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#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(gstmerc, "Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)")
"\n\tCyl, Sph&Ell\n\tlat_0= lon_0= k_0=";
struct pj_opaque {
double lamc;
double phic;
double c;
double n1;
double n2;
double XS;
double YS;
};
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double L, Ls, sinLs1, Ls1;
L = Q->n1*lp.lam;
Ls = Q->c + Q->n1 * log(pj_tsfn(-1.0 * lp.phi, -1.0 * sin(lp.phi), P->e));
sinLs1 = sin(L) / cosh(Ls);
Ls1 = log(pj_tsfn(-1.0 * asin(sinLs1), 0.0, 0.0));
xy.x = (Q->XS + Q->n2*Ls1) * P->ra;
xy.y = (Q->YS + Q->n2*atan(sinh(Ls) / cos(L))) * P->ra;
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 L, LC, sinC;
L = atan(sinh((xy.x * P->a - Q->XS) / Q->n2) / cos((xy.y * P->a - Q->YS) / Q->n2));
sinC = sin((xy.y * P->a - Q->YS) / Q->n2) / cosh((xy.x * P->a - Q->XS) / Q->n2);
LC = log(pj_tsfn(-1.0 * asin(sinC), 0.0, 0.0));
lp.lam = L / Q->n1;
lp.phi = -1.0 * pj_phi2(P->ctx, exp((LC - Q->c) / Q->n1), P->e);
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);
return pj_dealloc(P);
}
static void freeup (PJ *P) {
freeup_new (P);
return;
}
PJ *PROJECTION(gstmerc) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
Q->lamc = P->lam0;
Q->n1 = sqrt(1.0 + P->es * pow(cos(P->phi0), 4.0) / (1.0 - P->es));
Q->phic = asin(sin(P->phi0) / Q->n1);
Q->c = log(pj_tsfn(-1.0 * Q->phic, 0.0, 0.0))
- Q->n1 * log(pj_tsfn(-1.0 * P->phi0, -1.0 * sin(P->phi0), P->e));
Q->n2 = P->k0 * P->a * sqrt(1.0 - P->es) / (1.0 - P->es * sin(P->phi0) * sin(P->phi0));
Q->XS = 0;
Q->YS = -1.0 * Q->n2 * Q->phic;
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
#ifndef PJ_SELFTEST
int pj_gstmerc_selftest (void) {return 0;}
#else
int pj_gstmerc_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char s_args[] = {"+proj=gstmerc +a=6400000 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY s_fwd_expect[] = {
{ 223413.46640632182, 111769.14504058557},
{ 223413.46640632182, -111769.14504058668},
{-223413.46640632302, 111769.14504058557},
{-223413.46640632302, -111769.14504058668},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP s_inv_expect[] = {
{ 0.0017904931097109673, 0.0008952465544509083},
{ 0.0017904931097109673, -0.0008952465544509083},
{-0.0017904931097109673, 0.0008952465544509083},
{-0.0017904931097109673, -0.0008952465544509083},
};
return pj_generic_selftest (0, s_args, tolerance_xy, tolerance_lp, 4, 4, fwd_in, 0, s_fwd_expect, inv_in, 0, s_inv_expect);
}
#endif
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