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#define PJ_LIB__
#include <errno.h>
#include <math.h>
#include "proj.h"
#include "proj_internal.h"
PROJ_HEAD(ocea, "Oblique Cylindrical Equal Area") "\n\tCyl, Sph"
"lonc= alpha= or\n\tlat_1= lat_2= lon_1= lon_2=";
namespace { // anonymous namespace
struct pj_opaque {
double rok;
double rtk;
double sinphi;
double cosphi;
};
} // anonymous namespace
static PJ_XY ocea_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 t;
xy.y = sin(lp.lam);
t = cos(lp.lam);
xy.x = atan((tan(lp.phi) * Q->cosphi + Q->sinphi * xy.y) / t);
if (t < 0.)
xy.x += M_PI;
xy.x *= Q->rtk;
xy.y = Q->rok * (Q->sinphi * sin(lp.phi) - Q->cosphi * cos(lp.phi) * xy.y);
return xy;
}
static PJ_LP ocea_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);
xy.y /= Q->rok;
xy.x /= Q->rtk;
const double t = sqrt(1. - xy.y * xy.y);
const double s = sin(xy.x);
lp.phi = asin(xy.y * Q->sinphi + t * Q->cosphi * s);
lp.lam = atan2(t * Q->sinphi * s - xy.y * Q->cosphi,
t * cos(xy.x));
return lp;
}
PJ *PROJECTION(ocea) {
double phi_1, phi_2, lam_1, lam_2, lonz, alpha;
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;
Q->rok = 1. / P->k0;
Q->rtk = P->k0;
double lam_p, phi_p;
/*If the keyword "alpha" is found in the sentence then use 1point+1azimuth*/
if ( pj_param(P->ctx, P->params, "talpha").i) {
/*Define Pole of oblique transformation from 1 point & 1 azimuth*/
// ERO: I've added M_PI so that the alpha is the angle from point 1 to point 2
// from the North in a clockwise direction
// (to be consistent with omerc behavior)
alpha = M_PI + pj_param(P->ctx, P->params, "ralpha").f;
lonz = pj_param(P->ctx, P->params, "rlonc").f;
/*Equation 9-8 page 80 (http://pubs.usgs.gov/pp/1395/report.pdf)*/
// Actually slightliy modified to use atan2(), as it is suggested by
// Snyder for equation 9-1, but this is not mentioned here
lam_p = atan2(-cos(alpha) , -sin(P->phi0) * sin(alpha)) + lonz;
/*Equation 9-7 page 80 (http://pubs.usgs.gov/pp/1395/report.pdf)*/
phi_p = asin(cos(P->phi0) * sin(alpha));
/*If the keyword "alpha" is NOT found in the sentence then use 2points*/
} else {
/*Define Pole of oblique transformation from 2 points*/
phi_1 = pj_param(P->ctx, P->params, "rlat_1").f;
phi_2 = pj_param(P->ctx, P->params, "rlat_2").f;
lam_1 = pj_param(P->ctx, P->params, "rlon_1").f;
lam_2 = pj_param(P->ctx, P->params, "rlon_2").f;
/*Equation 9-1 page 80 (http://pubs.usgs.gov/pp/1395/report.pdf)*/
lam_p = atan2(cos(phi_1) * sin(phi_2) * cos(lam_1) -
sin(phi_1) * cos(phi_2) * cos(lam_2),
sin(phi_1) * cos(phi_2) * sin(lam_2) -
cos(phi_1) * sin(phi_2) * sin(lam_1) );
/* take care of P->lam0 wrap-around when +lam_1=-90*/
if (lam_1 == -M_HALFPI)
lam_p = -lam_p;
/*Equation 9-2 page 80 (http://pubs.usgs.gov/pp/1395/report.pdf)*/
double cos_lamp_m_minus_lam_1 = cos(lam_p - lam_1);
double tan_phi_1 = tan(phi_1);
if( tan_phi_1 == 0.0 ) {
// Not sure if we want to support this case, but at least this avoids
// a division by zero, and gives the same result as the below atan()
phi_p = (cos_lamp_m_minus_lam_1 >= 0.0 ) ? -M_HALFPI : M_HALFPI;
}
else {
phi_p = atan(- cos_lamp_m_minus_lam_1 / tan_phi_1);
}
}
P->lam0 = lam_p + M_HALFPI;
Q->cosphi = cos(phi_p);
Q->sinphi = sin(phi_p);
P->inv = ocea_s_inverse;
P->fwd = ocea_s_forward;
P->es = 0.;
return P;
}
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