PJ_poly.c
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#ifndef lint
static const char SCCSID[]="@(#)PJ_poly.c 4.1 94/02/15 GIE REL";
#endif
#define PROJ_PARMS__ \
double ml0; \
double *en;
#define PJ_LIB__
#include "projects.h"
PROJ_HEAD(poly, "Polyconic (American)")
"\n\tConic, Sph&Ell";
#define TOL 1e-10
#define CONV 1e-10
#define N_ITER 10
#define I_ITER 20
#define ITOL 1.e-12
FORWARD(e_forward); /* ellipsoid */
double ms, sp, cp;
if (fabs(lp.phi) <= TOL) { xy.x = lp.lam; xy.y = -P->ml0; }
else {
sp = sin(lp.phi);
ms = fabs(cp = cos(lp.phi)) > TOL ? pj_msfn(sp, cp, P->es) / sp : 0.;
xy.x = ms * sin(lp.lam *= sp);
xy.y = (pj_mlfn(lp.phi, sp, cp, P->en) - P->ml0) + ms * (1. - cos(lp.lam));
}
return (xy);
}
FORWARD(s_forward); /* spheroid */
double cot, E;
if (fabs(lp.phi) <= TOL) { xy.x = lp.lam; xy.y = P->ml0; }
else {
cot = 1. / tan(lp.phi);
xy.x = sin(E = lp.lam * sin(lp.phi)) * cot;
xy.y = lp.phi - P->phi0 + cot * (1. - cos(E));
}
return (xy);
}
INVERSE(e_inverse); /* ellipsoid */
xy.y += P->ml0;
if (fabs(xy.y) <= TOL) { lp.lam = xy.x; lp.phi = 0.; }
else {
double r, c, sp, cp, s2ph, ml, mlb, mlp, dPhi;
int i;
r = xy.y * xy.y + xy.x * xy.x;
for (lp.phi = xy.y, i = I_ITER; i ; --i) {
sp = sin(lp.phi);
s2ph = sp * ( cp = cos(lp.phi));
if (fabs(cp) < ITOL)
I_ERROR;
c = sp * (mlp = sqrt(1. - P->es * sp * sp)) / cp;
ml = pj_mlfn(lp.phi, sp, cp, P->en);
mlb = ml * ml + r;
mlp = P->one_es / (mlp * mlp * mlp);
lp.phi += ( dPhi =
( ml + ml + c * mlb - 2. * xy.y * (c * ml + 1.) ) / (
P->es * s2ph * (mlb - 2. * xy.y * ml) / c +
2.* (xy.y - ml) * (c * mlp - 1. / s2ph) - mlp - mlp ));
if (fabs(dPhi) <= ITOL)
break;
}
if (!i)
I_ERROR;
c = sin(lp.phi);
lp.lam = asin(xy.x * tan(lp.phi) * sqrt(1. - P->es * c * c)) / sin(lp.phi);
}
return (lp);
}
INVERSE(s_inverse); /* spheroid */
double B, dphi, tp;
int i;
if (fabs(xy.y = P->phi0 + xy.y) <= TOL) { lp.lam = xy.x; lp.phi = 0.; }
else {
lp.phi = xy.y;
B = xy.x * xy.x + xy.y * xy.y;
i = N_ITER;
do {
tp = tan(lp.phi);
lp.phi -= (dphi = (xy.y * (lp.phi * tp + 1.) - lp.phi -
.5 * ( lp.phi * lp.phi + B) * tp) /
((lp.phi - xy.y) / tp - 1.));
} while (fabs(dphi) > CONV && --i);
if (! i) I_ERROR;
lp.lam = asin(xy.x * tan(lp.phi)) / sin(lp.phi);
}
return (lp);
}
FREEUP; if (P) { if (P->en) pj_dalloc(P->en); pj_dalloc(P); } }
ENTRY1(poly, en)
if (P->es) {
if (!(P->en = pj_enfn(P->es))) E_ERROR_0;
P->ml0 = pj_mlfn(P->phi0, sin(P->phi0), cos(P->phi0), P->en);
P->inv = e_inverse;
P->fwd = e_forward;
} else {
P->ml0 = -P->phi0;
P->inv = s_inverse;
P->fwd = s_forward;
}
ENDENTRY(P)