// INVERSE(s_inverse) sphere
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
{
T N, M, xp, yp, z, Az, cz, sz, cAz;
N = this->m_proj_parm.hn * aasin(xy_y * this->m_proj_parm.rn);
M = this->m_proj_parm.hm * aasin(xy_x * this->m_proj_parm.rm * cos(N * this->m_proj_parm.two_r_n) / cos(N));
xp = 2. * sin(M);
yp = 2. * sin(N) * cos(M * this->m_proj_parm.two_r_m) / cos(M);
cAz = cos(Az = aatan2(xp, yp) - this->m_proj_parm.theta);
z = 2. * aasin(0.5 * boost::math::hypot(xp, yp));
sz = sin(z);
cz = cos(z);
lp_lat = aasin(this->m_proj_parm.sp0 * cz + this->m_proj_parm.cp0 * sz * cAz);
lp_lon = aatan2(sz * sin(Az),
this->m_proj_parm.cp0 * cz - this->m_proj_parm.sp0 * sz * cAz);
}
static PJ_XY t_forward(PJ_LP lp, PJ *P) { /* spheroid */
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double cosphi, coslam;
cosphi = cos(lp.phi);
coslam = cos(lp.lam);
lp.lam = adjlon(aatan2(cosphi * sin(lp.lam), sin(lp.phi)) + Q->lamp);
lp.phi = aasin(P->ctx, - cosphi * coslam);
return Q->link->fwd(lp, Q->link);
}
// FORWARD(s_forward) sphere
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
inline void fwd(T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
{
T Az, M, N, cp, sp, cl, shz;
cp = cos(lp_lat);
sp = sin(lp_lat);
cl = cos(lp_lon);
Az = aatan2(cp * sin(lp_lon), this->m_proj_parm.cp0 * sp - this->m_proj_parm.sp0 * cp * cl) + this->m_proj_parm.theta;
shz = sin(0.5 * aacos(this->m_proj_parm.sp0 * sp + this->m_proj_parm.cp0 * cp * cl));
M = aasin(shz * sin(Az));
N = aasin(shz * cos(Az) * cos(M) / cos(M * this->m_proj_parm.two_r_m));
xy_y = this->m_proj_parm.n * sin(N * this->m_proj_parm.two_r_n);
xy_x = this->m_proj_parm.m * sin(M * this->m_proj_parm.two_r_m) * cos(N) / cos(N * this->m_proj_parm.two_r_n);
}
inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
{
double Az, M, N, cp, sp, cl, shz;
cp = cos(lp_lat);
sp = sin(lp_lat);
cl = cos(lp_lon);
Az = aatan2(cp * sin(lp_lon), this->m_proj_parm.cp0 * sp - this->m_proj_parm.sp0 * cp * cl) + this->m_proj_parm.theta;
shz = sin(0.5 * aacos(this->m_proj_parm.sp0 * sp + this->m_proj_parm.cp0 * cp * cl));
M = aasin(shz * sin(Az));
N = aasin(shz * cos(Az) * cos(M) / cos(M * this->m_proj_parm.two_r_m));
xy_y = this->m_proj_parm.n * sin(N * this->m_proj_parm.two_r_n);
xy_x = this->m_proj_parm.m * sin(M * this->m_proj_parm.two_r_m) * cos(N) / cos(N * this->m_proj_parm.two_r_n);
}
static PJ_LP t_inverse(PJ_XY xy, PJ *P) { /* spheroid */
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double cosphi, t;
PJ_LP lp = Q->link->inv(xy, Q->link);
if (lp.lam != HUGE_VAL) {
cosphi = cos(lp.phi);
t = lp.lam - Q->lamp;
lp.lam = aatan2(cosphi * sin(t), - sin(lp.phi));
lp.phi = aasin(P->ctx,cosphi * cos(t));
}
return lp;
}
static PJ_LP o_inverse(PJ_XY xy, PJ *P) { /* spheroid */
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double coslam, sinphi, cosphi;
PJ_LP lp = Q->link->inv(xy, Q->link);
if (lp.lam != HUGE_VAL) {
coslam = cos(lp.lam -= Q->lamp);
sinphi = sin(lp.phi);
cosphi = cos(lp.phi);
lp.phi = aasin(P->ctx,Q->sphip * sinphi + Q->cphip * cosphi * coslam);
lp.lam = aatan2(cosphi * sin(lp.lam), Q->sphip * cosphi * coslam -
Q->cphip * sinphi);
}
return lp;
}
#endif #define PROJ_PARMS__ \ double theta; \ double m, n; \ double two_r_m, two_r_n, rm, rn, hm, hn; \ double cp0, sp0; #define PJ_LIB__ #include "projects.h" PROJ_HEAD(oea, "Oblated Equal Area") "\n\tMisc Sph\n\tn= m= theta="; FORWARD(s_forward); /* sphere */ double Az, hz, M, N, cp, sp, cl, shz; cp = cos(lp.phi); sp = sin(lp.phi); cl = cos(lp.lam); Az = aatan2(cp * sin(lp.lam), P->cp0 * sp - P->sp0 * cp * cl) + P->theta; shz = sin(0.5 * aacos(P->sp0 * sp + P->cp0 * cp * cl)); M = aasin(shz * sin(Az)); N = aasin(shz * cos(Az) * cos(M) / cos(M * P->two_r_m)); xy.y = P->n * sin(N * P->two_r_n); xy.x = P->m * sin(M * P->two_r_m) * cos(N) / cos(N * P->two_r_n); return (xy); } INVERSE(s_inverse); /* sphere */ double N, M, xp, yp, z, Az, cz, sz, cAz; N = P->hn * aasin(xy.y * P->rn); M = P->hm * aasin(xy.x * P->rm * cos(N * P->two_r_n) / cos(N)); xp = 2. * sin(M); yp = 2. * sin(N) * cos(M * P->two_r_m) / cos(M); cAz = cos(Az = aatan2(xp, yp) - P->theta);
