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#define PJ_LIB__
# include <errno.h>
# include "projects.h"
PROJ_HEAD(cass, "Cassini") "\n\tCyl, Sph&Ell";
# define EPS10 1e-10
# define C1 .16666666666666666666
# define C2 .00833333333333333333
# define C3 .04166666666666666666
# define C4 .33333333333333333333
# define C5 .06666666666666666666
struct pj_opaque {
double *en;
double m0;
};
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
double n, t, a1, c, a2, tn;
XY xy = {0.0, 0.0};
struct pj_opaque *Q = P->opaque;
xy.y = pj_mlfn (lp.phi, n = sin (lp.phi), c = cos (lp.phi), Q->en);
n = 1./sqrt(1. - P->es * n*n);
tn = tan(lp.phi); t = tn * tn;
a1 = lp.lam * c;
c *= P->es * c / (1 - P->es);
a2 = a1 * a1;
xy.x = n * a1 * (1. - a2 * t *
(C1 - (8. - t + 8. * c) * a2 * C2));
xy.y -= Q->m0 - n * tn * a2 *
(.5 + (5. - t + 6. * c) * a2 * C3);
return xy;
}
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0, 0.0};
xy.x = asin (cos (lp.phi) * sin (lp.lam));
xy.y = atan2 (tan (lp.phi), cos (lp.lam)) - P->phi0;
return xy;
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
double n, t, r, dd, d2, tn, ph1;
LP lp = {0.0, 0.0};
struct pj_opaque *Q = P->opaque;
ph1 = pj_inv_mlfn (P->ctx, Q->m0 + xy.y, P->es, Q->en);
tn = tan (ph1); t = tn*tn;
n = sin (ph1);
r = 1. / (1. - P->es * n * n);
n = sqrt (r);
r *= (1. - P->es) * n;
dd = xy.x / n;
d2 = dd * dd;
lp.phi = ph1 - (n * tn / r) * d2 *
(.5 - (1. + 3. * t) * d2 * C3);
lp.lam = dd * (1. + t * d2 *
(-C4 + (1. + 3. * t) * d2 * C5)) / cos (ph1);
return lp;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
double dd;
lp.phi = asin(sin(dd = xy.y + P->phi0) * cos(xy.x));
lp.lam = atan2(tan(xy.x), cos(dd));
return lp;
}
static void *destructor (PJ *P, int errlev) { /* Destructor */
if (0==P)
return 0;
if (0==P->opaque)
return pj_default_destructor (P, errlev);
pj_dealloc (P->opaque->en);
return pj_default_destructor (P, errlev);
}
PJ *PROJECTION(cass) {
/* Spheroidal? */
if (0==P->es) {
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
/* otherwise it's ellipsoidal */
P->opaque = pj_calloc (1, sizeof (struct pj_opaque));
if (0==P->opaque)
return pj_default_destructor (P, ENOMEM);
P->destructor = destructor;
P->opaque->en = pj_enfn (P->es);
if (0==P->opaque->en)
return pj_default_destructor (P, ENOMEM);
P->opaque->m0 = pj_mlfn (P->phi0, sin (P->phi0), cos (P->phi0), P->opaque->en);
P->inv = e_inverse;
P->fwd = e_forward;
return P;
}
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