inline void e_inverse(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat, Par const& par, ProjParm const& proj_parm)
{
T c;
if ((c = boost::math::hypot(xy_x, xy_y)) < epsilon10) {
lp_lat = par.phi0;
lp_lon = 0.;
return;
}
if (proj_parm.mode == obliq || proj_parm.mode == equit) {
T const x2 = xy_x * par.a;
T const y2 = xy_y * par.a;
//T const lat1 = par.phi0;
//T const lon1 = par.lam0;
T const azi1 = atan2(x2, y2);
T const s12 = sqrt(x2 * x2 + y2 * y2);
formula::result_direct<T> const dir =
formula::vincenty_direct
<
T, true
>::apply(par.lam0, par.phi0, s12, azi1, proj_parm.spheroid);
lp_lat = dir.lat2;
lp_lon = dir.lon2;
lp_lon -= par.lam0;
} else { /* Polar */
lp_lat = pj_inv_mlfn(proj_parm.mode == n_pole ? proj_parm.Mp - c : proj_parm.Mp + c,
par.es, proj_parm.en);
lp_lon = atan2(xy_x, proj_parm.mode == n_pole ? -xy_y : xy_y);
}
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
double s;
if ((s = fabs(lp_lat = pj_inv_mlfn(xy_y, this->m_par.es, this->m_proj_parm.en))) < HALFPI) {
s = sin(lp_lat);
lp_lon = xy_x * sqrt(1. - this->m_par.es * s * s) / cos(lp_lat);
} else if ((s - EPS10) < HALFPI)
lp_lon = 0.;
else throw proj_exception();;
return;
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
double s, rh;
rh = boost::math::hypot(xy_x, xy_y = this->m_proj_parm.am1 - xy_y);
lp_lat = pj_inv_mlfn(this->m_proj_parm.am1 + this->m_proj_parm.m1 - rh, this->m_par.es, this->m_proj_parm.en);
if ((s = fabs(lp_lat)) < HALFPI) {
s = sin(lp_lat);
lp_lon = rh * atan2(xy_x, xy_y) *
sqrt(1. - this->m_par.es * s * s) / cos(lp_lat);
} else if (fabs(s - HALFPI) <= EPS10)
lp_lon = 0.;
else throw proj_exception();;
}
inline void e_guam_inv(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat, Par const& par, ProjParm const& proj_parm)
{
T x2, t = 0.0;
int i;
x2 = 0.5 * xy_x * xy_x;
lp_lat = par.phi0;
for (i = 0; i < 3; ++i) {
t = par.e * sin(lp_lat);
lp_lat = pj_inv_mlfn(proj_parm.M1 + xy_y -
x2 * tan(lp_lat) * (t = sqrt(1. - t * t)), par.es, proj_parm.en);
}
lp_lon = xy_x * t / cos(lp_lat);
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double s, rh;
rh = hypot(xy.x, xy.y = Q->am1 - xy.y);
lp.phi = pj_inv_mlfn(P->ctx, Q->am1 + Q->m1 - rh, P->es, Q->en);
if ((s = fabs(lp.phi)) < M_HALFPI) {
s = sin(lp.phi);
lp.lam = rh * atan2(xy.x, xy.y) *
sqrt(1. - P->es * s * s) / cos(lp.phi);
} else if (fabs(s - M_HALFPI) <= EPS10)
lp.lam = 0.;
else I_ERROR;
return lp;
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
if ((this->m_proj_parm.rho = boost::math::hypot(xy_x, xy_y = this->m_proj_parm.rho0 - xy_y)) != 0.0 ) {
if (this->m_proj_parm.n < 0.) {
this->m_proj_parm.rho = -this->m_proj_parm.rho;
xy_x = -xy_x;
xy_y = -xy_y;
}
