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#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj.h"
#include "proj_internal.h"
PROJ_HEAD(lagrng, "Lagrange") "\n\tMisc Sph\n\tW=";
#define TOL 1e-10
namespace { // anonymous namespace
struct pj_opaque {
double a1;
double a2;
double hrw;
double hw;
double rw;
double w;
};
} // anonymous namespace
static PJ_XY lagrng_s_forward (PJ_LP lp, PJ *P) { /* Spheroidal, forward */
PJ_XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double v, c;
const double sin_phi = sin(lp.phi);
if (fabs(fabs(sin_phi) - 1) < TOL) {
xy.x = 0;
xy.y = lp.phi < 0 ? -2. : 2.;
} else {
v = Q->a1 * pow((1. + sin_phi)/(1. - sin_phi), Q->hrw);
lp.lam *= Q->rw;
c = 0.5 * (v + 1./v) + cos(lp.lam);
if (c < TOL) {
proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);
return xy;
}
xy.x = 2. * sin(lp.lam) / c;
xy.y = (v - 1./v) / c;
}
return xy;
}
static PJ_LP lagrng_s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double c, x2, y2p, y2m;
if (fabs(fabs(xy.y) - 2.) < TOL) {
lp.phi = xy.y < 0 ? -M_HALFPI : M_HALFPI;
lp.lam = 0;
} else {
x2 = xy.x * xy.x;
y2p = 2. + xy.y;
y2m = 2. - xy.y;
c = y2p * y2m - x2;
if (fabs(c) < TOL) {
proj_errno_set(P, PROJ_ERR_COORD_TRANSFM_OUTSIDE_PROJECTION_DOMAIN);
return lp;
}
lp.phi = 2. * atan(pow((y2p * y2p + x2) / (Q->a2 * (y2m * y2m + x2)), Q->hw)) - M_HALFPI;
lp.lam = Q->w * atan2(4. * xy.x, c);
}
return lp;
}
PJ *PROJECTION(lagrng) {
double sin_phi1;
struct pj_opaque *Q = static_cast<struct pj_opaque*>(calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, PROJ_ERR_OTHER /*ENOMEM*/);
P->opaque = Q;
if( pj_param(P->ctx, P->params, "tW").i )
Q->w = pj_param(P->ctx, P->params, "dW").f;
else
Q->w = 2;
if (Q->w <= 0)
{
proj_log_error(P, _("Invalid value for W: it should be > 0"));
return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);
}
Q->hw = 0.5 * Q->w;
Q->rw = 1. / Q->w;
Q->hrw = 0.5 * Q->rw;
sin_phi1 = sin(pj_param(P->ctx, P->params, "rlat_1").f);
if (fabs(fabs(sin_phi1) - 1.) < TOL)
{
proj_log_error(P, _("Invalid value for lat_1: |lat_1| should be < 90°"));
return pj_default_destructor(P, PROJ_ERR_INVALID_OP_ILLEGAL_ARG_VALUE);
}
Q->a1 = pow((1. - sin_phi1)/(1. + sin_phi1), Q->hrw);
Q->a2 = Q->a1 * Q->a1;
P->es = 0.;
P->inv = lagrng_s_inverse;
P->fwd = lagrng_s_forward;
return P;
}
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