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/* based upon Snyder and Linck, USGS-NMD */
#define PJ_LIB__
#include <errno.h>
#include "proj.h"
#include "proj_internal.h"
#include <math.h>
PROJ_HEAD(mil_os, "Miller Oblated Stereographic") "\n\tAzi(mod)";
PROJ_HEAD(lee_os, "Lee Oblated Stereographic") "\n\tAzi(mod)";
PROJ_HEAD(gs48, "Mod. Stereographic of 48 U.S.") "\n\tAzi(mod)";
PROJ_HEAD(alsk, "Mod. Stereographic of Alaska") "\n\tAzi(mod)";
PROJ_HEAD(gs50, "Mod. Stereographic of 50 U.S.") "\n\tAzi(mod)";
#define EPSLN 1e-12
namespace { // anonymous namespace
struct pj_opaque {
const COMPLEX *zcoeff; \
double cchio, schio; \
int n;
};
} // anonymous namespace
static PJ_XY mod_ster_e_forward (PJ_LP lp, PJ *P) { /* Ellipsoidal, forward */
PJ_XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double sinlon, coslon, esphi, chi, schi, cchi, s;
COMPLEX p;
sinlon = sin(lp.lam);
coslon = cos(lp.lam);
esphi = P->e * sin(lp.phi);
chi = 2. * atan(tan((M_HALFPI + lp.phi) * .5) *
pow((1. - esphi) / (1. + esphi), P->e * .5)) - M_HALFPI;
schi = sin(chi);
cchi = cos(chi);
const double denom = 1. + Q->schio * schi + Q->cchio * cchi * coslon;
if( denom == 0 ) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
s = 2. / denom;
p.r = s * cchi * sinlon;
p.i = s * (Q->cchio * schi - Q->schio * cchi * coslon);
p = pj_zpoly1(p, Q->zcoeff, Q->n);
xy.x = p.r;
xy.y = p.i;
return xy;
}
static PJ_LP mod_ster_e_inverse (PJ_XY xy, PJ *P) { /* Ellipsoidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
int nn;
COMPLEX p, fxy, fpxy, dp;
double den, rh = 0.0, z, sinz = 0.0, cosz = 0.0, chi, phi = 0.0, esphi;
p.r = xy.x;
p.i = xy.y;
for (nn = 20; nn ;--nn) {
fxy = pj_zpolyd1(p, Q->zcoeff, Q->n, &fpxy);
fxy.r -= xy.x;
fxy.i -= xy.y;
den = fpxy.r * fpxy.r + fpxy.i * fpxy.i;
dp.r = -(fxy.r * fpxy.r + fxy.i * fpxy.i) / den;
dp.i = -(fxy.i * fpxy.r - fxy.r * fpxy.i) / den;
p.r += dp.r;
p.i += dp.i;
if ((fabs(dp.r) + fabs(dp.i)) <= EPSLN)
break;
}
if (nn) {
rh = hypot(p.r, p.i);
z = 2. * atan(.5 * rh);
sinz = sin(z);
cosz = cos(z);
if (fabs(rh) <= EPSLN) {
/* if we end up here input coordinates were (0,0).
