static PJ_LP s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
lp.phi = xy.y / FYC;
if (fabs(lp.phi) >= 1.) {
if (fabs(lp.phi) > ONEEPS) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
} else {
lp.phi = (lp.phi < 0.) ? -M_HALFPI : M_HALFPI;
}
} else
lp.phi = asin(lp.phi);
lp.lam = xy.x / ( FXC * (2. * cos(C23 * (lp.phi *= 3.)) - 1.) );
if (fabs(lp.phi = sin(lp.phi) / CS) >= 1.) {
if (fabs(lp.phi) > ONEEPS) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
} else {
lp.phi = (lp.phi < 0.) ? -M_HALFPI : M_HALFPI;
}
} else
lp.phi = asin(lp.phi);
return lp;
}
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;
}
static PJ_LP mbtfpq_s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
double t;
lp.phi = RYC * xy.y;
if (fabs(lp.phi) > 1.) {
if (fabs(lp.phi) > ONETOL) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
else if (lp.phi < 0.) { t = -1.; lp.phi = -M_PI; }
else { t = 1.; lp.phi = M_PI; }
} else
lp.phi = 2. * asin(t = lp.phi);
lp.lam = RXC * xy.x / (1. + 2. * cos(lp.phi)/cos(0.5 * lp.phi));
lp.phi = RC * (t + sin(lp.phi));
if (fabs(lp.phi) > 1.)
if (fabs(lp.phi) > ONETOL) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
else lp.phi = lp.phi < 0. ? -M_HALFPI : M_HALFPI;
else
lp.phi = asin(lp.phi);
return lp;
}
static PJ_LP s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
long i;
double t, t1;
struct COEFS T;
int iters;
lp.lam = xy.x / FXC;
lp.phi = fabs(xy.y / FYC);
if (lp.phi >= 1.) { /* simple pathologic cases */
if (lp.phi > ONEEPS) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
else {
lp.phi = xy.y < 0. ? -M_HALFPI : M_HALFPI;
lp.lam /= X[NODES].c0;
}
} else { /* general problem */
/* in Y space, reduce to table interval */
i = isnan(lp.phi) ? -1 : lround(floor(lp.phi * NODES));
if( i < 0 || i >= NODES ) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
for (;;) {
if (Y[i].c0 > lp.phi) --i;
else if (Y[i+1].c0 <= lp.phi) ++i;
else break;
}
T = Y[i];
/* first guess, linear interp */
t = 5. * (lp.phi - T.c0)/(Y[i+1].c0 - T.c0);
/* make into root */
T.c0 = (float)(T.c0 - lp.phi);
for (iters = MAX_ITER; iters ; --iters) { /* Newton-Raphson */
t -= t1 = V(T,t) / DV(T,t);
if (fabs(t1) < EPS)
break;
}
if( iters == 0 )
pj_ctx_set_errno( P->ctx, PJD_ERR_NON_CONVERGENT );
lp.phi = (5 * i + t) * DEG_TO_RAD;
if (xy.y < 0.) lp.phi = -lp.phi;
lp.lam /= V(X[i], t);
}
return lp;
}
static PJ_XY calcofi_e_forward (PJ_LP lp, PJ *P) { /* Ellipsoidal, forward */
PJ_XY xy = {0.0,0.0};
double oy; /* pt O y value in Mercator */
double l1; /* l1 and l2 are distances calculated using trig that sum
to the east/west distance between point O and point xy */
double l2;
double ry; /* r is the point on the same station as o (60) and the same
line as xy xy, r, o form a right triangle */
if (fabs(fabs(lp.phi) - M_HALFPI) <= EPS10) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
xy.x = lp.lam;
xy.y = -log(pj_tsfn(lp.phi, sin(lp.phi), P->e)); /* Mercator transform xy*/
oy = -log(pj_tsfn(PT_O_PHI, sin(PT_O_PHI), P->e));
l1 = (xy.y - oy) * tan(ROTATION_ANGLE);
l2 = -xy.x - l1 + PT_O_LAMBDA;
ry = l2 * cos(ROTATION_ANGLE) * sin(ROTATION_ANGLE) + xy.y;
ry = pj_phi2(P->ctx, exp(-ry), P->e); /*inverse Mercator*/
xy.x = PT_O_LINE - RAD_TO_DEG *
