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#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(tpeqd, "Two Point Equidistant")
"\n\tMisc Sph\n\tlat_1= lon_1= lat_2= lon_2=";
struct pj_opaque {
double cp1, sp1, cp2, sp2, ccs, cs, sc, r2z0, z02, dlam2; \
double hz0, thz0, rhshz0, ca, sa, lp, lamc;
};
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0, 0.0};
struct pj_opaque *Q = P->opaque;
double t, z1, z2, dl1, dl2, sp, cp;
sp = sin(lp.phi);
cp = cos(lp.phi);
z1 = aacos(P->ctx, Q->sp1 * sp + Q->cp1 * cp * cos (dl1 = lp.lam + Q->dlam2));
z2 = aacos(P->ctx, Q->sp2 * sp + Q->cp2 * cp * cos (dl2 = lp.lam - Q->dlam2));
z1 *= z1;
z2 *= z2;
xy.x = Q->r2z0 * (t = z1 - z2);
t = Q->z02 - t;
xy.y = Q->r2z0 * asqrt (4. * Q->z02 * z2 - t * t);
if ((Q->ccs * sp - cp * (Q->cs * sin(dl1) - Q->sc * sin(dl2))) < 0.)
xy.y = -xy.y;
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 cz1, cz2, s, d, cp, sp;
cz1 = cos (hypot(xy.y, xy.x + Q->hz0));
cz2 = cos (hypot(xy.y, xy.x - Q->hz0));
s = cz1 + cz2;
d = cz1 - cz2;
lp.lam = - atan2(d, (s * Q->thz0));
lp.phi = aacos(P->ctx, hypot (Q->thz0 * s, d) * Q->rhshz0);
if ( xy.y < 0. )
lp.phi = - lp.phi;
/* lam--phi now in system relative to P1--P2 base equator */
sp = sin (lp.phi);
cp = cos (lp.phi);
lp.phi = aasin (P->ctx, Q->sa * sp + Q->ca * cp * (s = cos(lp.lam -= Q->lp)));
lp.lam = atan2 (cp * sin(lp.lam), Q->sa * cp * s - Q->ca * sp) + Q->lamc;
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(tpeqd) {
double lam_1, lam_2, phi_1, phi_2, A12, pp;
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
/* get control point locations */
phi_1 = pj_param(P->ctx, P->params, "rlat_1").f;
lam_1 = pj_param(P->ctx, P->params, "rlon_1").f;
phi_2 = pj_param(P->ctx, P->params, "rlat_2").f;
lam_2 = pj_param(P->ctx, P->params, "rlon_2").f;
if (phi_1 == phi_2 && lam_1 == lam_2)
E_ERROR(-25);
P->lam0 = adjlon (0.5 * (lam_1 + lam_2));
Q->dlam2 = adjlon (lam_2 - lam_1);
Q->cp1 = cos (phi_1);
Q->cp2 = cos (phi_2);
Q->sp1 = sin (phi_1);
Q->sp2 = sin (phi_2);
Q->cs = Q->cp1 * Q->sp2;
Q->sc = Q->sp1 * Q->cp2;
Q->ccs = Q->cp1 * Q->cp2 * sin(Q->dlam2);
Q->z02 = aacos(P->ctx, Q->sp1 * Q->sp2 + Q->cp1 * Q->cp2 * cos (Q->dlam2));
Q->hz0 = .5 * Q->z02;
A12 = atan2(Q->cp2 * sin (Q->dlam2),
Q->cp1 * Q->sp2 - Q->sp1 * Q->cp2 * cos (Q->dlam2));
Q->ca = cos(pp = aasin(P->ctx, Q->cp1 * sin(A12)));
Q->sa = sin(pp);
Q->lp = adjlon ( atan2 (Q->cp1 * cos(A12), Q->sp1) - Q->hz0);
Q->dlam2 *= .5;
Q->lamc = M_HALFPI - atan2(sin(A12) * Q->sp1, cos(A12)) - Q->dlam2;
Q->thz0 = tan (Q->hz0);
Q->rhshz0 = .5 / sin (Q->hz0);
Q->r2z0 = 0.5 / Q->z02;
Q->z02 *= Q->z02;
P->inv = s_inverse;
P->fwd = s_forward;
P->es = 0.;
return P;
}
#ifndef PJ_SELFTEST
int pj_tpeqd_selftest (void) {return 0;}
#else
int pj_tpeqd_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char e_args[] = {"+proj=tpeqd +ellps=GRS80 +lat_1=0.5 +lat_2=2 +n=0.5"};
char s_args[] = {"+proj=tpeqd +a=6400000 +lat_1=0.5 +lat_2=2 +n=0.5"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY e_fwd_expect[] = {
{-27750.758831679042, -222599.40369177726},
{-250434.93702403645, -222655.93819326628},
{-27750.758831679042, 222599.40369177726},
{-250434.93702403645, 222655.93819326628},
};
XY s_fwd_expect[] = {
{-27845.882978485075, -223362.43069526015},
{-251293.37876465076, -223419.15898590829},
{-27845.882978485075, 223362.43069526015},
{-251293.37876465076, 223419.15898590829},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP e_inv_expect[] = {
{-0.00089855554821257374, 1.2517966304145272},
{0.0008985555481998515, 1.2517966304145272},
{-0.00089855431859741167, 1.2482033692781642},
{0.00089855431859741167, 1.2482033692781642},
};
LP s_inv_expect[] = {
{-0.00089548606640108474, 1.2517904929571837},
{0.0008954860663883625, 1.2517904929571837},
{-0.000895484845182587, 1.248209506737604},
{0.00089548484516986475, 1.248209506737604},
};
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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