// FORWARD(e_forward) ellipsoid
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
{
CalculationType S, r, dr;
S = pj_mlfn(lp_lat, sin(lp_lat), cos(lp_lat), this->m_proj_parm.en) - this->m_proj_parm.M0;
dr = fS(S, this->m_proj_parm.C);
r = this->m_proj_parm.r0 - dr;
xy_x = this->m_par.k0 * (r * sin( lp_lon *= this->m_proj_parm.l ) );
xy_y = this->m_par.k0 * (this->m_proj_parm.r0 - r * cos(lp_lon) );
}
static PJ_XY lcca_e_forward (PJ_LP lp, PJ *P) { /* Ellipsoidal, forward */
PJ_XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double S, r, dr;
S = pj_mlfn(lp.phi, sin(lp.phi), cos(lp.phi), Q->en) - Q->M0;
dr = fS(S, Q->C);
r = Q->r0 - dr;
xy.x = P->k0 * (r * sin( lp.lam *= Q->l ) );
xy.y = P->k0 * (Q->r0 - r * cos(lp.lam) );
return xy;
}
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 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;
}
PROJ_HEAD(lcca, "Lambert Conformal Conic Alternative")
"\n\tConic, Sph&Ell\n\tlat_0=";
static double /* func to compute dr */
fS(double S, double C) {
return(S * ( 1. + S * S * C));
}
static double /* deriv of fs */
fSp(double S, double C) {
return(1. + 3.* S * S * C);
}
FORWARD(e_forward); /* ellipsoid */
double S, r, dr;
S = pj_mlfn(lp.phi, sin(lp.phi), cos(lp.phi), P->en) - P->M0;
dr = fS(S, P->C);
r = P->r0 - dr;
xy.x = P->k0 * (r * sin( lp.lam *= P->l ) );
xy.y = P->k0 * (P->r0 - r * cos(lp.lam) );
return (xy);
}
INVERSE(e_inverse); /* ellipsoid & spheroid */
double theta, dr, S, dif;
int i;
xy.x /= P->k0;
xy.y /= P->k0;
theta = atan2(xy.x , P->r0 - xy.y);
dr = xy.y - xy.x * tan(0.5 * theta);
lp.lam = theta / P->l;
S = dr;
