static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe;
double Cn = xy.y, Ce = xy.x;
/* normalize N, E */
Cn = (Cn - Q->Zb)/Q->Qn;
Ce = Ce/Q->Qn;
if (fabs(Ce) <= 2.623395162778) { /* 150 degrees */
/* norm. N, E -> compl. sph. LAT, LNG */
Cn += clenS(Q->utg, PROJ_ETMERC_ORDER, 2*Cn, 2*Ce, &dCn, &dCe);
Ce += dCe;
Ce = atan (sinh (Ce)); /* Replaces: Ce = 2*(atan(exp(Ce)) - FORTPI); */
/* compl. sph. LAT -> Gaussian LAT, LNG */
#ifdef _GNU_SOURCE
sincos (Cn, &sin_Cn, &cos_Cn);
sincos (Ce, &sin_Ce, &cos_Ce);
#else
sin_Cn = sin (Cn);
cos_Cn = cos (Cn);
sin_Ce = sin (Ce);
cos_Ce = cos (Ce);
#endif
Ce = atan2 (sin_Ce, cos_Ce*cos_Cn);
Cn = atan2 (sin_Cn*cos_Ce, hypot (sin_Ce, cos_Ce*cos_Cn));
/* Gaussian LAT, LNG -> ell. LAT, LNG */
lp.phi = gatg (Q->cgb, PROJ_ETMERC_ORDER, Cn);
lp.lam = Ce;
}
else
lp.phi = lp.lam = HUGE_VAL;
return lp;
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe;
double Cn = lp.phi, Ce = lp.lam;
/* ell. LAT, LNG -> Gaussian LAT, LNG */
Cn = gatg (Q->cbg, PROJ_ETMERC_ORDER, Cn);
/* Gaussian LAT, LNG -> compl. sph. LAT */
#ifdef _GNU_SOURCE
sincos (Cn, &sin_Cn, &cos_Cn);
sincos (Ce, &sin_Ce, &cos_Ce);
#else
sin_Cn = sin (Cn);
cos_Cn = cos (Cn);
sin_Ce = sin (Ce);
cos_Ce = cos (Ce);
#endif
Cn = atan2 (sin_Cn, cos_Ce*cos_Cn);
Ce = atan2 (sin_Ce*cos_Cn, hypot (sin_Cn, cos_Cn*cos_Ce));
/* compl. sph. N, E -> ell. norm. N, E */
Ce = asinhy ( tan (Ce) ); /* Replaces: Ce = log(tan(FORTPI + Ce*0.5)); */
Cn += clenS (Q->gtu, PROJ_ETMERC_ORDER, 2*Cn, 2*Ce, &dCn, &dCe);
Ce += dCe;
if (fabs (Ce) <= 2.623395162778) {
xy.y = Q->Qn * Cn + Q->Zb; /* Northing */
xy.x = Q->Qn * Ce; /* Easting */
} else
xy.x = xy.y = HUGE_VAL;
return xy;
}
cos_arg_r = cos(arg_r);
r = 2.0*cos_arg_r;
/* summation loop */
for (hr1 = 0.0, hr = *--p; a - p;) {
hr2 = hr1;
hr1 = hr;
hr = -hr2 + r*hr1 + *--p;
}
return(sin(arg_r)*hr);
}
FORWARD(e_forward); /* ellipsoid */
double sin_Cn, cos_Cn, cos_Ce, dCn, dCe;
double Cn = lp.phi, Ce = lp.lam;
/* ell. LAT, LNG -> Gaussian LAT, LNG */
Cn = gatg(P->cbg, 5, Cn);
/* Gaussian LAT, LNG -> compl. sph. LAT */
sin_Cn = sin(Cn);
cos_Cn = cos(Cn);
cos_Ce = cos(Ce);
Cn = atan2(sin_Cn, cos_Ce*cos_Cn);
Ce = atan2(sin(Ce)*cos_Cn, hypot(sin_Cn, cos_Cn*cos_Ce));
/* compl. sph. N, E -> ell. norm. N, E */
Ce = log(tan(M_PI_4 + Ce*0.5));
Cn += clenS(P->gtu, 5, 2.*Cn, 2.*Ce, &dCn, &dCe);
Ce += dCe;
if (fabs(Ce) <= 2.623395162778) {
xy.y = P->Qn * Cn + P->Zb; /* Northing */
xy.x = P->Qn * Ce; /* Easting */
} else
xy.x = xy.y = HUGE_VAL;
r = 2*cos_arg_r;
/* summation loop */
for (hr1 = 0, hr = *--p; a - p;) {
hr2 = hr1;
hr1 = hr;
hr = -hr2 + r*hr1 + *--p;
}
return(sin(arg_r)*hr);
}
FORWARD(e_forward); /* ellipsoid */
double sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe;
double Cn = lp.phi, Ce = lp.lam;
/* ell. LAT, LNG -> Gaussian LAT, LNG */
Cn = gatg(P->cbg, PROJ_ETMERC_ORDER, Cn);
/* Gaussian LAT, LNG -> compl. sph. LAT */
#ifdef _GNU_SOURCE
sincos(Cn, &sin_Cn, &cos_Cn);
sincos(Ce, &sin_Ce, &cos_Ce);
#else
sin_Cn = sin(Cn);
cos_Cn = cos(Cn);
sin_Ce = sin(Ce);
cos_Ce = cos(Ce);
#endif
Cn = atan2(sin_Cn, cos_Ce*cos_Cn);
Ce = atan2(sin_Ce*cos_Cn, hypot(sin_Cn, cos_Cn*cos_Ce));
