PJ_omerc.c
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#ifndef lint
static const char SCCSID[]="@(#)PJ_omerc.c 4.2 95/01/01 GIE REL";
#endif
#define PROJ_PARMS__ \
double alpha, lamc, lam1, phi1, lam2, phi2, Gamma, al, bl, el, \
singam, cosgam, sinrot, cosrot, u_0; \
int ellips, rot;
#define PJ_LIB__
#include "projects.h"
PROJ_HEAD(omerc, "Oblique Mercator")
"\n\tCyl, Sph&Ell\n\t no_rot rot_conv no_uoff and\n\t"
"alpha= lonc= or\n\t lon_1= lat_1= lon_2= lat_2=";
#define TOL 1.e-7
#define EPS 1.e-10
#define TSFN0(x) tan(.5 * (HALFPI - (x)))
FORWARD(e_forward); /* ellipsoid & spheroid */
double con, q, s, ul, us, vl, vs;
vl = sin(P->bl * lp.lam);
if (fabs(fabs(lp.phi) - HALFPI) <= EPS) {
ul = lp.phi < 0. ? -P->singam : P->singam;
us = P->al * lp.phi / P->bl;
} else {
q = P->el / (P->ellips ? pow(pj_tsfn(lp.phi, sin(lp.phi), P->e), P->bl)
: TSFN0(lp.phi));
s = .5 * (q - 1. / q);
ul = 2. * (s * P->singam - vl * P->cosgam) / (q + 1. / q);
con = cos(P->bl * lp.lam);
if (fabs(con) >= TOL) {
us = P->al * atan((s * P->cosgam + vl * P->singam) / con) / P->bl;
if (con < 0.)
us += PI * P->al / P->bl;
} else
us = P->al * P->bl * lp.lam;
}
if (fabs(fabs(ul) - 1.) <= EPS) F_ERROR;
vs = .5 * P->al * log((1. - ul) / (1. + ul)) / P->bl;
us -= P->u_0;
if (! P->rot) {
xy.x = us;
xy.y = vs;
} else {
xy.x = vs * P->cosrot + us * P->sinrot;
xy.y = us * P->cosrot - vs * P->sinrot;
}
return (xy);
}
INVERSE(e_inverse); /* ellipsoid & spheroid */
double q, s, ul, us, vl, vs;
if (! P->rot) {
us = xy.x;
vs = xy.y;
} else {
vs = xy.x * P->cosrot - xy.y * P->sinrot;
us = xy.y * P->cosrot + xy.x * P->sinrot;
}
us += P->u_0;
q = exp(- P->bl * vs / P->al);
s = .5 * (q - 1. / q);
vl = sin(P->bl * us / P->al);
ul = 2. * (vl * P->cosgam + s * P->singam) / (q + 1. / q);
if (fabs(fabs(ul) - 1.) < EPS) {
lp.lam = 0.;
lp.phi = ul < 0. ? -HALFPI : HALFPI;
} else {
lp.phi = P->el / sqrt((1. + ul) / (1. - ul));
if (P->ellips) {
if ((lp.phi = pj_phi2(pow(lp.phi, 1. / P->bl), P->e)) == HUGE_VAL)
I_ERROR;
} else
lp.phi = HALFPI - 2. * atan(lp.phi);
lp.lam = - atan2((s * P->cosgam -
vl * P->singam), cos(P->bl * us / P->al)) / P->bl;
}
return (lp);
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(omerc)
double con, com, cosph0, d, f, h, l, sinph0, p, j;
int azi;
P->rot = pj_param(P->params, "bno_rot").i == 0;
if( (azi = pj_param(P->params, "talpha").i) != 0.0) {
P->lamc = pj_param(P->params, "rlonc").f;
P->alpha = pj_param(P->params, "ralpha").f;
if ( fabs(P->alpha) <= TOL ||
fabs(fabs(P->phi0) - HALFPI) <= TOL ||
fabs(fabs(P->alpha) - HALFPI) <= TOL)
E_ERROR(-32);
} else {
P->lam1 = pj_param(P->params, "rlon_1").f;
P->phi1 = pj_param(P->params, "rlat_1").f;
P->lam2 = pj_param(P->params, "rlon_2").f;
P->phi2 = pj_param(P->params, "rlat_2").f;
if (fabs(P->phi1 - P->phi2) <= TOL ||
(con = fabs(P->phi1)) <= TOL ||
fabs(con - HALFPI) <= TOL ||
fabs(fabs(P->phi0) - HALFPI) <= TOL ||
fabs(fabs(P->phi2) - HALFPI) <= TOL) E_ERROR(-33);
}
com = (P->ellips = P->es > 0.) ? sqrt(P->one_es) : 1.;
if (fabs(P->phi0) > EPS) {
sinph0 = sin(P->phi0);
cosph0 = cos(P->phi0);
if (P->ellips) {
con = 1. - P->es * sinph0 * sinph0;
P->bl = cosph0 * cosph0;
P->bl = sqrt(1. + P->es * P->bl * P->bl / P->one_es);
P->al = P->bl * P->k0 * com / con;
d = P->bl * com / (cosph0 * sqrt(con));
} else {
P->bl = 1.;
P->al = P->k0;
d = 1. / cosph0;
}
if ((f = d * d - 1.) <= 0.)
f = 0.;
else {
f = sqrt(f);
if (P->phi0 < 0.)
f = -f;
}
P->el = f += d;
if (P->ellips) P->el *= pow(pj_tsfn(P->phi0, sinph0, P->e), P->bl);
else P->el *= TSFN0(P->phi0);
} else {
P->bl = 1. / com;
P->al = P->k0;
P->el = d = f = 1.;
}
if (azi) {
P->Gamma = asin(sin(P->alpha) / d);
P->lam0 = P->lamc - asin((.5 * (f - 1. / f)) *
tan(P->Gamma)) / P->bl;
} else {
if (P->ellips) {
h = pow(pj_tsfn(P->phi1, sin(P->phi1), P->e), P->bl);
l = pow(pj_tsfn(P->phi2, sin(P->phi2), P->e), P->bl);
} else {
h = TSFN0(P->phi1);
l = TSFN0(P->phi2);
}
f = P->el / h;
p = (l - h) / (l + h);
j = P->el * P->el;
j = (j - l * h) / (j + l * h);
if ((con = P->lam1 - P->lam2) < -PI)
P->lam2 -= TWOPI;
else if (con > PI)
P->lam2 += TWOPI;
P->lam0 = adjlon(.5 * (P->lam1 + P->lam2) - atan(
j * tan(.5 * P->bl * (P->lam1 - P->lam2)) / p) / P->bl);
P->Gamma = atan(2. * sin(P->bl * adjlon(P->lam1 - P->lam0)) /
(f - 1. / f));
P->alpha = asin(d * sin(P->Gamma));
}
P->singam = sin(P->Gamma);
P->cosgam = cos(P->Gamma);
f = pj_param(P->params, "brot_conv").i ? P->Gamma : P->alpha;
P->sinrot = sin(f);
P->cosrot = cos(f);
P->u_0 = pj_param(P->params, "bno_uoff").i ? 0. :
fabs(P->al * atan(sqrt(d * d - 1.) / P->cosrot) / P->bl);
if (P->phi0 < 0.)
P->u_0 = - P->u_0;
P->inv = e_inverse;
P->fwd = e_forward;
ENDENTRY(P)