lp_lat = this->m_proj_parm.c - this->m_proj_parm.rho;
if (this->m_proj_parm.ellips)
lp_lat = pj_inv_mlfn(lp_lat, this->m_par.es, this->m_proj_parm.en);
lp_lon = atan2(xy_x, xy_y) / this->m_proj_parm.n;
} else {
lp_lon = 0.;
lp_lat = this->m_proj_parm.n > 0. ? HALFPI : - HALFPI;
}
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
double theta, dr, S, dif;
int i;
xy_x /= this->m_par.k0;
xy_y /= this->m_par.k0;
theta = atan2(xy_x , this->m_proj_parm.r0 - xy_y);
dr = xy_y - xy_x * tan(0.5 * theta);
lp_lon = theta / this->m_proj_parm.l;
S = dr;
for (i = MAX_ITER; i ; --i) {
S -= (dif = (fS(S, this->m_proj_parm.C) - dr) / fSp(S, this->m_proj_parm.C));
if (fabs(dif) < DEL_TOL) break;
}
if (!i) throw proj_exception();
lp_lat = pj_inv_mlfn(S + this->m_proj_parm.M0, this->m_par.es, this->m_proj_parm.en);
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
double n, t, r, dd, d2, tn, ph1;
LP lp = {0.0, 0.0};
struct pj_opaque *Q = P->opaque;
ph1 = pj_inv_mlfn (P->ctx, Q->m0 + xy.y, P->es, Q->en);
tn = tan (ph1); t = tn*tn;
n = sin (ph1);
r = 1. / (1. - P->es * n * n);
n = sqrt (r);
r *= (1. - P->es) * n;
dd = xy.x / n;
d2 = dd * dd;
lp.phi = ph1 - (n * tn / r) * d2 *
(.5 - (1. + 3. * t) * d2 * C3);
lp.lam = dd * (1. + t * d2 *
(-C4 + (1. + 3. * t) * d2 * C5)) / cos (ph1);
return lp;
}
static PJ_LP e_inverse (PJ_XY xy, PJ *P) { /* Ellipsoidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double s, rh;
rh = hypot(xy.x, xy.y = Q->am1 - xy.y);
lp.phi = pj_inv_mlfn(P->ctx, Q->am1 + Q->m1 - rh, P->es, Q->en);
if ((s = fabs(lp.phi)) < M_HALFPI) {
s = sin(lp.phi);
lp.lam = rh * atan2(xy.x, xy.y) *
sqrt(1. - P->es * s * s) / cos(lp.phi);
} else if (fabs(s - M_HALFPI) <= EPS10)
lp.lam = 0.;
else {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
return lp;
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
if ((Q->rho = hypot(xy.x, xy.y = Q->rho0 - xy.y)) != 0.0 ) {
if (Q->n < 0.) {
Q->rho = -Q->rho;
xy.x = -xy.x;
xy.y = -xy.y;
}
lp.phi = Q->c - Q->rho;
if (Q->ellips)
lp.phi = pj_inv_mlfn(P->ctx, lp.phi, P->es, Q->en);
lp.lam = atan2(xy.x, xy.y) / Q->n;
} else {
lp.lam = 0.;
lp.phi = Q->n > 0. ? M_HALFPI : -M_HALFPI;
}
return lp;
}
static PJ_LP lcca_e_inverse (PJ_XY xy, PJ *P) { /* Ellipsoidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double theta, dr, S, dif;
int i;
xy.x /= P->k0;
xy.y /= P->k0;
theta = atan2(xy.x , Q->r0 - xy.y);
dr = xy.y - xy.x * tan(0.5 * theta);
lp.lam = theta / Q->l;
S = dr;
for (i = MAX_ITER; i ; --i) {
S -= (dif = (fS(S, Q->C) - dr) / fSp(S, Q->C));
if (fabs(dif) < DEL_TOL) break;
}
if (!i) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
lp.phi = pj_inv_mlfn(P->ctx, S + Q->M0, P->es, Q->en);
return lp;
}
