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#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(stere, "Stereographic") "\n\tAzi, Sph&Ell\n\tlat_ts=";
PROJ_HEAD(ups, "Universal Polar Stereographic") "\n\tAzi, Sph&Ell\n\tsouth";
struct pj_opaque {
double phits;
double sinX1;
double cosX1;
double akm1;
int mode;
};
#define sinph0 P->opaque->sinX1
#define cosph0 P->opaque->cosX1
#define EPS10 1.e-10
#define TOL 1.e-8
#define NITER 8
#define CONV 1.e-10
#define S_POLE 0
#define N_POLE 1
#define OBLIQ 2
#define EQUIT 3
static double ssfn_ (double phit, double sinphi, double eccen) {
sinphi *= eccen;
return (tan (.5 * (M_HALFPI + phit)) *
pow ((1. - sinphi) / (1. + sinphi), .5 * eccen));
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double coslam, sinlam, sinX = 0.0, cosX = 0.0, X, A, sinphi;
coslam = cos (lp.lam);
sinlam = sin (lp.lam);
sinphi = sin (lp.phi);
if (Q->mode == OBLIQ || Q->mode == EQUIT) {
sinX = sin (X = 2. * atan(ssfn_(lp.phi, sinphi, P->e)) - M_HALFPI);
cosX = cos (X);
}
switch (Q->mode) {
case OBLIQ:
A = Q->akm1 / (Q->cosX1 * (1. + Q->sinX1 * sinX +
Q->cosX1 * cosX * coslam));
xy.y = A * (Q->cosX1 * sinX - Q->sinX1 * cosX * coslam);
goto xmul; /* but why not just xy.x = A * cosX; break; ? */
case EQUIT:
A = Q->akm1 / (1. + cosX * coslam);
xy.y = A * sinX;
xmul:
xy.x = A * cosX;
break;
case S_POLE:
lp.phi = -lp.phi;
coslam = - coslam;
sinphi = -sinphi;
case N_POLE:
xy.x = Q->akm1 * pj_tsfn (lp.phi, sinphi, P->e);
xy.y = - xy.x * coslam;
break;
}
xy.x = xy.x * sinlam;
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 sinphi, cosphi, coslam, sinlam;
sinphi = sin(lp.phi);
cosphi = cos(lp.phi);
coslam = cos(lp.lam);
sinlam = sin(lp.lam);
switch (Q->mode) {
case EQUIT:
xy.y = 1. + cosphi * coslam;
goto oblcon;
case OBLIQ:
xy.y = 1. + sinph0 * sinphi + cosph0 * cosphi * coslam;
oblcon:
if (xy.y <= EPS10) F_ERROR;
xy.x = (xy.y = Q->akm1 / xy.y) * cosphi * sinlam;
xy.y *= (Q->mode == EQUIT) ? sinphi :
cosph0 * sinphi - sinph0 * cosphi * coslam;
break;
case N_POLE:
coslam = - coslam;
lp.phi = - lp.phi;
case S_POLE:
if (fabs (lp.phi - M_HALFPI) < TOL) F_ERROR;
xy.x = sinlam * ( xy.y = Q->akm1 * tan (M_FORTPI + .5 * lp.phi) );
xy.y *= coslam;
break;
}
return xy;
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double cosphi, sinphi, tp=0.0, phi_l=0.0, rho, halfe=0.0, halfpi=0.0;
int i;
rho = hypot (xy.x, xy.y);
switch (Q->mode) {
case OBLIQ:
case EQUIT:
cosphi = cos ( tp = 2. * atan2 (rho * Q->cosX1 , Q->akm1) );
sinphi = sin (tp);
if ( rho == 0.0 )
phi_l = asin (cosphi * Q->sinX1);
else
phi_l = asin (cosphi * Q->sinX1 + (xy.y * sinphi * Q->cosX1 / rho));
tp = tan (.5 * (M_HALFPI + phi_l));
xy.x *= sinphi;
xy.y = rho * Q->cosX1 * cosphi - xy.y * Q->sinX1* sinphi;
halfpi = M_HALFPI;
halfe = .5 * P->e;
break;
case N_POLE:
xy.y = -xy.y;
case S_POLE:
phi_l = M_HALFPI - 2. * atan (tp = - rho / Q->akm1);
halfpi = -M_HALFPI;
halfe = -.5 * P->e;
break;
}
for (i = NITER; i--; phi_l = lp.phi) {
sinphi = P->e * sin(phi_l);
lp.phi = 2. * atan (tp * pow ((1.+sinphi)/(1.-sinphi), halfe)) - halfpi;
if (fabs (phi_l - lp.phi) < CONV) {
if (Q->mode == S_POLE)
lp.phi = -lp.phi;
lp.lam = (xy.x == 0. && xy.y == 0.) ? 0. : atan2 (xy.x, xy.y);
return lp;
}
}
I_ERROR;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double c, rh, sinc, cosc;
sinc = sin (c = 2. * atan ((rh = hypot (xy.x, xy.y)) / Q->akm1));
cosc = cos (c);
lp.lam = 0.;
switch (Q->mode) {
case EQUIT:
if (fabs (rh) <= EPS10)
lp.phi = 0.;
else
lp.phi = asin (xy.y * sinc / rh);
if (cosc != 0. || xy.x != 0.)
lp.lam = atan2 (xy.x * sinc, cosc * rh);
break;
case OBLIQ:
if (fabs (rh) <= EPS10)
lp.phi = P->phi0;
else
lp.phi = asin (cosc * sinph0 + xy.y * sinc * cosph0 / rh);
if ((c = cosc - sinph0 * sin (lp.phi)) != 0. || xy.x != 0.)
