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#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(imw_p, "International Map of the World Polyconic")
"\n\tMod. Polyconic, Ell\n\tlat_1= and lat_2= [lon_1=]";
#define TOL 1e-10
#define EPS 1e-10
struct pj_opaque {
double P, Pp, Q, Qp, R_1, R_2, sphi_1, sphi_2, C2; \
double phi_1, phi_2, lam_1; \
double *en; \
int mode; /* = 0, phi_1 and phi_2 != 0, = 1, phi_1 = 0, = -1 phi_2 = 0 */
};
static int phi12(PJ *P, double *del, double *sig) {
struct pj_opaque *Q = P->opaque;
int err = 0;
if (!pj_param(P->ctx, P->params, "tlat_1").i ||
!pj_param(P->ctx, P->params, "tlat_2").i) {
err = -41;
} else {
Q->phi_1 = pj_param(P->ctx, P->params, "rlat_1").f;
Q->phi_2 = pj_param(P->ctx, P->params, "rlat_2").f;
*del = 0.5 * (Q->phi_2 - Q->phi_1);
*sig = 0.5 * (Q->phi_2 + Q->phi_1);
err = (fabs(*del) < EPS || fabs(*sig) < EPS) ? -42 : 0;
}
return err;
}
static XY loc_for(LP lp, PJ *P, double *yc) {
struct pj_opaque *Q = P->opaque;
XY xy;
if (! lp.phi) {
xy.x = lp.lam;
xy.y = 0.;
} else {
double xa, ya, xb, yb, xc, D, B, m, sp, t, R, C;
sp = sin(lp.phi);
m = pj_mlfn(lp.phi, sp, cos(lp.phi), Q->en);
xa = Q->Pp + Q->Qp * m;
ya = Q->P + Q->Q * m;
R = 1. / (tan(lp.phi) * sqrt(1. - P->es * sp * sp));
C = sqrt(R * R - xa * xa);
if (lp.phi < 0.) C = - C;
C += ya - R;
if (Q->mode < 0) {
xb = lp.lam;
yb = Q->C2;
} else {
t = lp.lam * Q->sphi_2;
xb = Q->R_2 * sin(t);
yb = Q->C2 + Q->R_2 * (1. - cos(t));
}
if (Q->mode > 0) {
xc = lp.lam;
*yc = 0.;
} else {
t = lp.lam * Q->sphi_1;
xc = Q->R_1 * sin(t);
*yc = Q->R_1 * (1. - cos(t));
}
D = (xb - xc)/(yb - *yc);
B = xc + D * (C + R - *yc);
xy.x = D * sqrt(R * R * (1 + D * D) - B * B);
if (lp.phi > 0)
xy.x = - xy.x;
xy.x = (B + xy.x) / (1. + D * D);
xy.y = sqrt(R * R - xy.x * xy.x);
if (lp.phi > 0)
xy.y = - xy.y;
xy.y += C + R;
}
return xy;
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
double yc;
xy = loc_for(lp, P, &yc);
return (xy);
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
XY t;
double yc;
lp.phi = Q->phi_2;
lp.lam = xy.x / cos(lp.phi);
do {
t = loc_for(lp, P, &yc);
lp.phi = ((lp.phi - Q->phi_1) * (xy.y - yc) / (t.y - yc)) + Q->phi_1;
lp.lam = lp.lam * xy.x / t.x;
} while (fabs(t.x - xy.x) > TOL || fabs(t.y - xy.y) > TOL);
return lp;
}
static void xy(PJ *P, double phi, double *x, double *y, double *sp, double *R) {
double F;
*sp = sin(phi);
*R = 1./(tan(phi) * sqrt(1. - P->es * *sp * *sp ));
F = P->opaque->lam_1 * *sp;
*y = *R * (1 - cos(F));
*x = *R * sin(F);
}
static void *freeup_new (PJ *P) { /* Destructor */
if (0==P)
return 0;
if (0==P->opaque)
return pj_dealloc (P);
pj_dealloc (P->opaque);
return pj_dealloc(P);
}
static void freeup (PJ *P) {
freeup_new (P);
return;
}
PJ *PROJECTION(imw_p) {
double del, sig, s, t, x1, x2, T2, y1, m1, m2, y2;
int i;
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
if (!(Q->en = pj_enfn(P->es))) E_ERROR_0;
if( (i = phi12(P, &del, &sig)) != 0)
E_ERROR(i);
if (Q->phi_2 < Q->phi_1) { /* make sure P->phi_1 most southerly */
del = Q->phi_1;
Q->phi_1 = Q->phi_2;
Q->phi_2 = del;
}
if (pj_param(P->ctx, P->params, "tlon_1").i)
Q->lam_1 = pj_param(P->ctx, P->params, "rlon_1").f;
else { /* use predefined based upon latitude */
sig = fabs(sig * RAD_TO_DEG);
if (sig <= 60) sig = 2.;
else if (sig <= 76) sig = 4.;
else sig = 8.;
Q->lam_1 = sig * DEG_TO_RAD;
}
Q->mode = 0;
if (Q->phi_1) xy(P, Q->phi_1, &x1, &y1, &Q->sphi_1, &Q->R_1);
else {
Q->mode = 1;
y1 = 0.;
x1 = Q->lam_1;
}
if (Q->phi_2) xy(P, Q->phi_2, &x2, &T2, &Q->sphi_2, &Q->R_2);
else {
Q->mode = -1;
T2 = 0.;
x2 = Q->lam_1;
}
m1 = pj_mlfn(Q->phi_1, Q->sphi_1, cos(Q->phi_1), Q->en);
m2 = pj_mlfn(Q->phi_2, Q->sphi_2, cos(Q->phi_2), Q->en);
t = m2 - m1;
s = x2 - x1;
y2 = sqrt(t * t - s * s) + y1;
Q->C2 = y2 - T2;
t = 1. / t;
Q->P = (m2 * y1 - m1 * y2) * t;
Q->Q = (y2 - y1) * t;
Q->Pp = (m2 * x1 - m1 * x2) * t;
Q->Qp = (x2 - x1) * t;
P->fwd = e_forward;
P->inv = e_inverse;
return P;
}
#ifndef PJ_SELFTEST
int pj_imw_p_selftest (void) {return 0;}
#else
int pj_imw_p_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char e_args[] = {"+proj=imw_p +ellps=GRS80 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY e_fwd_expect[] = {
{ 222588.4411393762, 55321.128653809537},
{ 222756.90637768712, -165827.58428832365},
{-222588.4411393762, 55321.128653809537},
{-222756.90637768712, -165827.58428832365},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP e_inv_expect[] = {
{ 0.0017966991379592214, 0.50090492361427374},
{ 0.0017966979081574697, 0.49909507588689922},
{-0.0017966991379592214, 0.50090492361427374},
{-0.0017966979081574697, 0.49909507588689922},
};
return pj_generic_selftest (e_args, 0, tolerance_xy, tolerance_lp, 4, 4, fwd_in, e_fwd_expect, 0, inv_in, e_inv_expect, 0);
}
#endif
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