(ry - PT_O_PHI) * DEG_TO_LINE / cos(ROTATION_ANGLE);
xy.y = PT_O_STATION + RAD_TO_DEG *
(ry - lp.phi) * DEG_TO_STATION / sin(ROTATION_ANGLE);
/* set a = 1, x0 = 0, and y0 = 0 so that no further unit adjustments
are done */
return xy;
}
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, sinphi, q, sinb=0.0, cosb=0.0, b=0.0;
coslam = cos(lp.lam);
sinlam = sin(lp.lam);
sinphi = sin(lp.phi);
q = pj_qsfn(sinphi, P->e, P->one_es);
if (Q->mode == OBLIQ || Q->mode == EQUIT) {
sinb = q / Q->qp;
cosb = sqrt(1. - sinb * sinb);
}
switch (Q->mode) {
case OBLIQ:
b = 1. + Q->sinb1 * sinb + Q->cosb1 * cosb * coslam;
break;
case EQUIT:
b = 1. + cosb * coslam;
break;
case N_POLE:
b = M_HALFPI + lp.phi;
q = Q->qp - q;
break;
case S_POLE:
b = lp.phi - M_HALFPI;
q = Q->qp + q;
break;
}
if (fabs(b) < EPS10) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
switch (Q->mode) {
case OBLIQ:
b = sqrt(2. / b);
xy.y = Q->ymf * b * (Q->cosb1 * sinb - Q->sinb1 * cosb * coslam);
goto eqcon;
break;
case EQUIT:
b = sqrt(2. / (1. + cosb * coslam));
xy.y = b * sinb * Q->ymf;
eqcon:
xy.x = Q->xmf * b * cosb * sinlam;
break;
case N_POLE:
case S_POLE:
if (q >= 0.) {
b = sqrt(q);
xy.x = b * sinlam;
xy.y = coslam * (Q->mode == S_POLE ? b : -b);
} else
xy.x = xy.y = 0.;
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 rho;
xy.x /= P->k0;
xy.y /= P->k0;
xy.y = Q->rho0 - xy.y;
rho = hypot(xy.x, xy.y);
if (rho != 0.0) {
if (Q->n < 0.) {
rho = -rho;
xy.x = -xy.x;
xy.y = -xy.y;
}
if (Q->ellips) {
lp.phi = pj_phi2(P->ctx, pow(rho / Q->c, 1./Q->n), P->e);
if (lp.phi == HUGE_VAL) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
} else
lp.phi = 2. * atan(pow(Q->c / rho, 1./Q->n)) - M_HALFPI;
lp.lam = atan2(xy.x, xy.y) / Q->n;
} else {
lp.lam = 0.;
lp.phi = Q->n > 0. ? M_HALFPI : -M_HALFPI;
}
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) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
lp.lam = asin(xy.x * tan(lp.phi)) / sin(lp.phi);
}
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;
}
static PJ_XY geos_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 r, Vx, Vy, Vz, tmp;
/* Calculation of geocentric latitude. */
lp.phi = atan (Q->radius_p2 * tan (lp.phi));
/* Calculation of the three components of the vector from satellite to
** position on earth surface (lon,lat).*/
r = (Q->radius_p) / hypot(Q->radius_p * cos (lp.phi), sin (lp.phi));
Vx = r * cos (lp.lam) * cos (lp.phi);
Vy = r * sin (lp.lam) * cos (lp.phi);
Vz = r * sin (lp.phi);
/* Check visibility. */
if (((Q->radius_g - Vx) * Vx - Vy * Vy - Vz * Vz * Q->radius_p_inv2) < 0.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
/* Calculation based on view angles from satellite. */
tmp = Q->radius_g - Vx;
if(Q->flip_axis) {
xy.x = Q->radius_g_1 * atan (Vy / hypot (Vz, tmp));
xy.y = Q->radius_g_1 * atan (Vz / tmp);
} else {
xy.x = Q->radius_g_1 * atan (Vy / tmp);
xy.y = Q->radius_g_1 * atan (Vz / hypot (Vy, tmp));
}
return xy;
}
static PJ_LP geos_s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double Vx, Vy, Vz, a, b, det, k;
/* Setting three components of vector from satellite to position.*/
Vx = -1.0;
if(Q->flip_axis) {
Vz = tan (xy.y / (Q->radius_g - 1.0));
Vy = tan (xy.x / (Q->radius_g - 1.0)) * sqrt (1.0 + Vz * Vz);
