248116270440242},
{-73.037301330021322, 17.24940835333777},
{-73.035895582251086, 17.245543027866539},
{-73.034503807150301, 17.246835091521532},
};
return pj_generic_selftest (e_args, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, e_fwd_expect, s_fwd_expect, inv_in, e_inv_expect, s_inv_expect);
}
#endif
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