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#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(poly, "Polyconic (American)")
"\n\tConic, Sph&Ell";
struct pj_opaque {
double ml0; \
double *en;
};
#define TOL 1e-10
#define CONV 1e-10
#define N_ITER 10
#define I_ITER 20
#define ITOL 1.e-12
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double ms, sp, cp;
if (fabs(lp.phi) <= TOL) {
xy.x = lp.lam;
xy.y = -Q->ml0;
} else {
sp = sin(lp.phi);
ms = fabs(cp = cos(lp.phi)) > TOL ? pj_msfn(sp, cp, P->es) / sp : 0.;
xy.x = ms * sin(lp.lam *= sp);
xy.y = (pj_mlfn(lp.phi, sp, cp, Q->en) - Q->ml0) + ms * (1. - cos(lp.lam));
}
return xy;
}
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double cot, E;
if (fabs(lp.phi) <= TOL) {
xy.x = lp.lam;
xy.y = Q->ml0;
} else {
cot = 1. / tan(lp.phi);
xy.x = sin(E = lp.lam * sin(lp.phi)) * cot;
xy.y = lp.phi - P->phi0 + cot * (1. - cos(E));
}
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.y += Q->ml0;
if (fabs(xy.y) <= TOL) {
lp.lam = xy.x;
lp.phi = 0.;
} else {
double r, c, sp, cp, s2ph, ml, mlb, mlp, dPhi;
int i;
r = xy.y * xy.y + xy.x * xy.x;
for (lp.phi = xy.y, i = I_ITER; i ; --i) {
sp = sin(lp.phi);
s2ph = sp * ( cp = cos(lp.phi));
if (fabs(cp) < ITOL)
I_ERROR;
c = sp * (mlp = sqrt(1. - P->es * sp * sp)) / cp;
ml = pj_mlfn(lp.phi, sp, cp, Q->en);
mlb = ml * ml + r;
mlp = P->one_es / (mlp * mlp * mlp);
lp.phi += ( dPhi =
( ml + ml + c * mlb - 2. * xy.y * (c * ml + 1.) ) / (
P->es * s2ph * (mlb - 2. * xy.y * ml) / c +
2.* (xy.y - ml) * (c * mlp - 1. / s2ph) - mlp - mlp ));
if (fabs(dPhi) <= ITOL)
break;
}
if (!i)
I_ERROR;
c = sin(lp.phi);
lp.lam = asin(xy.x * tan(lp.phi) * sqrt(1. - P->es * c * c)) / sin(lp.phi);
}
return lp;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
double B, dphi, tp;
int i;
if (fabs(xy.y = P->phi0 + xy.y) <= TOL) {
lp.lam = xy.x;
lp.phi = 0.;
} else {
lp.phi = xy.y;
B = xy.x * xy.x + xy.y * xy.y;
i = N_ITER;
do {
tp = tan(lp.phi);
lp.phi -= (dphi = (xy.y * (lp.phi * tp + 1.) - lp.phi -
.5 * ( lp.phi * lp.phi + B) * tp) /
((lp.phi - xy.y) / tp - 1.));
} while (fabs(dphi) > CONV && --i);
if (! i) I_ERROR;
lp.lam = asin(xy.x * tan(lp.phi)) / sin(lp.phi);
}
return lp;
}
static void *freeup_new (PJ *P) { /* Destructor */
if (0==P)
return 0;
if (0==P->opaque)
return pj_dealloc (P);
if (P->opaque->en)
pj_dealloc (P->opaque->en);
pj_dealloc (P->opaque);
return pj_dealloc(P);
}
static void freeup (PJ *P) {
freeup_new (P);
return;
}
PJ *PROJECTION(poly) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
if (P->es) {
if (!(Q->en = pj_enfn(P->es))) E_ERROR_0;
Q->ml0 = pj_mlfn(P->phi0, sin(P->phi0), cos(P->phi0), Q->en);
P->inv = e_inverse;
P->fwd = e_forward;
} else {
Q->ml0 = -P->phi0;
P->inv = s_inverse;
P->fwd = s_forward;
}
return P;
}
#ifndef PJ_SELFTEST
int pj_poly_selftest (void) {return 0;}
#else
int pj_poly_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char e_args[] = {"+proj=poly +ellps=GRS80 +lat_1=0.5 +lat_2=2"};
char s_args[] = {"+proj=poly +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY e_fwd_expect[] = {
{ 222605.285770237475, 110642.194561440483},
{ 222605.285770237475, -110642.194561440483},
{-222605.285770237475, 110642.194561440483},
{-222605.285770237475, -110642.194561440483},
};
XY s_fwd_expect[] = {
{ 223368.105210218986, 111769.110491224754},
{ 223368.105210218986, -111769.110491224754},
{-223368.105210218986, 111769.110491224754},
{-223368.105210218986, -111769.110491224754},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP e_inv_expect[] = {
{ 0.00179663056846135222, 0.000904369476631838518},
{ 0.00179663056846135222, -0.000904369476631838518},
{-0.00179663056846135222, 0.000904369476631838518},
{-0.00179663056846135222, -0.000904369476631838518},
};
LP s_inv_expect[] = {
{ 0.0017904931100023887, 0.000895246554454779222},
{ 0.0017904931100023887, -0.000895246554454779222},
{-0.0017904931100023887, 0.000895246554454779222},
{-0.0017904931100023887, -0.000895246554454779222},
};
return pj_generic_selftest (e_args, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, e_fwd_expect, s_fwd_expect, inv_in, e_inv_expect, s_inv_expect);
}
#endif
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