static PJ_LP 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);
PJ_XY t;
double yc = 0.0;
int i = 0;
const int N_MAX_ITER = 1000; /* Arbitrarily chosen number... */
lp.phi = Q->phi_2;
lp.lam = xy.x / cos(lp.phi);
do {
t = loc_for(lp, P, &yc);
const double denom = t.y - yc;
if( denom != 0 || fabs(t.y - xy.y) > TOL )
{
if( denom == 0 ) {
proj_errno_set(P, PJD_ERR_NON_CONVERGENT);
return proj_coord_error().lp;
}
lp.phi = ((lp.phi - Q->phi_1) * (xy.y - yc) / denom) + Q->phi_1;
}
if( t.x != 0 || fabs(t.x - xy.x) > TOL )
lp.lam = lp.lam * xy.x / t.x;
i ++;
} while (i < N_MAX_ITER &&
(fabs(t.x - xy.x) > TOL || fabs(t.y - xy.y) > TOL));
if( i == N_MAX_ITER )
{
proj_errno_set(P, PJD_ERR_NON_CONVERGENT);
return proj_coord_error().lp;
}
return lp;
}
PJ_COORD pj_fwd4d (PJ_COORD coo, PJ *P) {
int last_errno = proj_errno_reset(P);
if (!P->skip_fwd_prepare)
coo = fwd_prepare (P, coo);
if (HUGE_VAL==coo.v[0])
return proj_coord_error ();
/* Call the highest dimensional converter available */
if (P->fwd4d)
coo = P->fwd4d (coo, P);
else if (P->fwd3d)
coo.xyz = P->fwd3d (coo.lpz, P);
else if (P->fwd)
coo.xy = P->fwd (coo.lp, P);
else {
proj_errno_set (P, EINVAL);
return proj_coord_error ();
}
if (HUGE_VAL==coo.v[0])
return proj_coord_error ();
if (!P->skip_fwd_finalize)
coo = fwd_finalize (P, coo);
return error_or_coord(P, coo, last_errno);
}
PJ_XYZ pj_fwd3d(PJ_LPZ lpz, PJ *P) {
int last_errno;
PJ_COORD coo = {{0,0,0,0}};
coo.lpz = lpz;
last_errno = proj_errno_reset(P);
if (!P->skip_fwd_prepare)
coo = fwd_prepare (P, coo);
if (HUGE_VAL==coo.v[0])
return proj_coord_error ().xyz;
/* Do the transformation, using the lowest dimensional transformer feasible */
if (P->fwd3d)
coo.xyz = P->fwd3d(coo.lpz, P);
else if (P->fwd4d)
coo = P->fwd4d (coo, P);
else if (P->fwd)
coo.xy = P->fwd (coo.lp, P);
else {
proj_errno_set (P, EINVAL);
return proj_coord_error ().xyz;
}
if (HUGE_VAL==coo.v[0])
return proj_coord_error ().xyz;
if (!P->skip_fwd_finalize)
coo = fwd_finalize (P, coo);
return error_or_coord(P, coo, last_errno).xyz;
}
PJ_COORD proj_trans (PJ *P, PJ_DIRECTION direction, PJ_COORD coord) {
/***************************************************************************************
Apply the transformation P to the coordinate coord, preferring the 4D interfaces if
available.
See also pj_approx_2D_trans and pj_approx_3D_trans in pj_internal.c, which work
similarly, but prefers the 2D resp. 3D interfaces if available.
