int
pj_factors(LP lp, PJ *P, double h, struct FACTORS *fac) {
struct DERIVS der;
double cosphi, t, n, r;
/* check for forward and latitude or longitude overange */
if ((t = fabs(lp.phi)-HALFPI) > EPS || fabs(lp.lam) > 10.) {
pj_errno = -14;
return 1;
} else { /* proceed */
errno = pj_errno = 0;
if (fabs(t) <= EPS) /* adjust to pi/2 */
lp.phi = lp.phi < 0. ? -HALFPI : HALFPI;
else if (P->geoc)
lp.phi = atan(P->rone_es * tan(lp.phi));
lp.lam -= P->lam0; /* compute del lp.lam */
if (!P->over)
lp.lam = adjlon(lp.lam); /* adjust del longitude */
if (h <= 0.)
h = DEFAULT_H;
if (P->spc) /* get what projection analytic values */
P->spc(lp, P, fac);
if (((fac->code & (IS_ANAL_XL_YL+IS_ANAL_XP_YP)) !=
(IS_ANAL_XL_YL+IS_ANAL_XP_YP)) &&
pj_deriv(lp, h, P, &der))
return 1;
if (!(fac->code & IS_ANAL_XL_YL)) {
fac->der.x_l = der.x_l;
fac->der.y_l = der.y_l;
}
if (!(fac->code & IS_ANAL_XP_YP)) {
fac->der.x_p = der.x_p;
fac->der.y_p = der.y_p;
}
cosphi = cos(lp.phi);
if (!(fac->code & IS_ANAL_HK)) {
fac->h = hypot(fac->der.x_p, fac->der.y_p);
fac->k = hypot(fac->der.x_l, fac->der.y_l) / cosphi;
if (P->es) {
t = sin(lp.phi);
t = 1. - P->es * t * t;
n = sqrt(t);
fac->h *= t * n / P->one_es;
fac->k *= n;
r = t * t / P->one_es;
} else
r = 1.;
} else if (P->es) {
r = sin(lp.phi);
r = 1. - P->es * r * r;
r = r * r / P->one_es;
} else
r = 1.;
/* convergence */
if (!(fac->code & IS_ANAL_CONV)) {
fac->conv = - atan2(fac->der.y_l, fac->der.x_l);
if (fac->code & IS_ANAL_XL_YL)
fac->code |= IS_ANAL_CONV;
}
/* areal scale factor */
fac->s = (fac->der.y_p * fac->der.x_l - fac->der.x_p * fac->der.y_l) *
r / cosphi;
/* meridian-parallel angle theta prime */
fac->thetap = aasin(fac->s / (fac->h * fac->k));
/* Tissot ellips axis */
t = fac->k * fac->k + fac->h * fac->h;
fac->a = sqrt(t + 2. * fac->s);
t = (t = t - 2. * fac->s) <= 0. ? 0. : sqrt(t);
fac->b = 0.5 * (fac->a - t);
fac->a = 0.5 * (fac->a + t);
/* omega */
fac->omega = 2. * aasin((fac->a - fac->b)/(fac->a + fac->b));
}
return 0;
}
int pj_factors(LP lp, const PJ *P, double h, struct FACTORS *fac) {
double cosphi, t, n, r;
int err;
PJ_COORD coo = {{0, 0, 0, 0}};
coo.lp = lp;
/* Failing the 3 initial checks will most likely be due to */
/* earlier errors, so we leave errno alone */
if (0==fac)
return 1;
if (0==P)
return 1;
if (HUGE_VAL==lp.lam)
return 1;
/* But from here, we're ready to make our own mistakes */
err = proj_errno_reset (P);
/* Indicate that all factors are numerical approximations */
fac->code = 0;
/* Check for latitude or longitude overange */
if ((fabs (lp.phi)-M_HALFPI) > EPS || fabs (lp.lam) > 10.) {
proj_errno_set (P, PJD_ERR_LAT_OR_LON_EXCEED_LIMIT);
return 1;
}
/* Set a reasonable step size for the numerical derivatives */
h = fabs (h);
if (h < EPS)
h = DEFAULT_H;
/* If input latitudes are geocentric, convert to geographic */
if (P->geoc)
lp = proj_geocentric_latitude (P, PJ_INV, coo).lp;
/* If latitude + one step overshoots the pole, move it slightly inside, */
/* so the numerical derivative still exists */
if (fabs (lp.phi) > (M_HALFPI - h))
lp.phi = lp.phi < 0. ? -(M_HALFPI-h) : (M_HALFPI-h);
/* Longitudinal distance from central meridian */
lp.lam -= P->lam0;
if (!P->over)
lp.lam = adjlon(lp.lam);
/* Derivatives */
if (pj_deriv (lp, h, P, &(fac->der))) {
proj_errno_set (P, PJD_ERR_LAT_OR_LON_EXCEED_LIMIT);
return 1;
}
/* Scale factors */
cosphi = cos (lp.phi);
fac->h = hypot (fac->der.x_p, fac->der.y_p);
fac->k = hypot (fac->der.x_l, fac->der.y_l) / cosphi;
if (P->es != 0.0) {
t = sin(lp.phi);
t = 1. - P->es * t * t;
n = sqrt(t);
fac->h *= t * n / P->one_es;
fac->k *= n;
r = t * t / P->one_es;
} else
r = 1.;
/* Convergence */
fac->conv = -atan2 (fac->der.x_p, fac->der.y_p);
/* Areal scale factor */
fac->s = (fac->der.y_p * fac->der.x_l - fac->der.x_p * fac->der.y_l) * r / cosphi;
/* Meridian-parallel angle (theta prime) */
fac->thetap = aasin(P->ctx,fac->s / (fac->h * fac->k));
/* Tissot ellipse axis */
t = fac->k * fac->k + fac->h * fac->h;
fac->a = sqrt(t + 2. * fac->s);
t = t - 2. * fac->s;
t = t > 0? sqrt(t): 0;
fac->b = 0.5 * (fac->a - t);
fac->a = 0.5 * (fac->a + t);
/* Angular distortion */
fac->omega = 2. * aasin(P->ctx, (fac->a - fac->b) / (fac->a + fac->b) );
proj_errno_restore (P, err);
return 0;
}