} else {
Vy = tan (xy.x / (Q->radius_g - 1.0));
Vz = tan (xy.y / (Q->radius_g - 1.0)) * sqrt (1.0 + Vy * Vy);
}
/* Calculation of terms in cubic equation and determinant.*/
a = Vy * Vy + Vz * Vz + Vx * Vx;
b = 2 * Q->radius_g * Vx;
if ((det = (b * b) - 4 * a * Q->C) < 0.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
/* Calculation of three components of vector from satellite to position.*/
k = (-b - sqrt(det)) / (2 * a);
Vx = Q->radius_g + k * Vx;
Vy *= k;
Vz *= k;
/* Calculation of longitude and latitude.*/
lp.lam = atan2 (Vy, Vx);
lp.phi = atan (Vz * cos (lp.lam) / Vx);
return lp;
}
/* Measure numerical deviation after n roundtrips fwd-inv (or inv-fwd) */
double proj_roundtrip (PJ *P, PJ_DIRECTION direction, int n, PJ_COORD *coord) {
int i;
PJ_COORD t, org;
if (0==P)
return HUGE_VAL;
if (n < 1) {
proj_errno_set (P, EINVAL);
return HUGE_VAL;
}
/* in the first half-step, we generate the output value */
org = *coord;
*coord = proj_trans (P, direction, org);
t = *coord;
/* now we take n-1 full steps in inverse direction: We are */
/* out of phase due to the half step already taken */
for (i = 0; i < n - 1; i++)
t = proj_trans (P, direction, proj_trans (P, -direction, t) );
/* finally, we take the last half-step */
t = proj_trans (P, -direction, t);
/* checking for angular *input* since we do a roundtrip, and end where we begin */
if (proj_angular_input (P, direction))
return proj_lpz_dist (P, org, t);
return proj_xyz_dist (org, t);
}
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 LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double phip, lamp, phipp, lampp, cp, esp, con, delp;
int i;
phipp = 2. * (atan (exp (xy.y / Q->kR)) - M_FORTPI);
lampp = xy.x / Q->kR;
cp = cos (phipp);
phip = aasin (P->ctx, Q->cosp0 * sin (phipp) + Q->sinp0 * cp * cos (lampp));
lamp = aasin (P->ctx, cp * sin (lampp) / cos (phip));
con = (Q->K - log (tan (M_FORTPI + 0.5 * phip)))/Q->c;
for (i = NITER; i ; --i) {
esp = P->e * sin(phip);
delp = (con + log(tan(M_FORTPI + 0.5 * phip)) - Q->hlf_e *
log((1. + esp)/(1. - esp)) ) *
(1. - esp * esp) * cos(phip) * P->rone_es;
phip -= delp;
if (fabs(delp) < EPS)
break;
}
if (i) {
lp.phi = phip;
lp.lam = lamp / Q->c;
} else {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
return (lp);
}
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 vandg_s_forward (PJ_LP lp, PJ *P) { /* Spheroidal, forward */
PJ_XY xy = {0.0,0.0};
double al, al2, g, g2, p2;
p2 = fabs(lp.phi / M_HALFPI);
if ((p2 - TOL) > 1.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
if (p2 > 1.)
p2 = 1.;
if (fabs(lp.phi) <= TOL) {
xy.x = lp.lam;
xy.y = 0.;
} else if (fabs(lp.lam) <= TOL || fabs(p2 - 1.) < TOL) {
xy.x = 0.;
xy.y = M_PI * tan(.5 * asin(p2));
if (lp.phi < 0.) xy.y = -xy.y;
} else {
al = .5 * fabs(M_PI / lp.lam - lp.lam / M_PI);
al2 = al * al;
g = sqrt(1. - p2 * p2);
g = g / (p2 + g - 1.);
g2 = g * g;
p2 = g * (2. / p2 - 1.);
p2 = p2 * p2;
xy.x = g - p2; g = p2 + al2;
xy.x = M_PI * (al * xy.x + sqrt(al2 * xy.x * xy.x - g * (g2 - p2))) / g;
if (lp.lam < 0.) xy.x = -xy.x;
xy.y = fabs(xy.x / M_PI);
xy.y = 1. - xy.y * (xy.y + 2. * al);
if (xy.y < -TOL) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
if (xy.y < 0.)
