/Proj4/PJ_labrd.c
http://github.com/route-me/route-me · C · 112 lines · 104 code · 3 blank · 5 comment · 4 complexity · 9020484bd657bb2090dba4c2afc96a70 MD5 · raw file
- #ifndef lint
- static const char SCCSID[]="@(#)PJ_labrd.c 4.1 94/02/15 GIE REL";
- #endif
- #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)