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#define PROJ_PARMS__ \
double Az, kRg, p0s, A, C, Ca, Cb, Cc, Cd; \
int rot;
#define PJ_LIB__
#include <projects.h>
PROJ_HEAD(labrd, "Laborde") "\n\tCyl, Sph\n\tSpecial for Madagascar";
#define EPS 1.e-10
FORWARD(e_forward);
double V1, V2, ps, sinps, cosps, sinps2, cosps2, I1, I2, I3, I4, I5, I6,
x2, y2, t;
V1 = P->A * log( tan(FORTPI + .5 * lp.phi) );
t = P->e * sin(lp.phi);
V2 = .5 * P->e * P->A * log ((1. + t)/(1. - t));
ps = 2. * (atan(exp(V1 - V2 + P->C)) - FORTPI);
I1 = ps - P->p0s;
cosps = cos(ps); cosps2 = cosps * cosps;
sinps = sin(ps); sinps2 = sinps * sinps;
I4 = P->A * cosps;
I2 = .5 * P->A * I4 * sinps;
I3 = I2 * P->A * P->A * (5. * cosps2 - sinps2) / 12.;
I6 = I4 * P->A * P->A;
I5 = I6 * (cosps2 - sinps2) / 6.;
I6 *= P->A * P->A *
(5. * cosps2 * cosps2 + sinps2 * (sinps2 - 18. * cosps2)) / 120.;
t = lp.lam * lp.lam;
xy.x = P->kRg * lp.lam * (I4 + t * (I5 + t * I6));
xy.y = P->kRg * (I1 + t * (I2 + t * I3));
x2 = xy.x * xy.x;
y2 = xy.y * xy.y;
V1 = 3. * xy.x * y2 - xy.x * x2;
V2 = xy.y * y2 - 3. * x2 * xy.y;
xy.x += P->Ca * V1 + P->Cb * V2;
xy.y += P->Ca * V2 - P->Cb * V1;
return (xy);
}
INVERSE(e_inverse); /* ellipsoid & spheroid */
double x2, y2, V1, V2, V3, V4, t, t2, ps, pe, tpe, s,
I7, I8, I9, I10, I11, d, Re;
int i;
x2 = xy.x * xy.x;
y2 = xy.y * xy.y;
V1 = 3. * xy.x * y2 - xy.x * x2;
V2 = xy.y * y2 - 3. * x2 * xy.y;
V3 = xy.x * (5. * y2 * y2 + x2 * (-10. * y2 + x2 ));
V4 = xy.y * (5. * x2 * x2 + y2 * (-10. * x2 + y2 ));
xy.x += - P->Ca * V1 - P->Cb * V2 + P->Cc * V3 + P->Cd * V4;
xy.y += P->Cb * V1 - P->Ca * V2 - P->Cd * V3 + P->Cc * V4;
ps = P->p0s + xy.y / P->kRg;
pe = ps + P->phi0 - P->p0s;
for ( i = 20; i; --i) {
V1 = P->A * log(tan(FORTPI + .5 * pe));
tpe = P->e * sin(pe);
V2 = .5 * P->e * P->A * log((1. + tpe)/(1. - tpe));
t = ps - 2. * (atan(exp(V1 - V2 + P->C)) - FORTPI);
pe += t;
if (fabs(t) < EPS)
break;
}
/*
if (!i) {
} else {
}
*/
t = P->e * sin(pe);
t = 1. - t * t;
Re = P->one_es / ( t * sqrt(t) );
t = tan(ps);
t2 = t * t;
s = P->kRg * P->kRg;
d = Re * P->k0 * P->kRg;
I7 = t / (2. * d);
I8 = t * (5. + 3. * t2) / (24. * d * s);
d = cos(ps) * P->kRg * P->A;
I9 = 1. / d;
d *= s;
I10 = (1. + 2. * t2) / (6. * d);
I11 = (5. + t2 * (28. + 24. * t2)) / (120. * d * s);
x2 = xy.x * xy.x;
lp.phi = pe + x2 * (-I7 + I8 * x2);
lp.lam = xy.x * (I9 + x2 * (-I10 + x2 * I11));
return (lp);
}
FREEUP; if (P) pj_dalloc(P); }
ENTRY0(labrd)
double Az, sinp, R, N, t;
P->rot = pj_param(P->params, "bno_rot").i == 0;
Az = pj_param(P->params, "razi").f;
sinp = sin(P->phi0);
t = 1. - P->es * sinp * sinp;
N = 1. / sqrt(t);
R = P->one_es * N / t;
P->kRg = P->k0 * sqrt( N * R );
P->p0s = atan( sqrt(R / N) * tan(P->phi0) );
P->A = sinp / sin(P->p0s);
t = P->e * sinp;
P->C = .5 * P->e * P->A * log((1. + t)/(1. - t)) +
- P->A * log( tan(FORTPI + .5 * P->phi0))
+ log( tan(FORTPI + .5 * P->p0s));
t = Az + Az;
P->Ca = (1. - cos(t)) * ( P->Cb = 1. / (12. * P->kRg * P->kRg) );
P->Cb *= sin(t);
P->Cc = 3. * (P->Ca * P->Ca - P->Cb * P->Cb);
P->Cd = 6. * P->Ca * P->Cb;
P->inv = e_inverse;
P->fwd = e_forward;
ENDENTRY(P)
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