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#define PJ_LIB__
# 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 *freeup_new(PJ *P) { /* Destructor */
if (0==P)
return 0;
if (0==P->opaque)
return pj_dealloc (P);
pj_dealloc(P->opaque->en);
pj_dealloc(P->opaque);
return pj_dealloc(P);
}
static void freeup(PJ *P) { /* Destructor */
freeup_new (P);
return;
}
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 freeup_new (P);
P->opaque->en = pj_enfn (P->es);
if (0==P->opaque->en)
return freeup_new (P);
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;
}
#ifndef PJ_SELFTEST
int pj_cass_selftest (void) {return 0;}
#else
int pj_cass_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char e_args[] = {"+proj=cass +ellps=GRS80 +lat_1=0.5 +lat_2=2"};
char s_args[] = {"+proj=cass +R=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY e_fwd_expect[] = {
{ 222605.28577699114, 110642.22925399939},
{ 222605.28577699114, -110642.22925399939},
{-222605.28577699114, 110642.22925399939},
{-222605.28577699114, -110642.22925399939},
};
XY s_fwd_expect[] = {
{ 223368.10520348375, 111769.14504058579},
{ 223368.10520348375, -111769.14504058579},
{-223368.10520348375, 111769.14504058579},
{-223368.10520348375, -111769.14504058579},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP e_inv_expect[] = {
{ 0.0017966305684613522, 0.00090436947663183841},
{ 0.0017966305684613522, -0.00090436947663183841},
{-0.0017966305684613522, 0.00090436947663183841},
{-0.0017966305684613522, -0.00090436947663183841},
};
LP s_inv_expect[] = {
{ 0.0017904931100023887, 0.00089524655445477922},
{ 0.0017904931100023887, -0.00089524655445477922},
{-0.0017904931100023887, 0.00089524655445477922},
{-0.0017904931100023887, -0.00089524655445477922},
};
return pj_generic_selftest (e_args, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, e_fwd_expect, s_fwd_expect, inv_in, e_inv_expect, s_inv_expect);
}
#endif
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