***************************************************************************************/
if (0==P)
return coord;
if (P->inverted)
direction = -direction;
switch (direction) {
case PJ_FWD:
return pj_fwd4d (coord, P);
case PJ_INV:
return pj_inv4d (coord, P);
case PJ_IDENT:
return coord;
default:
break;
}
proj_errno_set (P, EINVAL);
return proj_coord_error ();
}
static PJ_COORD error_or_coord(PJ *P, PJ_COORD coord, int last_errno) {
if (proj_errno(P))
return proj_coord_error();
proj_errno_restore(P, last_errno);
return coord;
}
static PJ_COORD reverse_4d(PJ_COORD coo, PJ *P) {
struct pj_opaque *Q = (struct pj_opaque *) P->opaque;
unsigned int i;
PJ_COORD out;
out = proj_coord_error();
for (i=0; i<4; i++)
out.v[Q->axis[i]] = coo.v[i] * Q->sign[i];
return out;
}
static LP reverse_2d(XY xy, PJ *P) {
struct pj_opaque *Q = (struct pj_opaque *) P->opaque;
unsigned int i;
PJ_COORD out, in;
in.xy = xy;
out = proj_coord_error();
for (i=0; i<2; i++)
out.v[Q->axis[i]] = in.v[i] * Q->sign[i];
return out.lp;
}
static XY forward_2d(LP lp, PJ *P) {
struct pj_opaque *Q = (struct pj_opaque *) P->opaque;
unsigned int i;
PJ_COORD out, in;
in.lp = lp;
out = proj_coord_error();
for (i=0; i<2; i++)
out.v[i] = in.v[Q->axis[i]] * Q->sign[i];
return out.xy;
}
static LPZ reverse_3d(XYZ xyz, PJ *P) {
struct pj_opaque *Q = (struct pj_opaque *) P->opaque;
unsigned int i;
PJ_COORD in, out;
out = proj_coord_error();
in.xyz = xyz;
for (i=0; i<3; i++)
out.v[Q->axis[i]] = in.v[i] * Q->sign[i];
return out.lpz;
}
static XYZ forward_3d(LPZ lpz, PJ *P) {
struct pj_opaque *Q = (struct pj_opaque *) P->opaque;
unsigned int i;
PJ_COORD out, in;
in.lpz = lpz;
out = proj_coord_error();
for (i=0; i<3; i++)
out.v[i] = in.v[Q->axis[i]] * Q->sign[i];
return out.xyz;
}
static PJ_LPZ reverse_3d(PJ_XYZ in, PJ *P) {
struct pj_opaque *Q = (struct pj_opaque *) P->opaque;
PJ_COORD out;
double dt = 0.0;
out.xyz = in;
if (Q->t_obs != HUGE_VAL) {
dt = Q->t_epoch - Q->t_obs;
} else {
out = proj_coord_error(); /* in the 3D case +t_obs must be specified */
proj_log_debug(P, "deformation: +t_obs must be specified");
return out.lpz;
}
out.xyz = reverse_shift(P, in, dt);
return out.lpz;
}
static PJ_LP vandg_s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
double t, c0, c1, c2, c3, al, r2, r, m, d, ay, x2, y2;
x2 = xy.x * xy.x;
if ((ay = fabs(xy.y)) < TOL) {
lp.phi = 0.;
t = x2 * x2 + TPISQ * (x2 + HPISQ);
lp.lam = fabs(xy.x) <= TOL ? 0. :
.5 * (x2 - PISQ + sqrt(t)) / xy.x;
return (lp);
}
y2 = xy.y * xy.y;
r = x2 + y2; r2 = r * r;
c1 = - M_PI * ay * (r + PISQ);
c3 = r2 + M_TWOPI * (ay * r + M_PI * (y2 + M_PI * (ay + M_HALFPI)));
c2 = c1 + PISQ * (r - 3. * y2);
c0 = M_PI * ay;
c2 /= c3;
al = c1 / c3 - THIRD * c2 * c2;
m = 2. * sqrt(-THIRD * al);
d = C2_27 * c2 * c2 * c2 + (c0 * c0 - THIRD * c2 * c1) / c3;
const double al_mul_m = al * m;
if( al_mul_m == 0 ) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return proj_coord_error().lp;
}
d = 3. * d /al_mul_m;
t = fabs(d);
if ((t - TOL) <= 1.) {
d = t > 1. ? (d > 0. ? 0. : M_PI) : acos(d);
lp.phi = M_PI * (m * cos(d * THIRD + PI4_3) - THIRD * c2);
if (xy.y < 0.) lp.phi = -lp.phi;
t = r2 + TPISQ * (x2 - y2 + HPISQ);
lp.lam = fabs(xy.x) <= TOL ? 0. :
.5 * (r - PISQ + (t <= 0. ? 0. : sqrt(t))) / xy.x;
} else {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
return lp;
}
static PJ_XY sterea_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 cosc, sinc, cosl, k;
lp = pj_gauss(P->ctx, lp, Q->en);
sinc = sin(lp.phi);
cosc = cos(lp.phi);
cosl = cos(lp.lam);
const double denom = 1. + Q->sinc0 * sinc + Q->cosc0 * cosc * cosl;
if( denom == 0.0 ) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return proj_coord_error().xy;
}
k = P->k0 * Q->R2 / denom;
xy.x = k * cosc * sin(lp.lam);
xy.y = k * (Q->cosc0 * sinc - Q->sinc0 * cosc * cosl);
return xy;
}
static PJ_COORD parse_coord (const char *args) {
/*****************************************************************************
Attempt to interpret args as a PJ_COORD.