/* compl. sph. N, E -> ell. norm. N, E */
Ce = asinhy(tan(Ce)); /* Replaces: Ce = log(tan(FORTPI + Ce*0.5)); */
static PJ *setup(PJ *P) { /* general initialization */
double f, n, np, Z;
struct pj_opaque *Q = P->opaque;
if (P->es <= 0)
E_ERROR(-34);
/* flattening */
f = P->es / (1 + sqrt (1 - P->es)); /* Replaces: f = 1 - sqrt(1-P->es); */
/* third flattening */
np = n = f/(2 - f);
/* COEF. OF TRIG SERIES GEO <-> GAUSS */
/* cgb := Gaussian -> Geodetic, KW p190 - 191 (61) - (62) */
/* cbg := Geodetic -> Gaussian, KW p186 - 187 (51) - (52) */
/* PROJ_ETMERC_ORDER = 6th degree : Engsager and Poder: ICC2007 */
Q->cgb[0] = n*( 2 + n*(-2/3.0 + n*(-2 + n*(116/45.0 + n*(26/45.0 +
n*(-2854/675.0 ))))));
Q->cbg[0] = n*(-2 + n*( 2/3.0 + n*( 4/3.0 + n*(-82/45.0 + n*(32/45.0 +
n*( 4642/4725.0))))));
np *= n;
Q->cgb[1] = np*(7/3.0 + n*( -8/5.0 + n*(-227/45.0 + n*(2704/315.0 +
n*( 2323/945.0)))));
Q->cbg[1] = np*(5/3.0 + n*(-16/15.0 + n*( -13/9.0 + n*( 904/315.0 +
n*(-1522/945.0)))));
np *= n;
/* n^5 coeff corrected from 1262/105 -> -1262/105 */
Q->cgb[2] = np*( 56/15.0 + n*(-136/35.0 + n*(-1262/105.0 +
n*( 73814/2835.0))));
Q->cbg[2] = np*(-26/15.0 + n*( 34/21.0 + n*( 8/5.0 +
n*(-12686/2835.0))));
np *= n;
/* n^5 coeff corrected from 322/35 -> 332/35 */
Q->cgb[3] = np*(4279/630.0 + n*(-332/35.0 + n*(-399572/14175.0)));
Q->cbg[3] = np*(1237/630.0 + n*( -12/5.0 + n*( -24832/14175.0)));
np *= n;
Q->cgb[4] = np*(4174/315.0 + n*(-144838/6237.0 ));
Q->cbg[4] = np*(-734/315.0 + n*( 109598/31185.0));
np *= n;
Q->cgb[5] = np*(601676/22275.0 );
Q->cbg[5] = np*(444337/155925.0);
/* Constants of the projections */
/* Transverse Mercator (UTM, ITM, etc) */
np = n*n;
/* Norm. mer. quad, K&W p.50 (96), p.19 (38b), p.5 (2) */
Q->Qn = P->k0/(1 + n) * (1 + np*(1/4.0 + np*(1/64.0 + np/256.0)));
/* coef of trig series */
/* utg := ell. N, E -> sph. N, E, KW p194 (65) */
/* gtu := sph. N, E -> ell. N, E, KW p196 (69) */
Q->utg[0] = n*(-0.5 + n*( 2/3.0 + n*(-37/96.0 + n*( 1/360.0 +
n*( 81/512.0 + n*(-96199/604800.0))))));
Q->gtu[0] = n*( 0.5 + n*(-2/3.0 + n*( 5/16.0 + n*(41/180.0 +
n*(-127/288.0 + n*( 7891/37800.0 ))))));
Q->utg[1] = np*(-1/48.0 + n*(-1/15.0 + n*(437/1440.0 + n*(-46/105.0 +
n*( 1118711/3870720.0)))));
Q->gtu[1] = np*(13/48.0 + n*(-3/5.0 + n*(557/1440.0 + n*(281/630.0 +
n*(-1983433/1935360.0)))));
np *= n;
Q->utg[2] = np*(-17/480.0 + n*( 37/840.0 + n*( 209/4480.0 +
n*( -5569/90720.0 ))));
Q->gtu[2] = np*( 61/240.0 + n*(-103/140.0 + n*(15061/26880.0 +
n*(167603/181440.0))));
np *= n;
Q->utg[3] = np*(-4397/161280.0 + n*( 11/504.0 + n*( 830251/7257600.0)));
Q->gtu[3] = np*(49561/161280.0 + n*(-179/168.0 + n*(6601661/7257600.0)));
np *= n;
Q->utg[4] = np*(-4583/161280.0 + n*( 108847/3991680.0));
Q->gtu[4] = np*(34729/80640.0 + n*(-3418889/1995840.0));
np *= n;
Q->utg[5] = np*(-20648693/638668800.0);
Q->gtu[5] = np*(212378941/319334400.0);
/* Gaussian latitude value of the origin latitude */
Z = gatg (Q->cbg, PROJ_ETMERC_ORDER, P->phi0);
/* Origin northing minus true northing at the origin latitude */
/* i.e. true northing = N - P->Zb */
Q->Zb = - Q->Qn*(Z + clens(Q->gtu, PROJ_ETMERC_ORDER, 2*Z));
P->inv = e_inverse;
P->fwd = e_forward;
return P;
}