#include <string.h>
PROJ_HEAD(ob_tran, "General Oblique Transformation") "\n\tMisc Sph"
"\n\to_proj= plus parameters for projection"
"\n\to_lat_p= o_lon_p= (new pole) or"
"\n\to_alpha= o_lon_c= o_lat_c= or"
"\n\to_lon_1= o_lat_1= o_lon_2= o_lat_2=";
#define TOL 1e-10
FORWARD(o_forward); /* spheroid */
double coslam, sinphi, cosphi;
(void) xy;
coslam = cos(lp.lam);
sinphi = sin(lp.phi);
cosphi = cos(lp.phi);
lp.lam = adjlon(aatan2(cosphi * sin(lp.lam), P->sphip * cosphi * coslam +
P->cphip * sinphi) + P->lamp);
lp.phi = aasin(P->sphip * sinphi - P->cphip * cosphi * coslam);
return (P->link->fwd(lp, P->link));
}
FORWARD(t_forward); /* spheroid */
double cosphi, coslam;
(void) xy;
cosphi = cos(lp.phi);
coslam = cos(lp.lam);
lp.lam = adjlon(aatan2(cosphi * sin(lp.lam), sin(lp.phi)) + P->lamp);
lp.phi = aasin(- cosphi * coslam);
return (P->link->fwd(lp, P->link));
}
INVERSE(o_inverse); /* spheroid */
PJ *PROJECTION(ob_tran) {
double phip;
char *name;
ARGS args;
PJ *R; /* projection to rotate */
struct pj_opaque *Q = static_cast<struct pj_opaque*>(pj_calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return destructor(P, ENOMEM);
P->opaque = Q;
P->destructor = destructor;
/* get name of projection to be translated */
if (!(name = pj_param(P->ctx, P->params, "so_proj").s))
return destructor(P, PJD_ERR_NO_ROTATION_PROJ);
/* avoid endless recursion */
if( strcmp(name, "ob_tran") == 0 )
return destructor(P, PJD_ERR_FAILED_TO_FIND_PROJ);
/* Create the target projection object to rotate */
args = ob_tran_target_params (P->params);
R = pj_init_ctx (pj_get_ctx(P), args.argc, args.argv);
pj_dealloc (args.argv);
if (nullptr==R)
return destructor (P, PJD_ERR_UNKNOWN_PROJECTION_ID);
Q->link = R;
if (pj_param(P->ctx, P->params, "to_alpha").i) {
double lamc, phic, alpha;
lamc = pj_param(P->ctx, P->params, "ro_lon_c").f;
phic = pj_param(P->ctx, P->params, "ro_lat_c").f;
alpha = pj_param(P->ctx, P->params, "ro_alpha").f;
if (fabs(fabs(phic) - M_HALFPI) <= TOL)
return destructor(P, PJD_ERR_LAT_0_OR_ALPHA_EQ_90);
Q->lamp = lamc + aatan2(-cos(alpha), -sin(alpha) * sin(phic));
phip = aasin(P->ctx,cos(phic) * sin(alpha));
} else if (pj_param(P->ctx, P->params, "to_lat_p").i) { /* specified new pole */
Q->lamp = pj_param(P->ctx, P->params, "ro_lon_p").f;
phip = pj_param(P->ctx, P->params, "ro_lat_p").f;
} else { /* specified new "equator" points */
double lam1, lam2, phi1, phi2, con;
lam1 = pj_param(P->ctx, P->params, "ro_lon_1").f;
phi1 = pj_param(P->ctx, P->params, "ro_lat_1").f;
lam2 = pj_param(P->ctx, P->params, "ro_lon_2").f;
phi2 = pj_param(P->ctx, P->params, "ro_lat_2").f;
if (fabs(phi1 - phi2) <= TOL || (con = fabs(phi1)) <= TOL ||
fabs(con - M_HALFPI) <= TOL || fabs(fabs(phi2) - M_HALFPI) <= TOL)
return destructor(P, PJD_ERR_LAT_1_OR_2_ZERO_OR_90);
Q->lamp = atan2(cos(phi1) * sin(phi2) * cos(lam1) -
sin(phi1) * cos(phi2) * cos(lam2),
sin(phi1) * cos(phi2) * sin(lam2) -
cos(phi1) * sin(phi2) * sin(lam1));
phip = atan(-cos(Q->lamp - lam1) / tan(phi1));
}
if (fabs(phip) > TOL) { /* oblique */
Q->cphip = cos(phip);
Q->sphip = sin(phip);
P->fwd = Q->link->fwd ? o_forward : nullptr;
P->inv = Q->link->inv ? o_inverse : nullptr;
} else { /* transverse */
P->fwd = Q->link->fwd ? t_forward : nullptr;
P->inv = Q->link->inv ? t_inverse : nullptr;
}
/* Support some rather speculative test cases, where the rotated projection */
/* is actually latlong. We do not want scaling in that case... */
if (Q->link->right==PJ_IO_UNITS_RADIANS)
P->right = PJ_IO_UNITS_PROJECTED;
return P;
}