******************************************************************************/
int i;
const char *endp;
const char *dmsendp;
const char *prev = args;
PJ_COORD a = proj_coord (0,0,0,0);
T.dimensions_given = 0;
for (i = 0; i < 4; i++) {
/* proj_strtod doesn't read values like 123d45'678W so we need a bit */
/* of help from proj_dmstor. proj_strtod effectively ignores what */
/* comes after "d", so we use that fact that when dms is larger than */
/* d the value was stated in "dms" form. */
/* This could be avoided if proj_dmstor used the same proj_strtod() */
/* as gie, but that is not the case (yet). When we remove projects.h */
/* from the public API we can change that. */
double d = proj_strtod(prev, (char **) &endp);
double dms = PJ_TODEG(proj_dmstor (prev, (char **) &dmsendp));
/* TODO: When projects.h is removed, call proj_dmstor() in all cases */
if (d != dms && fabs(d) < fabs(dms) && fabs(dms) < fabs(d) + 1) {
d = dms;
endp = dmsendp;
}
/* A number like -81d00'00.000 will be parsed correctly by both */
/* proj_strtod and proj_dmstor but only the latter will return */
/* the correct end-pointer. */
if (d == dms && endp != dmsendp)
endp = dmsendp;
/* Break out if there were no more numerals */
if (prev==endp)
return i > 1? a: proj_coord_error ();
a.v[i] = d;
prev = endp;
T.dimensions_given++;
}
return a;
}
static PJ_XYZ forward_3d(PJ_LPZ lpz, PJ *P) {
struct pj_opaque *Q = (struct pj_opaque *) P->opaque;
PJ_COORD out, in;
PJ_XYZ shift;
double dt = 0.0;
in.lpz = lpz;
out = in;
if (Q->t_obs != HUGE_VAL) {
dt = Q->t_epoch - Q->t_obs;
} else {
out = proj_coord_error(); /* in the 3D case +t_obs must be specified */
proj_log_debug(P, "deformation: +t_obs must be specified");
return out.xyz;
}
shift = get_grid_shift(P, in.xyz);
out.xyz.x += dt * shift.x;
out.xyz.y += dt * shift.y;
out.xyz.z += dt * shift.z;
return out.xyz;
}
static PJ_COORD fwd_prepare (PJ *P, PJ_COORD coo) {
if (HUGE_VAL==coo.v[0] || HUGE_VAL==coo.v[1] || HUGE_VAL==coo.v[2])
return proj_coord_error ();
/* The helmert datum shift will choke unless it gets a sensible 4D coordinate */
if (HUGE_VAL==coo.v[2] && P->helmert) coo.v[2] = 0.0;
if (HUGE_VAL==coo.v[3] && P->helmert) coo.v[3] = 0.0;
/* Check validity of angular input coordinates */
if (INPUT_UNITS==PJ_IO_UNITS_RADIANS) {
double t;
/* check for latitude or longitude over-range */
t = (coo.lp.phi < 0 ? -coo.lp.phi : coo.lp.phi) - M_HALFPI;
if (t > PJ_EPS_LAT || coo.lp.lam > 10 || coo.lp.lam < -10) {
proj_errno_set (P, PJD_ERR_LAT_OR_LON_EXCEED_LIMIT);
return proj_coord_error ();
}
/* Clamp latitude to -90..90 degree range */
if (coo.lp.phi > M_HALFPI)
coo.lp.phi = M_HALFPI;
if (coo.lp.phi < -M_HALFPI)
coo.lp.phi = -M_HALFPI;
/* If input latitude is geocentrical, convert to geographical */
if (P->geoc)
coo = pj_geocentric_latitude (P, PJ_INV, coo);
/* Ensure longitude is in the -pi:pi range */
if (0==P->over)
coo.lp.lam = adjlon(coo.lp.lam);
if (P->hgridshift)
coo = proj_trans (P->hgridshift, PJ_INV, coo);
else if (P->helmert || (P->cart_wgs84 != nullptr && P->cart != nullptr)) {
coo = proj_trans (P->cart_wgs84, PJ_FWD, coo); /* Go cartesian in WGS84 frame */
if( P->helmert )
coo = proj_trans (P->helmert, PJ_INV, coo); /* Step into local frame */
coo = proj_trans (P->cart, PJ_INV, coo); /* Go back to angular using local ellps */
}
if (coo.lp.lam==HUGE_VAL)
return coo;
if (P->vgridshift)
coo = proj_trans (P->vgridshift, PJ_FWD, coo); /* Go orthometric from geometric */
/* Distance from central meridian, taking system zero meridian into account */
coo.lp.lam = (coo.lp.lam - P->from_greenwich) - P->lam0;
/* Ensure longitude is in the -pi:pi range */
if (0==P->over)
coo.lp.lam = adjlon(coo.lp.lam);
return coo;
}
/* We do not support gridshifts on cartesian input */
if (INPUT_UNITS==PJ_IO_UNITS_CARTESIAN && P->helmert)
return proj_trans (P->helmert, PJ_INV, coo);
return coo;
}