/Proj4/PJ_tmerc.c

  1#ifndef lint
  2static const char SCCSID[]="@(#)PJ_tmerc.c	4.2	94/06/02	GIE	REL";
  3#endif
  4#define PROJ_PARMS__ \
  5	double	esp; \
  6	double	ml0; \
  7	double	*en;
  8#define PJ_LIB__
  9#include	"projects.h"
 10PROJ_HEAD(tmerc, "Transverse Mercator") "\n\tCyl, Sph&Ell";
 11PROJ_HEAD(utm, "Universal Transverse Mercator (UTM)")
 12	"\n\tCyl, Sph\n\tzone= south";
 13#define EPS10	1.e-10
 14#define aks0	P->esp
 15#define aks5	P->ml0
 16#define FC1 1.
 17#define FC2 .5
 18#define FC3 .16666666666666666666
 19#define FC4 .08333333333333333333
 20#define FC5 .05
 21#define FC6 .03333333333333333333
 22#define FC7 .02380952380952380952
 23#define FC8 .01785714285714285714
 24FORWARD(e_forward); /* ellipse */
 25	double al, als, n, cosphi, sinphi, t;
 26
 27	sinphi = sin(lp.phi); cosphi = cos(lp.phi);
 28	t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
 29	t *= t;
 30	al = cosphi * lp.lam;
 31	als = al * al;
 32	al /= sqrt(1. - P->es * sinphi * sinphi);
 33	n = P->esp * cosphi * cosphi;
 34	xy.x = P->k0 * al * (FC1 +
 35		FC3 * als * (1. - t + n +
 36		FC5 * als * (5. + t * (t - 18.) + n * (14. - 58. * t)
 37		+ FC7 * als * (61. + t * ( t * (179. - t) - 479. ) )
 38		)));
 39	xy.y = P->k0 * (pj_mlfn(lp.phi, sinphi, cosphi, P->en) - P->ml0 +
 40		sinphi * al * lp.lam * FC2 * ( 1. +
 41		FC4 * als * (5. - t + n * (9. + 4. * n) +
 42		FC6 * als * (61. + t * (t - 58.) + n * (270. - 330 * t)
 43		+ FC8 * als * (1385. + t * ( t * (543. - t) - 3111.) )
 44		))));
 45	return (xy);
 46}
 47FORWARD(s_forward); /* sphere */
 48	double b, cosphi;
 49
 50	b = (cosphi = cos(lp.phi)) * sin(lp.lam);
 51	if (fabs(fabs(b) - 1.) <= EPS10) F_ERROR;
 52	xy.x = aks5 * log((1. + b) / (1. - b));
 53	if ((b = fabs( xy.y = cosphi * cos(lp.lam) / sqrt(1. - b * b) )) >= 1.) {
 54		if ((b - 1.) > EPS10) F_ERROR
 55		else xy.y = 0.;
 56	} else
 57		xy.y = acos(xy.y);
 58	if (lp.phi < 0.) xy.y = -xy.y;
 59	xy.y = aks0 * (xy.y - P->phi0);
 60	return (xy);
 61}
 62INVERSE(e_inverse); /* ellipsoid */
 63	double n, con, cosphi, d, ds, sinphi, t;
 64
 65	lp.phi = pj_inv_mlfn(P->ml0 + xy.y / P->k0, P->es, P->en);
 66	if (fabs(lp.phi) >= HALFPI) {
 67		lp.phi = xy.y < 0. ? -HALFPI : HALFPI;
 68		lp.lam = 0.;
 69	} else {
 70		sinphi = sin(lp.phi);
 71		cosphi = cos(lp.phi);
 72		t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
 73		n = P->esp * cosphi * cosphi;
 74		d = xy.x * sqrt(con = 1. - P->es * sinphi * sinphi) / P->k0;
 75		con *= t;
 76		t *= t;
 77		ds = d * d;
 78		lp.phi -= (con * ds / (1.-P->es)) * FC2 * (1. -
 79			ds * FC4 * (5. + t * (3. - 9. *  n) + n * (1. - 4 * n) -
 80			ds * FC6 * (61. + t * (90. - 252. * n +
 81				45. * t) + 46. * n
 82		   - ds * FC8 * (1385. + t * (3633. + t * (4095. + 1574. * t)) )
 83			)));
 84		lp.lam = d*(FC1 -
 85			ds*FC3*( 1. + 2.*t + n -
 86			ds*FC5*(5. + t*(28. + 24.*t + 8.*n) + 6.*n
 87		   - ds * FC7 * (61. + t * (662. + t * (1320. + 720. * t)) )
 88		))) / cosphi;
 89	}
 90	return (lp);
 91}
 92INVERSE(s_inverse); /* sphere */
 93	double h, g;
 94
 95	h = exp(xy.x / aks0);
 96	g = .5 * (h - 1. / h);
 97	h = cos(P->phi0 + xy.y / aks0);
 98	lp.phi = asin(sqrt((1. - h * h) / (1. + g * g)));
 99	if (xy.y < 0.) lp.phi = -lp.phi;
100	lp.lam = (g || h) ? atan2(g, h) : 0.;
101	return (lp);
102}
103FREEUP;
104	if (P) {
105		if (P->en)
106			pj_dalloc(P->en);
107		pj_dalloc(P);
108	}
109}
110	static PJ *
111setup(PJ *P) { /* general initialization */
112	if (P->es) {
113		if (!(P->en = pj_enfn(P->es)))
114			E_ERROR_0;
115		P->ml0 = pj_mlfn(P->phi0, sin(P->phi0), cos(P->phi0), P->en);
116		P->esp = P->es / (1. - P->es);
117		P->inv = e_inverse;
118		P->fwd = e_forward;
119	} else {
120		aks0 = P->k0;
121		aks5 = .5 * aks0;
122		P->inv = s_inverse;
123		P->fwd = s_forward;
124	}
125	return P;
126}
127ENTRY1(tmerc, en)
128ENDENTRY(setup(P))
129ENTRY1(utm, en)
130	int zone;
131
132	if (!P->es) E_ERROR(-34);
133	P->y0 = pj_param(P->params, "bsouth").i ? 10000000. : 0.;
134	P->x0 = 500000.;
135	if (pj_param(P->params, "tzone").i) /* zone input ? */
136		if ((zone = pj_param(P->params, "izone").i) > 0 && zone <= 60)
137			--zone;
138		else
139			E_ERROR(-35)
140	else /* nearest central meridian input */
141		if ((zone = floor((adjlon(P->lam0) + PI) * 30. / PI)) < 0)
142			zone = 0;
143		else if (zone >= 60)
144			zone = 59;
145	P->lam0 = (zone + .5) * PI / 30. - PI;
146	P->k0 = 0.9996;
147	P->phi0 = 0.;
148ENDENTRY(setup(P))