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/* PROJ.4 Cartographic Projection System
*/
#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(lcca, "Lambert Conformal Conic Alternative")
"\n\tConic, Sph&Ell\n\tlat_0=";
#define MAX_ITER 10
#define DEL_TOL 1e-12
struct pj_opaque {
double *en;
double r0, l, M0;
double C;
};
static double fS(double S, double C) { /* func to compute dr */
return S * ( 1. + S * S * C);
}
static double fSp(double S, double C) { /* deriv of fs */
return 1. + 3.* S * S * C;
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double S, r, dr;
S = pj_mlfn(lp.phi, sin(lp.phi), cos(lp.phi), Q->en) - Q->M0;
dr = fS(S, Q->C);
r = Q->r0 - dr;
xy.x = P->k0 * (r * sin( lp.lam *= Q->l ) );
xy.y = P->k0 * (Q->r0 - r * cos(lp.lam) );
return xy;
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double theta, dr, S, dif;
int i;
xy.x /= P->k0;
xy.y /= P->k0;
theta = atan2(xy.x , Q->r0 - xy.y);
dr = xy.y - xy.x * tan(0.5 * theta);
lp.lam = theta / Q->l;
S = dr;
for (i = MAX_ITER; i ; --i) {
S -= (dif = (fS(S, Q->C) - dr) / fSp(S, Q->C));
if (fabs(dif) < DEL_TOL) break;
}
if (!i) I_ERROR
lp.phi = pj_inv_mlfn(P->ctx, S + Q->M0, P->es, Q->en);
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) {
freeup_new (P);
return;
}
PJ *PROJECTION(lcca) {
double s2p0, N0, R0, tan0;
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
(Q->en = pj_enfn(P->es));
if (!Q->en) E_ERROR_0;
if (!pj_param(P->ctx, P->params, "tlat_0").i) E_ERROR(50);
if (P->phi0 == 0.) E_ERROR(51);
Q->l = sin(P->phi0);
Q->M0 = pj_mlfn(P->phi0, Q->l, cos(P->phi0), Q->en);
s2p0 = Q->l * Q->l;
R0 = 1. / (1. - P->es * s2p0);
N0 = sqrt(R0);
R0 *= P->one_es * N0;
tan0 = tan(P->phi0);
Q->r0 = N0 / tan0;
Q->C = 1. / (6. * R0 * N0);
P->inv = e_inverse;
P->fwd = e_forward;
return P;
}
#ifndef PJ_SELFTEST
int pj_lcca_selftest (void) {return 0;}
#else
int pj_lcca_selftest (void) {
double tolerance_lp = 1e-10;
double tolerance_xy = 1e-7;
char e_args[] = {"+proj=lcca +ellps=GRS80 +lat_0=1 +lat_1=0.5 +lat_2=2"};
LP fwd_in[] = {
{ 2, 1},
{ 2,-1},
{-2, 1},
{-2,-1}
};
XY e_fwd_expect[] = {
{ 222605.285770237417, 67.8060072715846616},
{ 222740.037637936533, -221125.539829601563},
{-222605.285770237417, 67.8060072715846616},
{-222740.037637936533, -221125.539829601563},
};
XY inv_in[] = {
{ 200, 100},
{ 200,-100},
{-200, 100},
{-200,-100}
};
LP e_inv_expect[] = {
{ 0.00179690290525662526, 1.00090436621350798},
{ 0.00179690192174008037, 0.999095632791497268},
{-0.00179690290525662526, 1.00090436621350798},
{-0.00179690192174008037, 0.999095632791497268},
};
return pj_generic_selftest (e_args, 0, tolerance_xy, tolerance_lp, 4, 4, fwd_in, e_fwd_expect, 0, inv_in, e_inv_expect, 0);
}
#endif
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