lp.lam = atan2 (xy.x * sinc * cosph0, c * rh);
break;
case N_POLE:
xy.y = -xy.y;
case S_POLE:
if (fabs (rh) <= EPS10)
lp.phi = P->phi0;
else
lp.phi = asin (Q->mode == S_POLE ? - cosc : cosc);
lp.lam = (xy.x == 0. && xy.y == 0.) ? 0. : atan2 (xy.x, xy.y);
break;
}
return lp;
}
static void *freeup_new (PJ *P) { /* Destructor */
if (0==P)
return 0;
pj_dealloc (P->opaque);
return pj_dealloc(P);
}
static void freeup (PJ *P) {
freeup_new (P);
return;
}
static PJ *setup(PJ *P) { /* general initialization */
double t;
struct pj_opaque *Q = P->opaque;
if (fabs ((t = fabs (P->phi0)) - M_HALFPI) < EPS10)
Q->mode = P->phi0 < 0. ? S_POLE : N_POLE;
else
Q->mode = t > EPS10 ? OBLIQ : EQUIT;
Q->phits = fabs (Q->phits);
if (P->es) {
double X;
switch (Q->mode) {
case N_POLE:
case S_POLE:
if (fabs (Q->phits - M_HALFPI) < EPS10)
Q->akm1 = 2. * P->k0 /
sqrt (pow (1+P->e,1+P->e) * pow (1-P->e,1-P->e));
else {
Q->akm1 = cos (Q->phits) /
pj_tsfn (Q->phits, t = sin (Q->phits), P->e);
t *= P->e;
Q->akm1 /= sqrt(1. - t * t);
}
break;
case EQUIT:
case OBLIQ:
t = sin (P->phi0);
X = 2. * atan (ssfn_(P->phi0, t, P->e)) - M_HALFPI;
t *= P->e;
Q->akm1 = 2. * P->k0 * cos (P->phi0) / sqrt(1. - t * t);
Q->sinX1 = sin (X);
Q->cosX1 = cos (X);
break;
}
P->inv = e_inverse;
P->fwd = e_forward;
} else {
switch (Q->mode) {
case OBLIQ:
sinph0 = sin (P->phi0);
cosph0 = cos (P->phi0);
case EQUIT:
Q->akm1 = 2. * P->k0;
break;
case S_POLE:
case N_POLE:
Q->akm1 = fabs (Q->phits - M_HALFPI) >= EPS10 ?
cos (Q->phits) / tan (M_FORTPI - .5 * Q->phits) :
2. * P->k0 ;
break;
}
P->inv = s_inverse;
P->fwd = s_forward;
}
return P;
}
PJ *PROJECTION(stere) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
Q->phits = pj_param (P->ctx, P->params, "tlat_ts").i ?
pj_param (P->ctx, P->params, "rlat_ts").f : M_HALFPI;
return setup(P);
}
PJ *PROJECTION(ups) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
/* International Ellipsoid */
P->phi0 = pj_param(P->ctx, P->params, "bsouth").i ? - M_HALFPI: M_HALFPI;
if (!P->es) E_ERROR(-34);
P->k0 = .994;
P->x0 = 2000000.;
P->y0 = 2000000.;
Q->phits = M_HALFPI;
P->lam0 = 0.;
return setup(P);
}
#ifndef PJ_SELFTEST
int pj_stere_selftest (void) {return 0;}
#else
int pj_stere_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char e_args[] = {"+proj=stere +ellps=GRS80 +lat_1=0.5 +lat_2=2 +n=0.5"};
char s_args[] = {"+proj=stere +a=6400000 +lat_1=0.5 +lat_2=2 +n=0.5"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY e_fwd_expect[] = {
{ 222644.8545501172, 110610.8834741739},
{ 222644.8545501172, -110610.8834741739},
{-222644.8545501172, 110610.8834741739},
{-222644.8545501172, -110610.8834741739},
};
XY s_fwd_expect[] = {
{ 223407.81025950745, 111737.938996443},
{ 223407.81025950745, -111737.938996443},
{-223407.81025950745, 111737.938996443},
{-223407.81025950745, -111737.938996443},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP e_inv_expect[] = {
{ 0.0017966305682022392, 0.00090436947502443507},
{ 0.0017966305682022392, -0.00090436947502443507},
{-0.0017966305682022392, 0.00090436947502443507},
{-0.0017966305682022392, -0.00090436947502443507},
};
LP s_inv_expect[] = {
{ 0.001790493109747395, 0.00089524655465513144},
{ 0.001790493109747395, -0.00089524655465513144},
{-0.001790493109747395, 0.00089524655465513144},
{-0.001790493109747395, -0.00089524655465513144},
};
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
#ifndef PJ_SELFTEST
int pj_ups_selftest (void) {return 0;}
#else
int pj_ups_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char e_args[] = {"+proj=ups +ellps=GRS80 +lat_1=0.5 +lat_2=2 +n=0.5"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY e_fwd_expect[] = {
{2433455.5634384668, -10412543.301512826},
{2448749.1185681992, -10850493.419804076},
{1566544.4365615332, -10412543.301512826},
{1551250.8814318008, -10850493.419804076},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP e_inv_expect[] = {
{-44.998567498074834, 64.9182362867341},
{-44.995702709112308, 64.917020250675748},
{-45.004297076028529, 64.915804280954518},
{-45.001432287066002, 64.914588377560719},
};
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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