xy.y = 0.;
else
xy.y = sqrt(xy.y) * (lp.phi < 0. ? -M_PI : M_PI);
}
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) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
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) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
c = sin(lp.phi);
lp.lam = asin(xy.x * tan(lp.phi) * sqrt(1. - P->es * c * c)) / sin(lp.phi);
}
return lp;
}
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double coslam, cosphi, sinphi;
sinphi = sin(lp.phi);
cosphi = cos(lp.phi);
coslam = cos(lp.lam);
switch (Q->mode) {
case EQUIT:
xy.y = 1. + cosphi * coslam;
goto oblcon;
case OBLIQ:
xy.y = 1. + Q->sinb1 * sinphi + Q->cosb1 * cosphi * coslam;
oblcon:
if (xy.y <= EPS10) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
xy.y = sqrt(2. / xy.y);
xy.x = xy.y * cosphi * sin(lp.lam);
xy.y *= Q->mode == EQUIT ? sinphi :
Q->cosb1 * sinphi - Q->sinb1 * cosphi * coslam;
break;
case N_POLE:
coslam = -coslam;
/*-fallthrough*/
case S_POLE:
if (fabs(lp.phi + P->phi0) < EPS10) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
xy.y = M_FORTPI - lp.phi * .5;
xy.y = 2. * (Q->mode == S_POLE ? cos(xy.y) : sin(xy.y));
xy.x = xy.y * sin(lp.lam);
xy.y *= coslam;
break;
}
return xy;
}
int proj_errno_restore (const PJ *P, int err) {
/******************************************************************************
Use proj_errno_restore when the current function succeeds, but the
error flag was set on entry, and stored/reset using proj_errno_reset
in order to monitor for new errors.
See usage example under proj_errno_reset ()
******************************************************************************/
if (0==err)
return 0;
proj_errno_set (P, err);
return 0;
}
static PJ_LP s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double rh;
rh = hypot(xy.x, xy.y = Q->cphi1 - xy.y);
lp.phi = Q->cphi1 + Q->phi1 - rh;
if (fabs(lp.phi) > M_HALFPI) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
if (fabs(fabs(lp.phi) - M_HALFPI) <= EPS10)
lp.lam = 0.;
else
lp.lam = rh * atan2(xy.x, xy.y) / cos(lp.phi);
return lp;
}
static PJ_LP collg_s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
lp.phi = xy.y / FYC - 1.;
if (fabs(lp.phi = 1. - lp.phi * lp.phi) < 1.)
lp.phi = asin(lp.phi);
else if (fabs(lp.phi) > ONEEPS) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
} else {
lp.phi = lp.phi < 0. ? -M_HALFPI : M_HALFPI;
}
if ((lp.lam = 1. - sin(lp.phi)) <= 0.)
lp.lam = 0.;
else
lp.lam = xy.x / (FXC * sqrt(lp.lam));
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_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);
double s, rh;
rh = hypot(xy.x, xy.y = Q->am1 - xy.y);
lp.phi = pj_inv_mlfn(P->ctx, Q->am1 + Q->m1 - rh, P->es, Q->en);
if ((s = fabs(lp.phi)) < M_HALFPI) {
s = sin(lp.phi);
lp.lam = rh * atan2(xy.x, xy.y) *
sqrt(1. - P->es * s * s) / cos(lp.phi);
} else if (fabs(s - M_HALFPI) <= EPS10)
lp.lam = 0.;
else {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
return lp;
}
static PJ_XY s_forward (PJ_LP lp, PJ *P) { /* Spheroidal, forward */
PJ_XY xy = {0.0,0.0};
long i;
double dphi;
(void) P;
dphi = fabs(lp.phi);
i = isnan(lp.phi) ? -1 : lround(floor(dphi * C1));
if( i < 0 ){
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
if (i >= NODES) i = NODES - 1;
dphi = RAD_TO_DEG * (dphi - RC1 * i);
xy.x = V(X[i], dphi) * FXC * lp.lam;
xy.y = V(Y[i], dphi) * FYC;
if (lp.phi < 0.) xy.y = -xy.y;
return xy;