* pj_inv() adds P->lam0 to lp.lam, this way we are
* sure to get the correct offset */
lp.lam = 0.0;
lp.phi = P->phi0;
return lp;
}
chi = aasin(P->ctx, cosz * Q->schio + p.i * sinz * Q->cchio / rh);
phi = chi;
for (nn = 20; nn ;--nn) {
double dphi;
esphi = P->e * sin(phi);
dphi = 2. * atan(tan((M_HALFPI + chi) * .5) *
pow((1. + esphi) / (1. - esphi), P->e * .5)) - M_HALFPI - phi;
phi += dphi;
if (fabs(dphi) <= EPSLN)
break;
}
}
if (nn) {
lp.phi = phi;
lp.lam = atan2(p.r * sinz, rh * Q->cchio * cosz - p.i *
Q->schio * sinz);
} else
lp.lam = lp.phi = HUGE_VAL;
return lp;
}
static PJ *setup(PJ *P) { /* general initialization */
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double esphi, chio;
if (P->es != 0.0) {
esphi = P->e * sin(P->phi0);
chio = 2. * atan(tan((M_HALFPI + P->phi0) * .5) *
pow((1. - esphi) / (1. + esphi), P->e * .5)) - M_HALFPI;
} else
chio = P->phi0;
Q->schio = sin(chio);
Q->cchio = cos(chio);
P->inv = mod_ster_e_inverse;
P->fwd = mod_ster_e_forward;
return P;
}
/* Miller Oblated Stereographic */
PJ *PROJECTION(mil_os) {
static const COMPLEX AB[] = {
{0.924500, 0.},
{0., 0.},
{0.019430, 0.}
};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
Q->n = 2;
P->lam0 = DEG_TO_RAD * 20.;
P->phi0 = DEG_TO_RAD * 18.;
Q->zcoeff = AB;
P->es = 0.;
return setup(P);
}
/* Lee Oblated Stereographic */
PJ *PROJECTION(lee_os) {
static const COMPLEX AB[] = {
{0.721316, 0.},
{0., 0.},
{-0.0088162, -0.00617325}
};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
Q->n = 2;
P->lam0 = DEG_TO_RAD * -165.;
P->phi0 = DEG_TO_RAD * -10.;
Q->zcoeff = AB;
P->es = 0.;
return setup(P);
}
PJ *PROJECTION(gs48) {
static const COMPLEX /* 48 United States */
AB[] = {
{0.98879, 0.},
{0., 0.},
{-0.050909, 0.},
{0., 0.},
{0.075528, 0.}
};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
Q->n = 4;
P->lam0 = DEG_TO_RAD * -96.;
P->phi0 = DEG_TO_RAD * 39.;
Q->zcoeff = AB;
P->es = 0.;
P->a = 6370997.;
return setup(P);
}
PJ *PROJECTION(alsk) {
static const COMPLEX ABe[] = { /* Alaska ellipsoid */
{ .9945303, 0.},
{ .0052083, -.0027404},
{ .0072721, .0048181},
{-.0151089, -.1932526},
{ .0642675, -.1381226},
{ .3582802, -.2884586},
};
static const COMPLEX ABs[] = { /* Alaska sphere */
{ .9972523, 0.},
{ .0052513, -.0041175},
{ .0074606, .0048125},
{-.0153783, -.1968253},
{ .0636871, -.1408027},
{ .3660976, -.2937382}
};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
Q->n = 5;
P->lam0 = DEG_TO_RAD * -152.;
P->phi0 = DEG_TO_RAD * 64.;
if (P->es != 0.0) { /* fixed ellipsoid/sphere */
Q->zcoeff = ABe;
P->a = 6378206.4;
P->e = sqrt(P->es = 0.00676866);
} else {
Q->zcoeff = ABs;
P->a = 6370997.;
}
return setup(P);
}
PJ *PROJECTION(gs50) {
static const COMPLEX ABe[] = { /* GS50 ellipsoid */
{ .9827497, 0.},
{ .0210669, .0053804},
{-.1031415, -.0571664},
{-.0323337, -.0322847},
{ .0502303, .1211983},
{ .0251805, .0895678},
{-.0012315, -.1416121},
{ .0072202, -.1317091},
{-.0194029, .0759677},
{-.0210072, .0834037}
};
static const COMPLEX ABs[] = { /* GS50 sphere */
{ .9842990, 0.},
{ .0211642, .0037608},
{-.1036018, -.0575102},
{-.0329095, -.0320119},
{ .0499471, .1223335},
{ .0260460, .0899805},
{ .0007388, -.1435792},
{ .0075848, -.1334108},
{-.0216473, .0776645},
{-.0225161, .0853673}
};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(calloc (1, sizeof (struct pj_opaque)));
if (nullptr==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
Q->n = 9;
P->lam0 = DEG_TO_RAD * -120.;
P->phi0 = DEG_TO_RAD * 45.;
if (P->es != 0.0) { /* fixed ellipsoid/sphere */
Q->zcoeff = ABe;
P->a = 6378206.4;
P->e = sqrt(P->es = 0.00676866);
} else {
Q->zcoeff = ABs;
P->a = 6370997.;
}
return setup(P);
}
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