#define PJ_LIB__ #include PROJ_HEAD(tmerc, "Transverse Mercator") "\n\tCyl, Sph&Ell"; struct pj_opaque { double esp; \ double ml0; \ double *en; }; #define EPS10 1.e-10 #define FC1 1. #define FC2 .5 #define FC3 .16666666666666666666 #define FC4 .08333333333333333333 #define FC5 .05 #define FC6 .03333333333333333333 #define FC7 .02380952380952380952 #define FC8 .01785714285714285714 static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */ XY xy = {0.0, 0.0}; struct pj_opaque *Q = P->opaque; double al, als, n, cosphi, sinphi, t; /* * Fail if our longitude is more than 90 degrees from the * central meridian since the results are essentially garbage. * Is error -20 really an appropriate return value? * * http://trac.osgeo.org/proj/ticket/5 */ if( lp.lam < -M_HALFPI || lp.lam > M_HALFPI ) { xy.x = HUGE_VAL; xy.y = HUGE_VAL; pj_ctx_set_errno( P->ctx, -14 ); return xy; } sinphi = sin (lp.phi); cosphi = cos (lp.phi); t = fabs (cosphi) > 1e-10 ? sinphi/cosphi : 0.; t *= t; al = cosphi * lp.lam; als = al * al; al /= sqrt (1. - P->es * sinphi * sinphi); n = Q->esp * cosphi * cosphi; xy.x = P->k0 * al * (FC1 + FC3 * als * (1. - t + n + FC5 * als * (5. + t * (t - 18.) + n * (14. - 58. * t) + FC7 * als * (61. + t * ( t * (179. - t) - 479. ) ) ))); xy.y = P->k0 * (pj_mlfn(lp.phi, sinphi, cosphi, Q->en) - Q->ml0 + sinphi * al * lp.lam * FC2 * ( 1. + FC4 * als * (5. - t + n * (9. + 4. * n) + FC6 * als * (61. + t * (t - 58.) + n * (270. - 330 * t) + FC8 * als * (1385. + t * ( t * (543. - t) - 3111.) ) )))); return (xy); } static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */ XY xy = {0.0,0.0}; double b, cosphi; /* * Fail if our longitude is more than 90 degrees from the * central meridian since the results are essentially garbage. * Is error -20 really an appropriate return value? * * http://trac.osgeo.org/proj/ticket/5 */ if( lp.lam < -M_HALFPI || lp.lam > M_HALFPI ) { xy.x = HUGE_VAL; xy.y = HUGE_VAL; pj_ctx_set_errno( P->ctx, -14 ); return xy; } cosphi = cos(lp.phi); b = cosphi * sin (lp.lam); if (fabs (fabs (b) - 1.) <= EPS10) F_ERROR; xy.x = P->opaque->ml0 * log ((1. + b) / (1. - b)); xy.y = cosphi * cos (lp.lam) / sqrt (1. - b * b); b = fabs ( xy.y ); if (b >= 1.) { if ((b - 1.) > EPS10) F_ERROR else xy.y = 0.; } else xy.y = acos (xy.y); if (lp.phi < 0.) xy.y = -xy.y; xy.y = P->opaque->esp * (xy.y - P->phi0); 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 n, con, cosphi, d, ds, sinphi, t; lp.phi = pj_inv_mlfn(P->ctx, Q->ml0 + xy.y / P->k0, P->es, Q->en); if (fabs(lp.phi) >= M_HALFPI) { lp.phi = xy.y < 0. ? -M_HALFPI : M_HALFPI; lp.lam = 0.; } else { sinphi = sin(lp.phi); cosphi = cos(lp.phi); t = fabs (cosphi) > 1e-10 ? sinphi/cosphi : 0.; n = Q->esp * cosphi * cosphi; d = xy.x * sqrt (con = 1. - P->es * sinphi * sinphi) / P->k0; con *= t; t *= t; ds = d * d; lp.phi -= (con * ds / (1.-P->es)) * FC2 * (1. - ds * FC4 * (5. + t * (3. - 9. * n) + n * (1. - 4 * n) - ds * FC6 * (61. + t * (90. - 252. * n + 45. * t) + 46. * n - ds * FC8 * (1385. + t * (3633. + t * (4095. + 1574. * t)) ) ))); lp.lam = d*(FC1 - ds*FC3*( 1. + 2.*t + n - ds*FC5*(5. + t*(28. + 24.*t + 8.*n) + 6.*n - ds * FC7 * (61. + t * (662. + t * (1320. + 720. * t)) ) ))) / cosphi; } return lp; } static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */ LP lp = {0.0, 0.0}; double h, g; h = exp(xy.x / P->opaque->esp); g = .5 * (h - 1. / h); h = cos (P->phi0 + xy.y / P->opaque->esp); lp.phi = asin(sqrt((1. - h * h) / (1. + g * g))); if (xy.y < 0.) lp.phi = -lp.phi; lp.lam = (g || h) ? atan2 (g, h) : 0.; 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; } static PJ *setup(PJ *P) { /* general initialization */ struct pj_opaque *Q = P->opaque; if (P->es) { if (!(Q->en = pj_enfn(P->es))) E_ERROR_0; Q->ml0 = pj_mlfn(P->phi0, sin(P->phi0), cos(P->phi0), Q->en); Q->esp = P->es / (1. - P->es); P->inv = e_inverse; P->fwd = e_forward; } else { Q->esp = P->k0; Q->ml0 = .5 * Q->esp; P->inv = s_inverse; P->fwd = s_forward; } return P; } PJ *PROJECTION(tmerc) { struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque)); if (0==Q) return freeup_new (P); P->opaque = Q; return setup(P); } #ifndef PJ_SELFTEST int pj_tmerc_selftest (void) {return 0;} #else int pj_tmerc_selftest (void) { double tolerance_lp = 1e-10; double tolerance_xy = 1e-7; char e_args[] = {"+proj=tmerc +ellps=GRS80 +lat_1=0.5 +lat_2=2 +n=0.5"}; char s_args[] = {"+proj=tmerc +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[] = { { 222650.79679577847, 110642.22941192707}, { 222650.79679577847, -110642.22941192707}, {-222650.79679577847, 110642.22941192707}, {-222650.79679577847, -110642.22941192707}, }; XY s_fwd_expect[] = { { 223413.46640632232, 111769.14504059685}, { 223413.46640632232, -111769.14504059685}, {-223413.46640632208, 111769.14504059685}, {-223413.46640632208, -111769.14504059685}, }; XY inv_in[] = { { 200, 100}, { 200,-100}, {-200, 100}, {-200,-100} }; LP e_inv_expect[] = { { 0.0017966305681649396, 0.00090436947663183841}, { 0.0017966305681649396, -0.00090436947663183841}, {-0.0017966305681649396, 0.00090436947663183841}, {-0.0017966305681649396, -0.00090436947663183841}, }; LP s_inv_expect[] = { { 0.0017904931097048034, 0.00089524670602767842}, { 0.0017904931097048034, -0.00089524670602767842}, {-0.001790493109714345, 0.00089524670602767842}, {-0.001790493109714345, -0.00089524670602767842}, }; 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