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double rho;
if (fabs(fabs(lp.phi) - M_HALFPI) < EPS10) {
if ((lp.phi * Q->n) <= 0.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
rho = 0.;
} else {
rho = Q->c * (Q->ellips ? pow(pj_tsfn(lp.phi, sin(lp.phi),
P->e), Q->n) : pow(tan(M_FORTPI + .5 * lp.phi), -Q->n));
}
lp.lam *= Q->n;
xy.x = P->k0 * (rho * sin( lp.lam) );
xy.y = P->k0 * (Q->rho0 - rho * cos(lp.lam) );
return xy;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double cosz=0.0, rh, sinz=0.0;
rh = hypot(xy.x, xy.y);
if ((lp.phi = rh * .5 ) > 1.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
lp.phi = 2. * asin(lp.phi);
if (Q->mode == OBLIQ || Q->mode == EQUIT) {
sinz = sin(lp.phi);
cosz = cos(lp.phi);
}
switch (Q->mode) {
case EQUIT:
lp.phi = fabs(rh) <= EPS10 ? 0. : asin(xy.y * sinz / rh);
xy.x *= sinz;
xy.y = cosz * rh;
break;
case OBLIQ:
lp.phi = fabs(rh) <= EPS10 ? P->phi0 :
asin(cosz * Q->sinb1 + xy.y * sinz * Q->cosb1 / rh);
xy.x *= sinz * Q->cosb1;
xy.y = (cosz - sin(lp.phi) * Q->sinb1) * rh;
break;
case N_POLE:
xy.y = -xy.y;
lp.phi = M_HALFPI - lp.phi;
break;
case S_POLE:
lp.phi -= M_HALFPI;
break;
}
lp.lam = (xy.y == 0. && (Q->mode == EQUIT || Q->mode == OBLIQ)) ?
0. : atan2(xy.x, xy.y);
return (lp);
}
int proj_vgrid_init(PJ* P, const char *grids) {
/**********************************************
Initizalize and populate gridlist.
Takes a PJ-object and the plus-parameter
name that is used in the proj-string to
specify the grids to load, e.g. "+grids".
The + should be left out here.
Returns the number of loaded grids.
***********************************************/
/* prepend "s" to the "grids" string to allow usage with pj_param */
char *sgrids = (char *) pj_malloc( (strlen(grids)+1+1) *sizeof(char) );
sprintf(sgrids, "%s%s", "s", grids);
if (P->vgridlist_geoid == NULL) {
P->vgridlist_geoid = pj_gridlist_from_nadgrids(
P->ctx,
pj_param(P->ctx, P->params, sgrids).s,
&(P->vgridlist_geoid_count)
);
if( P->vgridlist_geoid == NULL || P->vgridlist_geoid_count == 0 ) {
pj_dealloc(sgrids);
return 0;
}
}
if (P->vgridlist_geoid_count == 0) {
proj_errno_set(P, PJD_ERR_FAILED_TO_LOAD_GRID);
}
pj_dealloc(sgrids);
return P->vgridlist_geoid_count;
}
static PJ_XY calcofi_s_forward (PJ_LP lp, PJ *P) { /* Spheroidal, forward */
PJ_XY xy = {0.0,0.0};
double oy;
double l1;
double l2;
double ry;
if (fabs(fabs(lp.phi) - M_HALFPI) <= EPS10) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
xy.x = lp.lam;
xy.y = log(tan(M_FORTPI + .5 * lp.phi));
oy = log(tan(M_FORTPI + .5 * PT_O_PHI));
l1 = (xy.y - oy) * tan(ROTATION_ANGLE);
l2 = -xy.x - l1 + PT_O_LAMBDA;
ry = l2 * cos(ROTATION_ANGLE) * sin(ROTATION_ANGLE) + xy.y;
ry = M_HALFPI - 2. * atan(exp(-ry));
xy.x = PT_O_LINE - RAD_TO_DEG *
(ry - PT_O_PHI) * DEG_TO_LINE / cos(ROTATION_ANGLE);
xy.y = PT_O_STATION + RAD_TO_DEG *
(ry - lp.phi) * DEG_TO_STATION / sin(ROTATION_ANGLE);
return xy;
}
static PJ_LP lcca_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);
double theta, dr, S, dif;
int i;
xy.x /= P->k0;
xy.y /= P->k0;
theta = atan2(xy.x , Q->r0 - xy.y);
dr = xy.y - xy.x * tan(0.5 * theta);
lp.lam = theta / Q->l;
S = dr;
for (i = MAX_ITER; i ; --i) {
S -= (dif = (fS(S, Q->C) - dr) / fSp(S, Q->C));
if (fabs(dif) < DEL_TOL) break;
}
if (!i) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
lp.phi = pj_inv_mlfn(P->ctx, S + Q->M0, P->es, Q->en);
return lp;
}