#ifndef lint
static const char SCCSID[]="@(#)PJ_bipc.c 4.1 94/02/15 GIE REL";
#endif
#define PROJ_PARMS__ \
int noskew;
#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
FORWARD(s_forward); /* spheroid */
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) - HALFPI) < EPS10) {
Az = lp.phi < 0. ? 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 (P->noskew) {
t = xy.x;
xy.x = -xy.x * cAzc - xy.y * sAzc;
xy.y = -xy.y * cAzc + t * sAzc;
}
return (xy);
}
INVERSE(s_inverse); /* spheroid */
double t, r, rp, rl, al, z, fAz, Az, s, c, Av;
int neg, i;
if (P->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);
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(bipc)
P->noskew = pj_param(P->params, "bns").i;
P->inv = s_inverse;
P->fwd = s_forward;
P->es = 0.;
ENDENTRY(P)
