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/* projection scale factors */
#define PJ_LIB__
#include "proj.h"
#include "proj_internal.h"
#include "proj_math.h"
#include "proj_internal.h"
#include <errno.h>
#ifndef DEFAULT_H
#define DEFAULT_H 1e-5 /* radian default for numeric h */
#endif
#define EPS 1.0e-12
int pj_factors(PJ_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 (nullptr==fac)
return 1;
if (nullptr==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 = pj_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;
}
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